ML23331A688

Appendix 4, Ujv Report Z-1296, SKODA MCP Calculation of Cask Criticality for Atabor Internals of Thickness 4 Mm, Nuclear Research Institute, Division of Reactor Services, August 2005

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Z-1296 MCNP Calculation of Cask Criticality for ATABOR Internals, th. 4 mm Nuclear Research Institute ez a.s.

1 / 159 Nuclear Research Institute ez a.s.

Division of Reactor Services

ÚJV Report: Z - 1296 MCNP Calculation of Cask Criticality for ATABOR Internals, th. 4 mm Revision 2 Prepared by:

Stanislav Flíbor Dept. Manager:

Ing. Milan Marek, CSc.

DRS Manager:

Ing. Jan Kysela, CSc.

ez, August 2005

Z-1296 MCNP Calculation of Cask Criticality for ATABOR Internals, th. 4 mm Nuclear Research Institute ez a.s.

2 / 159 ABSTRACT This Report deals with the behaviour of transport and storage cask for spent fuel from research reactors with respect to criticality according to the criteria of the Decree 317 /

2002Col. on type licensing and transport. The calculations have been performed for the following types of fuel: IRT-2M with 90% enrichment, IRT-3M with 90% enrichment, S-36 with 36% enrichment, S-36 with 36% enrichment in stainless steel sheath, VVR-M with 36%

enrichment, VVR-M2 with 36% enrichment, VVR-M5 with 36% enrichment, VVR-M5 with 90% enrichment, VVR-M7 with 90% enrichment, TVR-S with 2% enrichment in stainless steel sheath, TVR-S with 80% enrichment in stainless steel sheath.

Subcriticality calculations for IRT-2M with enrichment 80%, IRT-2M with enrichment 36%, IRT-3M with enrichment 36%, IRT-3M U-Mo with enrichment 19,5%,

IRT-4M with enrichment 19,7% and fuel EK-10 with enrichment 10% are stated in the report MCNP subcriticality calculation for the Atabor basket, thickness 4mm (file number Z-1172, UJV ez, March 2004 and in its Supplement No.1 from May 2004) which is the part of Safety documentation Ae 10992/ Dok, revision 1 which was approved by SONS in the frame of licensing process of old VPVR cask in the year 2004 (see also Appendix 4A).

In case of EK-10, the possibility that fuel assembly is dismounted on particular rods and these rods are closed in stainless steel sheat cylindrical (19 rods) or square (49 rods), are calculated. During subcriticality calculations of VPVR cask the same software, material and geometrical model was used as for Skoda VPVR/M cask.

Results summary from the report Z-1172 Fuel type Keff IRT-2M with enrichment 36% 235U 0.671 IRT-2M with enrichment 80% 235U 0.603 IRT-3M with enrichment 36% 235U 0.751 IRT-3M U-Mo with enrichment 19.5% 235U 0.759 IRT-4M with enrichment 19.7% 235U 0.676 EK-10 with enrichment 10% 235U 0.500 EK-10 with enrichment 10% 235U (in cylindrical sheat) 0.372 EK-10 with enrichment 10% 235U (in square sheat) 0.460

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1. Table of Contents

1.

Table of Contents........................................................................................................... 3

2.

Introduction.................................................................................................................... 8

3.

Material composition...................................................................................................... 8

4.

Calculation................................................................................................................... 10 4.1 General setup of calculation..................................................................................... 10 4.2 Calculation options................................................................................................... 12

5.

Determination of resulting keff value............................................................................ 13

6.

IRT-2M fuel with 235U 90% enrichment..................................................................... 14 6.1 Material composition of fuel.................................................................................... 14 6.2 Model of a cask with fuel......................................................................................... 15 6.3 Cask criticality calculation results............................................................................ 17 6.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C).......................................................................................................... 17 6.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 19 6.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C).......................................................................................................... 20 6.3.4 Results of calculations for individual tolerances(temperature 27 °C).............. 21 6.4 Results of calculations for a group of casks under normal transport conditions...... 22 6.5 Results of calculations for a group of casks under transport accident conditions.... 23 6.6 Conclusion................................................................................................................ 24 6.6.1 Evaluation of an individual isolated cask......................................................... 24 6.6.2 Assessment of a group of casks under normal transport conditions................ 25 6.6.3 Assessment of a group of casks under transport accident conditions............. 26

7.

IRT-3M fuel with 90% enrichment of 235U.................................................................. 27 7.1 Material composition of fuel.................................................................................... 27 7.2 Model of a cask with fuel......................................................................................... 28 7.3 Cask criticality calculation results............................................................................ 30 7.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C).......................................................................................................... 30 7.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 32 7.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C).......................................................................................................... 33 7.3.4 Results of calculations for individual tolerances(temperature 27 °C).............. 34 7.4 Results of calculations for a group of casks under normal transport conditions...... 35 7.5 Results of calculations for a group of casks under transport accident conditions.... 36 7.6 Conclusion................................................................................................................ 37 7.6.1 Evaluation of an individual isolated cask......................................................... 37 7.6.2 Assessment of a group of casks under normal transport conditions................ 38 7.6.3 Assessment of a group of casks under transport accident conditions............. 39

8.

S-36 fuel with 36% enrichment of 235U....................................................................... 40 8.1 Material composition of fuel.................................................................................... 40 8.2 Model of a cask with fuel......................................................................................... 41 8.3 Cask criticality calculation results............................................................................ 43 8.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C).......................................................................................................... 43

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4 / 159 8.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 45 8.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C).......................................................................................................... 46 8.3.4 Results of calculations for individual tolerances(temperature 27 °C).............. 47 8.4 Results of calculations for a group of casks under normal transport conditions...... 48 8.5 Results of calculations for a group of casks under transport accident conditions.... 49 8.6 Conclusion................................................................................................................ 50 8.6.1 Evaluation of an individual isolated cask......................................................... 50 8.6.2 Assessment of a group of casks under normal transport conditions................ 51 8.6.3 Assessment of a group of casks under transport accident conditions............. 52

9.

S-36 fuel with 36% enrichment of 235U - 36 rods in a stainless steel sheath............... 53 9.1 Material composition of fuel.................................................................................... 53 9.2 Model of a cask with fuel......................................................................................... 54 9.3 Cask criticality calculation results............................................................................ 56 9.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C).......................................................................................................... 56 9.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 58 9.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C).......................................................................................................... 59 9.3.4 Results of calculations for individual tolerances(temperature 27 °C).............. 60 9.4 Results of calculations for a group of casks under normal transport conditions...... 61 9.5 Results of calculations for a group of casks under transport accident conditions.... 62 9.6 Conclusion................................................................................................................ 63 9.6.1 Evaluation of an individual isolated cask......................................................... 63 9.6.2 Assessment of a group of casks under normal transport conditions................ 64 9.6.3 Assessment of a group of casks under transport accident conditions............. 65

10.

VVR-M fuel with 36% enrichment of 235U.................................................................. 66 10.1 Material composition of fuel.................................................................................... 66 10.2 Model of a cask with fuel......................................................................................... 67 10.3 Cask criticality calculation results............................................................................ 69 10.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C).......................................................................................................... 69 10.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C) 71 10.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C).......................................................................................................... 72 10.3.4 Results of calculations for individual tolerances (temperature 27 °C)............. 73 10.4 Results of calculations for a group of casks under normal transport conditions...... 74 10.5 Results of calculations for a group of casks under transport accident conditions.... 75 10.6 Conclusion................................................................................................................ 76 10.6.1 Evaluation of an individual isolated cask......................................................... 76 10.6.2 Assessment of a group of casks under normal transport conditions................ 77 10.6.3 Assessment of a group of casks under transport accident conditions............. 78

11.

VVR-M2 fuel with 36% enrichment of 235U................................................................ 79 11.1 Material composition of fuel.................................................................................... 79 11.2 Model of a cask with fuel......................................................................................... 80 11.3 Cask criticality calculation results............................................................................ 82

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5 / 159 11.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C).......................................................................................................... 82 11.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 84 11.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C).......................................................................................................... 85 11.3.4 Results of calculations for individual tolerances (temperature 27 °C)............. 86 11.4 Results of calculations for a group of casks under normal transport conditions...... 87 11.5 Results of calculations for a group of casks under transport accident conditions.... 88 11.6 Conclusion................................................................................................................ 89 11.6.1 Evaluation of an individual isolated cask......................................................... 89 11.6.2 Assessment of a group of casks under normal transport conditions................ 90 11.6.3 Assessment of a group of casks under transport accident conditions............. 91

12.

VVR-M5 fuel with 36% enrichment of 235U................................................................ 92 12.1 Material composition of fuel.................................................................................... 92 12.2 Model of a cask with fuel......................................................................................... 93 12.3 Cask criticality calculation results............................................................................ 95 12.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C).......................................................................................................... 95 12.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 97 12.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C).......................................................................................................... 98 12.3.4 Results of calculations for individual tolerances(temperature 27 °C).............. 99 12.4 Results of calculations for a group of casks under normal transport conditions.... 100 12.5 Results of calculations for a group of casks under transport accident conditions.. 101 12.6 Conclusion.............................................................................................................. 102 12.6.1 Evaluation of an individual isolated cask....................................................... 102 12.6.2 Assessment of a group of casks under normal transport conditions.............. 103 12.6.3 Assessment of a group of casks under transport accident conditions........... 104

13.

VVR-M5 fuel with 90% enrichment of 235U............................................................ 105 13.1 Material composition of fuel.................................................................................. 105 13.2 Model of a cask with fuel....................................................................................... 106 13.3 Cask criticality calculation results.......................................................................... 108 13.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)........................................................................................................ 108 13.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 110 13.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)........................................................................................................ 111 13.3.4 Results of calculations for individual tolerances(temperature 27 °C)............ 112 13.4 Results of calculations for a group of casks under normal transport conditions.... 113 13.5 Results of calculations for a group of casks under transport accident conditions.. 114 13.6 Conclusion.............................................................................................................. 115 13.6.1 Evaluation of an individual isolated cask....................................................... 115 13.6.2 Assessment of a group of casks under normal transport conditions.............. 116 13.6.3 Assessment of a group of casks under transport accident conditions........... 117

14.

VVR-M7 fuel with 90% enrichment of 235U.............................................................. 118 14.1 Material composition of fuel.................................................................................. 118 14.2 Model of a cask with fuel....................................................................................... 119

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6 / 159 14.3 Cask criticality calculation results.......................................................................... 121 14.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)........................................................................................................ 121 14.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 123 14.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)........................................................................................................ 124 14.3.4 Results of calculations for individual tolerances(temperature 27 °C)............ 125 14.4 Results of calculations for a group of casks under normal transport conditions.... 126 14.5 Results of calculations for a group of casks under transport accident conditions.. 127 14.6 Conclusion.............................................................................................................. 128 14.6.1 Evaluation of an individual isolated cask....................................................... 128 14.6.2 Assessment of a group of casks under normal transport conditions.............. 129 14.6.3 Assessment of a group of casks under transport accident conditions........... 130

15.

TVR-S fuel with 2% enrichment of 235U................................................................... 131 15.1 Material composition of fuel.................................................................................. 131 15.2 Model of a cask with fuel....................................................................................... 132 15.3 Cask criticality calculation results.......................................................................... 134 15.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)........................................................................................................ 134 15.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 136 15.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)........................................................................................................ 137 15.3.4 Results of calculations for individual tolerances(temperature 27 °C)............ 138 15.4 Results of calculations for a group of casks under normal transport conditions.... 139 15.5 Results of calculations for a group of casks under transport accident conditions.. 140 15.6 Conclusion.............................................................................................................. 141 15.6.1 Evaluation of an individual isolated cask....................................................... 141 15.6.2 Assessment of a group of casks under normal transport conditions.............. 142 15.6.3 Assessment of a group of casks under transport accident conditions........... 143

16.

TVR-S fuel with 80% enrichment of 235U................................................................ 144 16.1 Material composition of fuel.................................................................................. 144 16.2 Model of a cask with fuel....................................................................................... 145 16.3 Cask criticality calculation results.......................................................................... 147 16.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)........................................................................................................ 147 16.3.2 Results of calculations for flooding a standing cask with water (temperature 27

°C) 149 16.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)........................................................................................................ 150 16.3.4 Results of calculations for individual tolerances(temperature 27 °C)............ 151 16.4 Results of calculations for a group of casks under normal transport conditions.... 152 16.5 Results of calculations for a group of casks under transport accident conditions.. 153 16.6 Conclusion.............................................................................................................. 154 16.6.1 Evaluation of an individual isolated cask....................................................... 154 16.6.2 Assessment of a group of casks under normal transport conditions.............. 155 16.6.3 Assessment of a group of casks under transport accident conditions........... 156

17.

Summary.................................................................................................................... 157

18.

References.................................................................................................................. 158

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19.

Appendix 1: VPVR Cask........................................................................................... 159

Z-1296 MCNP Calculation of Cask Criticality for ATABOR Internals, th. 4 mm 2.Introduction Nuclear Research Institute ez a.s.

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2. Introduction The Report includes calculation documentation related to the bahaviour of transport and storage cask for spent fuel from research reactors with respect to keeping the subcriticality of the entire system. The Report objective is to demonstrate that the cask satisfies the requirements of the Decree 317/2002 Col. on type licensing and transport.

The calculations of criticality for individual types of fuel are performed using the MCNP 4C program. It is a 3D computational program operating based on the Monte Carlo method. A group of effective cross-section libraries DLC-200 designated for this program has been used for the calculations.

The computational model for the simulation of considered states has been prepared based on supplied -KODA JS a.s. documentation:

Ae30340P (Ae 006 057 resp.) -VPVR cask Ae30942P (Ae 006 058 resp.) - Basket Ae 11540/Dok, Rev. 0 - Calculation of temperatures

3. Material composition The composition of materials used for the calculation has been compiled based on information indicated in the supplied documentation. Chemical composition of individual materials and used libraries are indicated in Tab. 1. Libraries of effective cross-sections at a temperature of 300 °K (26,85 °C) were used for all calculations.

Tab. 1: Chemical composition of used materials Material Element Library Weight portion

[weight %]

Water H2O 0 - 0.998 g.cm-3 H

O 1001.60c 8016.60c 11.19 88.81 Air 0,001161 g.cm-3 O

N 8016.60c 7014.60c 25 75 ATABOR 7,9 g.cm-3 B10 B11 C

N Si P

S Cr Mn Fe Co Ni 5010.60c 5011.60c 6000.60c 7014.60c 14000.60c 15031.60c 16000.60c 24000.50c 25055.60c 26000.50c 27059.60c 28000.50c 0.2388 0.9612 0.03 0.1 0.75 0.045 0.03 18 2

65.645 0.2 12 Fuel rod cladding 2,7 g.cm-3 Al 13027.60c 100

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9 / 159 Material Element Library Weight portion

[weight %]

Body 7,72 g.cm-3 C

Al Si P

S Ti V

Cr Mn Fe Co Ni Cu As Nb Mo Sn W

6000.60c 13027.60c 14000.60c 15031.60c 16000.60c 22000.60c 23000.60c 24000.50c 25055.60c 26000.50c 27059.60c 28000.50c 29000.50c 33075.35c 41093.60c 42000.60c 50000.35c 74000.55c 0.12 0.038 0.5 0.025 0.02 0.05 0.03 0.21 1.6 96.674 0.012 0.28 0.21 0.012 0.004 0.15 0.055 0.01 Fuel Specific for individual types

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4. Calculation 4.1 General setup of calculation The calculations are performed using MCNP 4C program in the mode for the calculation of system criticality - KCODE. 50 inactive cycles of calculation (keff is not calculated) were used for the calculation of initial distribution of points for the start of calculation. 550 cycles with 2000 starting points in each cycle were used to determine the calculated value of keff. One check calculation has also been performed with 550 cycles and 100 000 starting points (check calculation in the Tables of criticality calculations for the change of water density).

All calculations have been made for fuel with the maximum multiplication capability, i.e. for fresh fuel with no burnout. The basic model of a cask with fuel is made with a space around of ~ 30 cm filled with water according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 84 (Fig. 1). As the system criticality calculations for real higher temperatures do not show any significant temperature dependence, all calculations were performed for the temperature of 27 °C, unless specified otherwise. All calculations always consider low limit of B content in ATABOR, i.e. weight 1.2 %, and the smallest possible thickness of the internals, i.e. 3.6 mm.

Fig. 1: Basic model of a cask with surrounding space and a level of 0 cm for flooding a standing cask - longitudinal section Voda Hladina 0 cm

Z-1296 MCNP Calculation of Cask Criticality for ATABOR Internals, th. 4 mm 4.Calculation Nuclear Research Institute ez a.s.

11 / 159 Fig. 2: Basic model of a cask with surrounding space and a level of 0 cm for flooding a cask in lying position - cross section Hladina 0 cm

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12 / 159 4.2 Calculation options The calculations have been made for the following options:

1. Filling of the cask internal space with water of a density varying in the interval of

<0; 0.998>.cm-3 (the model of a cask with fuel is surrounded by ~ 30 cm of water, only inside the cask the water density value varies in a given interval).

2. Gradual flooding of the standing cask internal space with water (the cask rests on the lower shock absorber, the entire cask is surrounded by ~ 30 cm of water, water level inside the cask keeps rising, the level of 0 cm corresponds to the bottom inside the cask - see Fig. 1).

3. Gradual flooding of the lying cask internal space (the cask rests on its side, the entire cask is surrounded by ~ 30 cm of water, water level inside the cask keeps rising, the level of 0 cm corresponds to the internal cask wall - see Fig. 2).

4. Calculations for temperature states as indicated in [Ae 11540/Dok, Rev. 0].

5. Calculations for specified tolerances of B in ATABOR (B concentrations in ATABOR vary in the range of weight 1.2 % 1.6 % ).

6. Calculations for specified tolerances of ATABOR internals thickness (the thickness of ATABOR internals varies from 3.6 4 mm).

7. Calculations for tolerances of total U weight in fuel (the total fuel volume does not change, fuel density changes as well as the total weight of U in fuel in the range of weight 5 % ).

8. Calculations for tolerances of 235U fuel enrichment (the total fuel volume does not change, fuel density and enrichment of 235U weight 1 % change).

9. Calculations for specified tolerances of matrix in fuel (the total fuel volume does not change, fuel density and content of matrix in fuel weight 10 % change).

10. Change of the geometrical configuration inside the cask (as the performed test has not proved any deformation of the internals inside the cask, subject to calculation is only that alternative when all rods group towards the cask centre).

11. Calculations for specified tolerances of active fuel length (fuel composition does not change, its volume and density change).

12. Infinite number of casks with water outside the cask (above and below the cask ~ 30 cm of water, a gap filled with water between the casks).

13. Infinite number of casks with water outside and inside the cask (above and below the cask ~ 30 cm of water, a gap filled with water between the casks).

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5. Determination of resulting keff value According to §47 of the SÚJB Decree 195/1999 Col. the resulting keff value was determined as follows:

i i

stat vyp eff k

k k

2

vyp k

calculated keff value stat

error of calculated keff value at the level of probability/reliability of 95%/95%

k systematic method error i

error of systematic method error, vyp k

and calculated values differences for individual tolerances To determine the systematic error, such experiments have been chosen from the set of benchmark experiments indicated in [3] which approximate the issue under investigation the most with respect to the type of fuel, 235U concentration, lattice and moderator. The models for individual experiments were prepared by different authors, therefore, the calculated keff values can be considred independent. The chosen experiments and calculated keff values are indicated in Table 2. The systematic method error determined in this way has the following value k

= 0.006 + 0.015 Tab. 2: Benchmark experiments Enrichment keff 2 94.008 %

1.0028 0.0008 94.008 %

0.9842 0.0008 94.260 %

0.9828 0.0009 94.260 %

0.9876 0.0009 94.520 %

1.0035 0.0008 94.520 %

0.9861 0.0009 Field of cubes made of Oralloy in water [1]

94.520 %

0.9865 0.0008 17 %

0.9978 0.0008 17 %

1.0005 0.0008 17 %

1.0022 0.0007 17 %

0.9991 0.0009 17 %

0.9975 0.0008 Water moderated U(17%)O2 cylindrical rods [2]

17 %

0.9956 0.0007

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6. IRT-2M fuel with 235U 90% enrichment 6.1 Material composition of fuel Enrichment 90.00%

Used library of effective cross sections 235U weight portion 31.50%

92235.60c 238U weight portion 3.50%

92238.60c Al weight portion 65.00%

13027.60c 235U weight 170.00 g

238U weight 18.89 g

Al weight 350.79 g

Total 539.68 g

Active part length 58 cm Fuel volume 156.95 cm3 U density 1.2035 g.cm-3 Fuel density 3.4386 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1

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15 / 159 6.2 Model of a cask with fuel Fig. 3: Model of IRT-2M fuel with 90% enrichment of 235U - cross section Fig. 4: Cask with IRT-2M fuel with 90% enrichment of 235U - cross section

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16 / 159 Fig. 5: Cask with IRT-2M fuel with 90% enrichment of 235U - longitudinal section

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17 / 159 6.3 Cask criticality calculation results 6.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 3: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0410 0.0001 0.15 0.1657 0.0006 0.01 0.0565 0.0002 0.16 0.1718 0.0006 0.02 0.0702 0.0003 0.17 0.1777 0.0007 0.03 0.0822 0.0003 0.18 0.1834 0.0006 0.04 0.0922 0.0004 0.19 0.1888 0.0007 0.05 0.1012 0.0004 0.2 0.1957 0.0006 0.06 0.1088 0.0004 0.3 0.2553 0.0009 0.07 0.1158 0.0004 0.4 0.3145 0.0011 0.08 0.1232 0.0005 0.5 0.3701 0.0011 0.09 0.1294 0.0005 0.6 0.4212 0.0013 0.1 0.1355 0.0005 0.7 0.4675 0.0013 0.11 0.1422 0.0005 0.8 0.5097 0.0013 0.12 0.1477 0.0005 0.9 0.5469 0.0014 0.13 0.1540 0.0006 0.998203 0.5794 0.0014 0.14 0.1603 0.0006 Check calc.

0.5801 0.0002

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18 / 159 Diagram 1: Dependence of keff on water density inside the cask

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19 / 159 6.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 4: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0409 0.0001 50 0.5437 0.0014 5

0.0474 0.0002 55 0.5575 0.0014 10 0.0535 0.0003 60 0.5670 0.0014 15 0.1221 0.0006 65 0.5755 0.0014 20 0.2684 0.0010 70 0.5803 0.0014 25 0.3677 0.0011 75 0.5812 0.0015 30 0.4320 0.0012 80 0.5793 0.0014 35 0.4778 0.0013 85 0.5801 0.0014 40 0.5057 0.0014 90 0.5800 0.0014 45 0.5279 0.0014 Diagram 2: Dependence of keff on the level height inside the cask

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20 / 159 6.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 5: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0410 0.0001 32.5 0.5270 0.0013 2.5 0.0503 0.0002 35 0.5340 0.0014 5

0.0923 0.0005 37.5 0.5384 0.0014 7.5 0.1865 0.0009 40 0.5501 0.0013 10 0.2817 0.0010 42.5 0.5600 0.0014 12.5 0.3105 0.0010 45 0.5610 0.0014 15 0.3532 0.0011 47.5 0.5674 0.0014 17.5 0.4078 0.0012 50 0.5748 0.0013 20 0.4313 0.0012 52.5 0.5746 0.0014 22.5 0.4554 0.0013 55 0.5775 0.0014 25 0.4875 0.0013 57.5 0.5826 0.0014 27.5 0.5047 0.0014 60 0.5800 0.0013 30 0.5138 0.0014 Diagram 3: Dependence of keff on the level height inside the cask

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21 / 159 6.3.4 Results of calculations for individual tolerances(temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 6: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. to Ae 11540/Dok Rev. 0 149.10 °C 0.0408 0.0001 179.36 °C 0.0409 0.0001 120.51 °C 0.0409 0.0001 152.07 °C 0.0408 0.0001 293.3 °C 0.0409 0.0002 Calculations for B concentrations in ATABOR 1.2 %

0.0410 0.0001 1.6%

0.0399 0.0001 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0410 0.0001 4.0 mm 0.0415 0.0001 Calculations for tolerances of total U weight in fuel

-5%

0.0391 0.0001

+5%

0.0428 0.0001 Calculations for 235U enrichment tolerances

-1%

0.0409 0.0001

+1 0.0409 0.0001 Calculations for specified tolerances of matrix content

-10%

0.0408 0.0001

+10%

0.0412 0.0001 Calculations of rods displacement inside the lattice Grouping of rods 0.0415 0.0001 Calculations for tolerances of active fuel part length

-2 cm 0.0415 0.0001

+2 cm 0.0405 0.0001

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22 / 159 6.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 7: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0424 0.0001 2

0.0414 0.0001 4

0.0411 0.0001 6

0.0411 0.0001 8

0.0409 0.0001 10 0.0411 0.0001 Diagram 4: keff dependence on the distance between the casks under normal transport conditions

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23 / 159 6.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 8: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.5816 0.0014 2

0.5808 0.0014 4

0.5794 0.0014 6

0.5798 0.0013 8

0.5794 0.0014 10 0.5795 0.0015 Diagram 5: : keff dependence on the distance between the casks under transport accident conditions

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24 / 159 6.6 Conclusion 6.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.5826 stat calculated keff value error 0.0015 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C

-0.00010 calculations for cask temperature states - 179.36 °C

-0.00003 calculations for cask temperature states - 120.51 °C

-0.00002 calculations for cask temperature states - 152.07 °C

-0.00005 calculations for cask temperature states - 293.3 °C 0.00002 calculations for B concentrations in ATABOR - 1.2% B 0.00006 calculations for B concentrations in ATABOR - 1.6% B

-0.00095 calculations for ATABOR internals thickness tolerances - 3.6mm 0.00006 calculations for ATABOR internals thickness tolerances - 4 mm 0.00060 decrease of total U weight in fuel (-5% U)

-0.00183 increase of total U weight in fuel (+5% U) 0.00191 decrease of U enrichment (-1% 235U) 0.00002 increase of U enrichment (+1% 235U) 0.00005 reduction of matrix content in fuel (-10%)

-0.00011 increase of matrix content in fuel (+10%)

0.00032 calculations of grouping of rods 0.00059 reduction of active length of fuel (-2 cm) 0.00057 increase of active length of fuel (+2 cm)

-0.00042 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) in 6.3.2 - Calculation results for flooding a standing cask, 6.3.3 - Calculation results for flooding a cask resting on its side for point ii) in 6.3.4 - Calculation results for individual tolerances for point iii) in 6.3.4 - Calculation results for individual tolerances, for point iv) in 6.3.4 - Calculation results for individual tolerances for point v) in 6.3.1 - Results of calculations for the change of water density inside the

cask, and 6.3.2 - Calculation results for flooding a standing cask, 6.3.3 - Calculation results for flooding a cask resting on its side for point vi) in 6.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.6053 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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25 / 159 6.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0424 stat calculated keff value error 0.0001 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.0636 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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26 / 159 6.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.5816 stat calculated keff value error 0.0015 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.6041 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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27 / 159

7. IRT-3M fuel with 90% enrichment of 235U 7.1 Material composition of fuel Enrichment 90.00%

Used library of effective cross sections 235U weight portion 31.50%

92235.60c 238U weight portion 3.50%

92238.60c Al weight portion 65.00%

13027.60c 235U weight 300.00 g

238U weight 33.33 g

Al weight 619.05 g

Total 952.38 g

Active part length 58 cm Fuel volume 376.93 cm3 U density 0.8843 g.cm-3 Fuel density 2.5267 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1

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28 / 159 7.2 Model of a cask with fuel Fig. 6: Model of IRT-3M fuel with 90% enrichment of 235U - cross section Fig. 7: Cask with IRT-3M fuel with 90% enrichment of 235U - cross section

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29 / 159 Fig. 8: Cask with IRT-3M fuel with 90% enrichment of 235U - longitudinal section

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30 / 159 7.3 Cask criticality calculation results 7.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 9: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0702 0.0002 0.15 0.2411 0.0008 0.01 0.0919 0.0003 0.16 0.2480 0.0008 0.02 0.1118 0.0004 0.17 0.2549 0.0008 0.03 0.1288 0.0004 0.18 0.2626 0.0009 0.04 0.1429 0.0005 0.19 0.2700 0.0008 0.05 0.1550 0.0005 0.2 0.2770 0.0008 0.06 0.1669 0.0005 0.3 0.3440 0.0011 0.07 0.1767 0.0006 0.4 0.4092 0.0012 0.08 0.1863 0.0006 0.5 0.4700 0.0013 0.09 0.1946 0.0007 0.6 0.5269 0.0014 0.1 0.2036 0.0007 0.7 0.5790 0.0015 0.11 0.2106 0.0007 0.8 0.6268 0.0015 0.12 0.2183 0.0007 0.9 0.6693 0.0016 0.13 0.2263 0.0008 0.998203 0.7087 0.0016 0.14 0.2340 0.0008 Check calc.

0.7078 0.0002

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31 / 159 Diagram 6: Dependence of keff on water density inside the cask

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32 / 159 7.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 10: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0703 0.0002 50 0.6645 0.0017 5

0.0779 0.0003 55 0.6801 0.0016 10 0.0859 0.0004 60 0.6908 0.0016 15 0.1674 0.0007 65 0.6997 0.0017 20 0.3341 0.0012 70 0.7073 0.0016 25 0.4517 0.0013 75 0.7076 0.0016 30 0.5285 0.0014 80 0.7085 0.0016 35 0.5789 0.0014 85 0.7075 0.0016 40 0.6168 0.0014 90 0.7077 0.0016 45 0.6435 0.0015 Diagram 6: Dependence of keff on the level height inside the cask

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33 / 159 7.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 11: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0704 0.0002 32.5 0.6406 0.0015 2.5 0.0837 0.0003 35 0.6499 0.0015 5

0.1327 0.0006 37.5 0.6570 0.0016 7.5 0.2378 0.0010 40 0.6706 0.0016 10 0.3380 0.0012 42.5 0.6823 0.0017 12.5 0.3757 0.0014 45 0.6836 0.0015 15 0.4315 0.0014 47.5 0.6934 0.0015 17.5 0.4945 0.0015 50 0.7008 0.0016 20 0.5212 0.0015 52.5 0.7021 0.0017 22.5 0.5526 0.0015 55 0.7049 0.0016 25 0.5943 0.0016 57.5 0.7096 0.0016 27.5 0.6134 0.0015 60 0.7075 0.0015 30 0.6237 0.0015 Diagram 7: Dependence of keff on the level height inside the cask

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34 / 159 7.3.4 Results of calculations for individual tolerances(temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 12: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. to Ae 11540/Dok Rev. 0 149.10 °C 0.0704 0.0002 179.36 °C 0.0703 0.0002 120.51 °C 0.0706 0.0002 152.07 °C 0.0704 0.0002 293.3 °C 0.0705 0.0002 Calculations for B concentrations in ATABOR 1.2 %

0.0702 0.0002 1.6%

0.0690 0.0002 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0702 0.0002 4.0 mm 0.0716 0.0002 Calculations for tolerances of total U weight in fuel

-5%

0.0672 0.0002

+5%

0.0733 0.0002 Calculations for 235U enrichment tolerances

-1%

0.0704 0.0002

+1 0.0703 0.0002 Calculations for specified tolerances of matrix content

-10%

0.0698 0.0002

+10%

0.0712 0.0002 Calculations for rods displacement inside the lattice Grouping of rods 0.0710 0.0002 Calculations for tolerances of active fuel part length

-2 cm 0.0715 0.0002

+2 cm 0.0694 0.0002

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35 / 159 7.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 13: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0728 0.0002 2

0.0712 0.0002 4

0.0706 0.0002 6

0.0703 0.0002 8

0.0705 0.0002 10 0.0705 0.0002 Diagram 8: keff dependence on the distance between the casks under normal transport conditions

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36 / 159 7.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 14: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.7074 0.0017 2

0.7079 0.0016 4

0.7071 0.0016 6

0.7076 0.0015 8

0.7087 0.0017 10 0.7090 0.0016 Diagram 9: keff dependence on the distance between the casks under transport accident conditions

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37 / 159 7.6 Conclusion 7.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.7096 stat calculated keff value error 0.0017 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C 0.00016 calculations for cask temperature states - 179.36 °C 0.00011 calculations for cask temperature states - 120.51 °C 0.00039 calculations for cask temperature states - 152.07 °C 0.00020 calculations for cask temperature states - 293.3 °C 0.00029 calculations for B concentrations in ATABOR - 1.2% B 0.00000 calculations for B concentrations in ATABOR - 1.6% B

-0.00117 calculations for ATABOR internals thickness tolerances-3.6mm 0.00000 calculations for ATABOR internals thickness tolerances - 4 mm 0.00141 decrease of total U weight in fuel (-5% U)

-0.00296 increase of total U weight in fuel (+5% U) 0.00312 decrease of U enrichment (-1% 235U) 0.00015 increase of U enrichment (+1% 235U) 0.00011 reduction of matrix content in fuel (-10%)

-0.00037 increase of matrix content in fuel (+10%)

0.00099 calculations of grouping of rods 0.00084 reduction of active length of fuel (-2 cm) 0.00125 increase of active length of fuel (+2 cm)

-0.00082 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) in 7.3.2 - Calculation results for flooding a standing cask, 7.3.3 - Calculation results for flooding a cask resting on its side for point ii) in 7.3.4 - Calculation results for individual tolerances for point iii) in 7.3.4 - Calculation results for individual tolerances, for point iv) in 7.3.4 - Calculation results for individual tolerances for point v) in 7.3.1 - Results of calculations for the change of water density inside the

cask, and 7.3.2 - Calculation results for flooding a standing cask, 7.3.3 - Calculation results for flooding a cask resting on its side for point vi) in 7.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.7331 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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38 / 159 7.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0728 stat calculated keff value error 0.0002 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.0941 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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39 / 159 7.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.7090 stat calculated keff value error 0.0017 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.7317 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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40 / 159

8. S-36 fuel with 36% enrichment of 235U 8.1 Material composition of fuel Enrichment 36.00%

Used library of effective cross sections 235U weight portion 11.10%

92235.60c 238U weight portion 19.74 92238.60c Al weight portion 65.00%

13027.60c O weight portion 4.16%

8016.30c 235U weight 141.80 g

238U weight 252.09 g

Al weight 830.29 g

O weight 53.19 Total 1277.37 g

Active part length 50 cm Fuel volume 280.45 cm3 U density 1.4045 g.cm-3 Fuel density 4.5548 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1 O mol. weight 15.9994 g.mol-1

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41 / 159 8.2 Model of a cask with fuel Fig. 9: Model of S-36 fuel with 36% enrichment of 235U-cross section Fig. 10: Cask with S-36 fuel with 36% enrichment of 235U - cross section

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42 / 159 Fig. 11: Cask with S-36 fuel with 36% enrichment of 235U - longitudinal section

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43 / 159 8.3 Cask criticality calculation results 8.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 15: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0432 0.0001 0.15 0.1503 0.0006 0.01 0.0561 0.0002 0.16 0.1559 0.0006 0.02 0.0678 0.0003 0.17 0.1606 0.0006 0.03 0.0775 0.0003 0.18 0.1663 0.0007 0.04 0.0858 0.0003 0.19 0.1712 0.0007 0.05 0.0938 0.0004 0.2 0.1763 0.0007 0.06 0.1000 0.0004 0.3 0.2312 0.0009 0.07 0.1061 0.0004 0.4 0.2845 0.0010 0.08 0.1121 0.0005 0.5 0.3361 0.0012 0.09 0.1177 0.0004 0.6 0.3823 0.0012 0.1 0.1235 0.0005 0.7 0.4259 0.0013 0.11 0.1288 0.0005 0.8 0.4649 0.0013 0.12 0.1342 0.0005 0.9 0.4992 0.0014 0.13 0.1396 0.0005 0.998203 0.5314 0.0014 0.14 0.1443 0.0005 Check calc.

0.5309 0.0002

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44 / 159 Diagram 10: Dependence of keff on water density inside the cask

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45 / 159 8.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 16: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0432 0.0001 50 0.5093 0.0013 5

0.0501 0.0002 55 0.5204 0.0028 10 0.0598 0.0003 60 0.5273 0.0014 15 0.1542 0.0007 65 0.5302 0.0014 20 0.2777 0.0011 70 0.5302 0.0014 25 0.3598 0.0012 75 0.5292 0.0015 30 0.4146 0.0013 80 0.5296 0.0014 35 0.4505 0.0013 85 0.5298 0.0015 40 0.4748 0.0014 90 0.5305 0.0014 45 0.4957 0.0013 Diagram 11: Dependence of keff on the level height inside the cask

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46 / 159 8.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 17: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0432 0.0001 32.5 0.4814 0.0014 2.5 0.0506 0.0002 35 0.4872 0.0013 5

0.0872 0.0004 37.5 0.4938 0.0013 7.5 0.1664 0.0008 40 0.5031 0.0014 10 0.2570 0.0010 42.5 0.5114 0.0014 12.5 0.2833 0.0011 45 0.5128 0.0014 15 0.3229 0.0012 47.5 0.5170 0.0014 17.5 0.3742 0.0013 50 0.5258 0.0014 20 0.3908 0.0013 52.5 0.5250 0.0014 22.5 0.4158 0.0013 55 0.5268 0.0014 25 0.4444 0.0014 57.5 0.5284 0.0015 27.5 0.4617 0.0014 60 0.5294 0.0015 30 0.4672 0.0013 Diagram 12: Dependence of keff on the level height inside the cask

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47 / 159 8.3.4 Results of calculations for individual tolerances(temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 18: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. to Ae 11540/Dok Rev. 0 149.10 °C 0.0433 0.0001 179.36 °C 0.0433 0.0002 120.51 °C 0.0436 0.0002 152.07 °C 0.0434 0.0001 293.3 °C 0.0435 0.0001 Calculations for B concentrations in ATABOR 1.2 %

0.0432 0.0001 1.6%

0.0424 0.0002 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0432 0.0001 4.0 mm 0.0446 0.0002 Calculations for tolerances of total U weight in fuel

-5%

0.0402 0.0001

+5%

0.0463 0.0002 Calculations for 235U enrichment tolerances

-1%

0.0433 0.0002

+1 0.0433 0.0001 Calculations for specified tolerances of matrix content

-10%

0.0428 0.0001

+10%

0.0442 0.0002 Calculations for rods displacement inside the lattice Grouping of rods 0.0436 0.0002 Calculations for tolerances of active fuel part length

-2 cm 0.0444 0.0001

+2 cm 0.0424 0.0002

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48 / 159 8.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 19: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0445 0.0001 2

0.0434 0.0001 4

0.0434 0.0001 6

0.0432 0.0001 8

0.0431 0.0001 10 0.0431 0.0001 Diagram 13: keff dependence on the distance between the casks under normal transport conditions

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49 / 159 8.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 20: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.5294 0.0014 2

0.5294 0.0014 4

0.5304 0.0014 6

0.5283 0.0013 8

0.5294 0.0014 10 0.5288 0.0014 Diagram 14: keff dependence on the distance between the casks under transport accident conditions

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50 / 159 8.6 Conclusion 8.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.5314 stat calculated keff value error 0.0028 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C 0.00016 calculations for cask temperature states - 179.36 °C 0.00011 calculations for cask temperature states - 120.51 °C 0.00039 calculations for cask temperature states - 152.07 °C 0.00020 calculations for cask temperature states - 293.3 °C 0.00029 Calculations for B concentrations in ATABOR - 1.2% B 0.00002 Calculations for B concentrations in ATABOR - 1.6% B

-0.00078 Calculations for ATABOR internals thickness tolerances-3.6mm 0.00002 Calculations for ATABOR internals thickness tolerances - 4 mm 0.00141 decrease of total U weight in fuel (-5% U)

-0.00296 increase of total U weight in fuel (+5% U) 0.00312 decrease of U enrichment (-1% 235U) 0.00015 increase of U enrichment (+1% 235U) 0.00011 reduction of matrix content in fuel (-10%)

-0.00037 increase of matrix content in fuel (+10%)

0.00099 calculations of grouping of rods 0.00044 reduction of active length of fuel (-2 cm) 0.00125 increase of active length of fuel (+2 cm)

-0.00082 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) v 8.3.2 - Calculation results for flooding a standing cask, 8.3.3 - Calculation results for flooding a cask resting on its side for point ii) v 8.3.4 - Calculation results for individual tolerances for point iii) v 8.3.4 - Calculation results for individual tolerances, for point iv) v 8.3.4 - Calculation results for individual tolerances for point v) v 8.3.1 - Results of calculations for the change of water density inside the

cask, and 8.3.2 - Calculation results for flooding a standing cask, 8.3.3 - Calculation results for flooding a cask resting on its side for point vi) v 8.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.5559 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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51 / 159 8.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0445 stat calculated keff value error 0.0001 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.0656 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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52 / 159 8.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.5304 stat calculated keff value error 0.0014 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.5528 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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53 / 159

9. S-36 fuel with 36% enrichment of 235U - 36 rods in a stainless steel sheath 9.1 Material composition of fuel Enrichment 36.00%

Used library of effective cross sections 235U weight portion 11.10%

92235.60c 238U weight portion 19.74 92238.60c Al weight portion 65.00%

13027.60c O weight portion 4.16%

8016.30c 235U weight 141.80 g

238U weight 252.09 g

Al weight 830.29 g

O weight 53.19 Total 1277.37 g

Active part length 50 cm Fuel volume 280.45 cm3 U density 1.4045 g.cm-3 Fuel density 4.5548 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1 O mol. weight 15.9994 g.mol-1

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54 / 159 9.2 Model of a cask with fuel Fig. 12: Model of S-36 fuel in a stainless steel sheath with 36% enrichment of 235U - cross section Fig. 13: Cask with S-36 fuel in a stainless steel sheath with 36% enrichment of 235U - cross section

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55 / 159 Fig. 14: Cask with S-36 fuel in a stainless steel sheath with 36% enrichment of 235U -

longitudinal section

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56 / 159 9.3 Cask criticality calculation results 9.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 21: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.1083 0.0003 0.15 0.2469 0.0007 0.01 0.1262 0.0004 0.16 0.2522 0.0007 0.02 0.1416 0.0005 0.17 0.2564 0.0008 0.03 0.1550 0.0005 0.18 0.2614 0.0008 0.04 0.1667 0.0005 0.19 0.2660 0.0008 0.05 0.1772 0.0005 0.2 0.2697 0.0008 0.06 0.1866 0.0006 0.3 0.3099 0.0009 0.07 0.1953 0.0006 0.4 0.3442 0.0015 0.08 0.2032 0.0006 0.5 0.3753 0.0016 0.09 0.2110 0.0007 0.6 0.4028 0.0017 0.1 0.2176 0.0007 0.7 0.4293 0.0018 0.11 0.2243 0.0007 0.8 0.4547 0.0018 0.12 0.2308 0.0007 0.9 0.4802 0.0019 0.13 0.2362 0.0008 0.998203 0.5022 0.0021 0.14 0.2418 0.0007 Check calc.

0.5019 0.0002

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57 / 159 Diagram 15: Dependence of keff on water density inside the cask

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58 / 159 9.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 22: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.1082 0.0004 50 0.5006 0.0039 5

0.1737 0.0009 55 0.5007 0.0014 10 0.2697 0.0013 60 0.5018 0.0015 15 0.3411 0.0016 65 0.5018 0.0014 20 0.3899 0.0018 70 0.5031 0.0017 25 0.4229 0.0018 75 0.5008 0.0015 30 0.4471 0.0019 80 0.5004 0.0015 35 0.4653 0.0020 85 0.5003 0.0014 40 0.4769 0.0019 90 0.5009 0.0015 45 0.4882 0.0015 Diagram 16: Dependence of keff on the level height inside the cask

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59 / 159 9.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 23: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.1086 0.0003 32.5 0.4477 0.0013 2.5 0.1181 0.0003 35 0.4576 0.0014 5

0.1435 0.0005 37.5 0.4620 0.0015 7.5 0.1867 0.0007 40 0.4730 0.0014 10 0.2371 0.0009 42.5 0.4822 0.0014 12.5 0.2679 0.0011 45 0.4870 0.0014 15 0.2983 0.0011 47.5 0.4902 0.0015 17.5 0.3405 0.0011 50 0.4976 0.0014 20 0.3645 0.0012 52.5 0.4996 0.0013 22.5 0.3883 0.0012 55 0.4991 0.0014 25 0.4089 0.0013 57.5 0.5020 0.0013 27.5 0.4324 0.0013 60 0.5020 0.0014 30 0.4405 0.0012 Diagram 17: Dependence of keff on the level height inside the cask

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60 / 159 9.3.4 Results of calculations for individual tolerances(temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 24: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. toAe 11540/Dok Rev. 0 149.10 °C 0.1076 0.0003 179.36 °C 0.1075 0.0002 120.51 °C 0.1075 0.0003 152.07 °C 0.1075 0.0002 293.3 °C 0.1075 0.0003 Calculations for B concentrations in ATABOR 1.2 %

0.1083 0.0003 1.6%

0.1069 0.0003 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.1083 0.0003 4.0 mm 0.1091 0.0003 Calculations for tolerances of total U weight in fuel

-5%

0.1031 0.0003

+5%

0.1138 0.0003 Calculations for 235U enrichment tolerances

-1%

0.1094 0.0003

+1 0.1078 0.0003 Calculations for specified tolerances of matrix content

-10%

0.1060 0.0003

+10%

0.1120 0.0003 Calculations for rods displacement inside the lattice Grouping of rods 0.1099 0.0003 Calculations for tolerances of active fuel part length

-2 cm 0.1128 0.0003

+2 cm 0.1043 0.0003

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61 / 159 9.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 25: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.1108 0.0003 2

0.1090 0.0003 4

0.1085 0.0003 6

0.1088 0.0003 8

0.1082 0.0003 10 0.1087 0.0003 Diagram 18: keff dependence on the distance between the casks under normal transport conditions

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62 / 159 9.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 26: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.5018 0.0013 2

0.5016 0.0015 4

0.5014 0.0014 6

0.5017 0.0015 8

0.5009 0.0015 10 0.5022 0.0014 Diagram 19: keff dependence on the distance between the casks under transport accident conditions

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63 / 159 9.6 Conclusion 9.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.5031 stat calculated keff value error 0.0039 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C

-0.00064 calculations for cask temperature states - 179.36 °C

-0.00068 calculations for cask temperature states - 120.51 °C

-0.00067 calculations for cask temperature states - 152.07 °C

-0.00071 calculations for cask temperature states - 293.3 °C

-0.00067 Calculations for B concentrations in ATABOR - 1.2% B 0.00011 Calculations for B concentrations in ATABOR - 1.6% B

-0.00131 Calculations for ATABOR internals thickness tolerances-3.6mm 0.00011 Calculations for ATABOR internals thickness tolerances - 4 mm 0.00095 decrease of total U weight in fuel (-5% U)

-0.00507 increase of total U weight in fuel (+5% U) 0.00557 decrease of U enrichment (-1% 235U) 0.00116 increase of U enrichment (+1% 235U)

-0.00036 reduction of matrix content in fuel (-10%)

-0.00218 increase of matrix content in fuel (+10%)

0.00378 calculations of grouping of rods 0.00167 reduction of active length of fuel (-2 cm) 0.00465 increase of active length of fuel (+2 cm)

-0.00385 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) v 9.3.2 - Calculation results for flooding a standing cask, 9.3.3 - Calculation results for flooding a cask resting on its side for point ii) v 9.3.4 - Calculation results for individual tolerances for point iii) v 9.3.4 - Calculation results for individual tolerances, for point iv) v 9.3.4 - Calculation results for individual tolerances for point v) v 9.3.1 - Results of calculations for the change of water density inside the

cask, and 9.3.2 - Calculation results for flooding a standing cask, 9.3.3 - Calculation results for flooding a cask resting on its side for point vi) v 9.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.5316 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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64 / 159 9.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.1108 stat calculated keff value error 0.0003 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.1321 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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65 / 159 9.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.5022 stat calculated keff value error 0.0015 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.5247 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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66 / 159

10. VVR-M fuel with 36% enrichment of 235U 10.1 Material composition of fuel Enrichment 36.00%

Used library of effective cross sections 235U weight portion 12.60%

92235.60c 238U weight portion 22.40 92238.60c Al weight portion 65.00%

13027.60c 235U weight 38.40 g

238U weight 68.27 g

Al weight 198.10 g

Total 304.76 g

Active part length 60 cm Fuel volume 79.87 cm3 U density 1.3356 g.cm-3 Fuel density 3.8159 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1

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67 / 159 10.2 Model of a cask with fuel Fig. 15: Model of VVR-M fuel with 36% enrichment of 235U - cross section Fig. 16: Cask with VVR-M fuel with 36% enrichment of 235U - cross section

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68 / 159 Fig. 17: Cask with VVR-M fuel with 36% enrichment of 235U - longitudinal section

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69 / 159 10.3 Cask criticality calculation results 10.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 27: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0432 0.0001 0.15 0.1532 0.0005 0.01 0.0568 0.0002 0.16 0.1581 0.0006 0.02 0.0694 0.0003 0.17 0.1636 0.0006 0.03 0.0799 0.0003 0.18 0.1684 0.0006 0.04 0.0891 0.0003 0.19 0.1735 0.0006 0.05 0.0966 0.0004 0.2 0.1786 0.0007 0.06 0.1037 0.0004 0.3 0.2304 0.0008 0.07 0.1102 0.0004 0.4 0.2798 0.0010 0.08 0.1156 0.0004 0.5 0.3265 0.0011 0.09 0.1216 0.0005 0.6 0.3686 0.0012 0.1 0.1265 0.0005 0.7 0.4085 0.0013 0.11 0.1318 0.0005 0.8 0.4412 0.0013 0.12 0.1377 0.0005 0.9 0.4723 0.0014 0.13 0.1427 0.0005 0.998203 0.4986 0.0013 0.14 0.1482 0.0005 Check calc.

0.4987 0.0002

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70 / 159 Diagram 20: Dependence of keff on water density inside the cask

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71 / 159 10.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 28: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0432 0.0001 50 0.4626 0.0015 5

0.0461 0.0002 55 0.4735 0.0014 10 0.0498 0.0002 60 0.4820 0.0014 15 0.0734 0.0004 65 0.4902 0.0014 20 0.1930 0.0008 70 0.4938 0.0015 25 0.2894 0.0011 75 0.4977 0.0014 30 0.3531 0.0012 80 0.4980 0.0014 35 0.3953 0.0013 85 0.4987 0.0014 40 0.4250 0.0013 90 0.4967 0.0014 45 0.4449 0.0014 Diagram 21: Dependence of keff on the level height inside the cask

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72 / 159 10.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 29: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0433 0.0001 32.5 0.4532 0.0013 2.5 0.0514 0.0002 35 0.4599 0.0014 5

0.0865 0.0004 37.5 0.4630 0.0013 7.5 0.1692 0.0008 40 0.4741 0.0015 10 0.2511 0.0011 42.5 0.4815 0.0013 12.5 0.2706 0.0011 45 0.4827 0.0014 15 0.3100 0.0011 47.5 0.4892 0.0014 17.5 0.3566 0.0013 50 0.4949 0.0014 20 0.3734 0.0012 52.5 0.4930 0.0013 22.5 0.3935 0.0013 55 0.4962 0.0013 25 0.4229 0.0013 57.5 0.4981 0.0014 27.5 0.4364 0.0013 60 0.4982 0.0014 30 0.4419 0.0013 Diagram 22: Dependence of keff on the level height inside the cask

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73 / 159 10.3.4 Results of calculations for individual tolerances (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 30: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. toAe 11540/Dok Rev. 0 149.10 °C 0.0433 0.0001 179.36 °C 0.0432 0.0001 120.51 °C 0.0431 0.0001 152.07 °C 0.0432 0.0001 293.3 °C 0.0432 0.0001 Calculations for B concentrations in ATABOR 1.2 %

0.0432 0.0001 1.6%

0.0422 0.0001 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0432 0.0001 4.0 mm 0.0432 0.0001 Calculations for tolerances of total U weight in fuel

-5%

0.0411 0.0001

+5%

0.0453 0.0001 Calculations for 235U enrichment tolerances

-1%

0.0434 0.0001

+1 0.0429 0.0001 Calculations for specified tolerances of matrix content

-10%

0.0427 0.0001

+10%

0.0438 0.0001 Calculations for rods displacement inside the lattice Grouping of rods 0.0437 0.0001 Calculations for tolerances of active fuel part length

-2 cm 0.0438 0.0001

+2 cm 0.0426 0.0001

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74 / 159 10.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 31: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0447 0.0001 2

0.0435 0.0001 4

0.0433 0.0001 6

0.0431 0.0001 8

0.0433 0.0001 10 0.0431 0.0001 Diagram 23: keff dependence on the distance between the casks under normal transport conditions

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75 / 159 10.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 32: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.4988 0.0015 2

0.4991 0.0013 4

0.4991 0.0015 6

0.5001 0.0014 8

0.4987 0.0015 10 0.4989 0.0014 Diagram 24: keff dependence on the distance between the casks under transport accident conditions

Z-1296 MCNP Calculation of Cask Criticality for ATABOR Internals, th. 4 mm 10.VVR-M fuel with 36% enrichment of 235U Nuclear Research Institute ez a.s.

76 / 159 10.6 Conclusion 10.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.4987 stat calculated keff value error 0.0015 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C 0.00007 calculations for cask temperature states - 179.36 °C 0.00003 calculations for cask temperature states - 120.51 °C

-0.00013 calculations for cask temperature states - 152.07 °C 0.00000 calculations for cask temperature states - 293.3 °C 0.00002 Calculations for B concentrations in ATABOR - 1.2% B 0.00000 Calculations for B concentrations in ATABOR - 1.6% B

-0.00098 Calculations for ATABOR internals thickness tolerances-3.6mm 0.00000 Calculations for ATABOR internals thickness tolerances - 4 mm 0.00006 decrease of total U weight in fuel (-5% U)

-0.00207 increase of total U weight in fuel (+5% U) 0.00210 decrease of U enrichment (-1% 235U) 0.00020 increase of U enrichment (+1% 235U)

-0.00024 reduction of matrix content in fuel (-10%)

-0.00046 increase of matrix content in fuel (+10%)

0.00058 calculations of grouping of rods 0.00048 reduction of active length of fuel (-2 cm) 0.00065 increase of active length of fuel (+2 cm)

-0.00054 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) v 10.3.2 - Calculation results for flooding a standing cask, 10.3.3 - Calculation results for flooding a cask resting on its side for point ii) v 10.3.4 - Calculation results for individual tolerances for point iii) v 10.3.4 - Calculation results for individual tolerances, for point iv) v 10.3.4 - Calculation results for individual tolerances for point v) v 9.3.1 - Results of calculations for the change of water density inside the

cask, and 10.3.2 - Calculation results for flooding a standing cask, 10.3.3 - Calculation results for flooding a cask resting on its side for point vi) v 10.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.5216 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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77 / 159 10.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0447 stat calculated keff value error 0.0001 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.0659 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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78 / 159 10.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.5001 stat calculated keff value error 0.0015 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.5226 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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79 / 159

11. VVR-M2 fuel with 36% enrichment of 235U 11.1 Material composition of fuel Enrichment 36.00%

Used library of effective cross sections 235U weight portion 19.03%

92235.60c 238U weight portion 33.83 92238.60c Al weight portion 40.00%

13027.60c O weight portion 7.14%

235U weight 45.00 g

238U weight 80.00 g

Al weight 94.59 g

O weight 16.88 Total 236.47 g

Active part length 60 cm Fuel volume 114.09 cm3 U density 1.0956 g.cm-3 Fuel density 2.0726 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1 O mol. weight 15.9994

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80 / 159 11.2 Model of a cask with fuel Fig. 18: Model of VVR-M2 fuel with 36% enrichment of 235U - cross section Fig. 19: Cask with VVR-M2 fuel with 36% enrichment of 235U - cross section

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81 / 159 Fig. 20: Cask with VVR-M2 fuel with 36% enrichment of 235U - longitudinal section

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82 / 159 11.3 Cask criticality calculation results 11.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 33: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0353 0.0001 0.15 0.1300 0.0005 0.01 0.0469 0.0002 0.16 0.1349 0.0006 0.02 0.0576 0.0002 0.17 0.1398 0.0005 0.03 0.0667 0.0003 0.18 0.1442 0.0006 0.04 0.0743 0.0003 0.19 0.1488 0.0006 0.05 0.0811 0.0003 0.2 0.1536 0.0006 0.06 0.0868 0.0003 0.3 0.2007 0.0008 0.07 0.0923 0.0004 0.4 0.2476 0.0009 0.08 0.0974 0.0004 0.5 0.2913 0.0011 0.09 0.1024 0.0004 0.6 0.3329 0.0012 0.1 0.1071 0.0004 0.7 0.3700 0.0013 0.11 0.1121 0.0004 0.8 0.4026 0.0013 0.12 0.1163 0.0004 0.9 0.4330 0.0014 0.13 0.1210 0.0005 0.998203 0.4582 0.0013 0.14 0.1258 0.0005 Check calc.

0.4554 0.0002

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83 / 159 Diagram 25: Dependence of keff on water density inside the cask

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84 / 159 11.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 34: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0353 0.0001 50 0.4226 0.0013 5

0.0381 0.0002 55 0.4340 0.0013 10 0.0414 0.0002 60 0.4438 0.0013 15 0.0622 0.0003 65 0.4495 0.0014 20 0.1716 0.0008 70 0.4566 0.0014 25 0.2614 0.0011 75 0.4593 0.0013 30 0.3218 0.0012 80 0.4606 0.0013 35 0.3599 0.0013 85 0.4593 0.0014 40 0.3878 0.0012 90 0.4594 0.0013 45 0.4086 0.0013 Diagram 26: Dependence of keff on the level height inside the cask

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85 / 159 11.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 35: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0353 0.0001 32.5 0.4163 0.0013 2.5 0.0425 0.0002 35 0.4222 0.0012 5

0.0731 0.0004 37.5 0.4271 0.0013 7.5 0.1497 0.0007 40 0.4355 0.0014 10 0.2273 0.0010 42.5 0.4427 0.0013 12.5 0.2467 0.0010 45 0.4438 0.0013 15 0.2819 0.0011 47.5 0.4495 0.0014 17.5 0.3256 0.0012 50 0.4553 0.0012 20 0.3405 0.0012 52.5 0.4567 0.0013 22.5 0.3591 0.0012 55 0.4564 0.0014 25 0.3863 0.0013 57.5 0.4590 0.0013 27.5 0.3990 0.0013 60 0.4589 0.0014 30 0.4058 0.0012 Diagram 27: Dependence of keff on the level height inside the cask

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86 / 159 11.3.4 Results of calculations for individual tolerances (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 36: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. toAe 11540/Dok Rev. 0 149.10 °C 0.0353 0.0001 179.36 °C 0.0352 0.0001 120.51 °C 0.0353 0.0001 152.07 °C 0.0353 0.0001 293.3 °C 0.0353 0.0001 Calculations for B concentrations in ATABOR 1.2 %

0.0353 0.0001 1.6%

0.0345 0.0001 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0353 0.0001 4.0 mm 0.0354 0.0001 Calculations for tolerances of total U weight in fuel

-5%

0.0336 0.0001

+5%

0.0370 0.0001 Calculations for 235U enrichment tolerances

-1%

0.0355 0.0001

+1 0.0352 0.0001 Calculations for specified tolerances of matrix content

-10%

0.0353 0.0001

+10%

0.0353 0.0001 Calculations for rods displacement inside the lattice Grouping of rods 0.0357 0.0001 Calculations for tolerances of active fuel part length

-2 cm 0.0358 0.0001

+2 cm 0.0348 0.0001

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87 / 159 11.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 37: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0364 0.0001 2

0.0357 0.0001 4

0.0354 0.0001 6

0.0353 0.0001 8

0.0354 0.0001 10 0.0354 0.0001 Diagram 28: keff dependence on the distance between the casks under normal transport conditions

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88 / 159 11.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 38: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.4605 0.0013 2

0.4594 0.0014 4

0.4579 0.0014 6

0.4587 0.0013 8

0.4600 0.0013 10 0.4596 0.0014 Diagram 29: keff dependence on the distance between the casks under transport accident conditions

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89 / 159 11.6 Conclusion 11.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.4606 stat calculated keff value error 0.0014 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C 0.00003 calculations for cask temperature states - 179.36 °C

-0.00011 calculations for cask temperature states - 120.51 °C 0.00002 calculations for cask temperature states - 152.07 °C

-0.00001 calculations for cask temperature states - 293.3 °C 0.00006 Calculations for B concentrations in ATABOR - 1.2% B 0.00002 Calculations for B concentrations in ATABOR - 1.6% B

-0.00075 Calculations for ATABOR internals thickness tolerances-3.6mm 0.00002 Calculations for ATABOR internals thickness tolerances - 4 mm 0.00010 decrease of total U weight in fuel (-5% U)

-0.00166 increase of total U weight in fuel (+5% U) 0.00170 decrease of U enrichment (-1% 235U) 0.00019 increase of U enrichment (+1% 235U)

-0.00013 reduction of matrix content in fuel (-10%)

-0.00003 increase of matrix content in fuel (+10%)

-0.00002 calculations of grouping of rods 0.00039 reduction of active length of fuel (-2 cm) 0.00054 increase of active length of fuel (+2 cm)

-0.00049 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) v 11.3.2 - Calculation results for flooding a standing cask, 9.3.3 - Calculation results for flooding a cask resting on its side for point ii) v 11.3.4 - Calculation results for individual tolerances for point iii) v 11.3.4 - Calculation results for individual tolerances, for point iv) v 11.3.4 - Calculation results for individual tolerances for point v) v 11.3.1 - Results of calculations for the change of water density inside the

cask, and 11.3.2 - Calculation results for flooding a standing cask, 11.3.3 - Calculation results for flooding a cask resting on its side for point vi) v 11.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.4832 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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90 / 159 11.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0364 stat calculated keff value error 0.0001 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.0575 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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91 / 159 11.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.4605 stat calculated keff value error 0.0014 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.4829 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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92 / 159

12. VVR-M5 fuel with 36% enrichment of 235U 12.1 Material composition of fuel Enrichment 36.00%

Used library of effective cross sections 235U weight portion 19.03%

92235.60c 238U weight portion 33.83 92238.60c Al weight portion 40.00%

13027.60c O weight portion 7.14%

235U weight 65.00 g

238U weight 115.56 g

Al weight 136.63 g

O weight 24.38 Total 341.56 g

Active part length 60 cm Fuel volume 122.49 cm3 U density 1.4740 g.cm-3 Fuel density 2.7885 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1 O mol. weight 15.9994

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93 / 159 12.2 Model of a cask with fuel Fig. 21: Model of VVR-M5 fuel with 36% enrichment of 235U - cross section Fig. 22: Cask with VVR-M5 fuel with 36% enrichment of 235U - cross section

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94 / 159 Fig. 23: Cask with VVR-M5 fuel with 36% enrichment of 235U - longitudinal section

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95 / 159 12.3 Cask criticality calculation results 12.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 39: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0498 0.0001 0.15 0.1735 0.0006 0.01 0.0651 0.0002 0.16 0.1790 0.0006 0.02 0.0790 0.0003 0.17 0.1844 0.0007 0.03 0.0914 0.0003 0.18 0.1903 0.0007 0.04 0.1006 0.0004 0.19 0.1951 0.0007 0.05 0.1100 0.0004 0.2 0.2015 0.0007 0.06 0.1178 0.0004 0.3 0.2573 0.0009 0.07 0.1251 0.0005 0.4 0.3117 0.0011 0.08 0.1317 0.0005 0.5 0.3625 0.0012 0.09 0.1381 0.0005 0.6 0.4081 0.0012 0.1 0.1440 0.0005 0.7 0.4497 0.0014 0.11 0.1502 0.0005 0.8 0.4852 0.0014 0.12 0.1559 0.0005 0.9 0.5163 0.0015 0.13 0.1621 0.0006 0.998203 0.5446 0.0016 0.14 0.1675 0.0006 Check calc.

0.5454 0.0002

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96 / 159 Diagram 30: Dependence of keff on water density inside the cask

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97 / 159 12.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 40: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0498 0.0002 50 0.5043 0.0021 5

0.0533 0.0003 55 0.5169 0.0022 10 0.0569 0.0003 60 0.5292 0.0020 15 0.0837 0.0006 65 0.5363 0.0020 20 0.2154 0.0014 70 0.5417 0.0022 25 0.3220 0.0017 75 0.5460 0.0021 30 0.3893 0.0019 80 0.5458 0.0020 35 0.4357 0.0020 85 0.5456 0.0021 40 0.4674 0.0019 90 0.5424 0.0021 45 0.4881 0.0021 Diagram 31: Dependence of keff on the level height inside the cask

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98 / 159 12.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 41: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0498 0.0001 32.5 0.4979 0.0015 2.5 0.0591 0.0002 35 0.5032 0.0015 5

0.0979 0.0005 37.5 0.5087 0.0015 7.5 0.1901 0.0008 40 0.5189 0.0015 10 0.2765 0.0011 42.5 0.5272 0.0015 12.5 0.2974 0.0011 45 0.5283 0.0014 15 0.3414 0.0012 47.5 0.5342 0.0015 17.5 0.3929 0.0013 50 0.5408 0.0015 20 0.4093 0.0014 52.5 0.5424 0.0014 22.5 0.4317 0.0014 55 0.5432 0.0017 25 0.4627 0.0014 57.5 0.5452 0.0022 27.5 0.4776 0.0014 60 0.5446 0.0021 30 0.4863 0.0015 Diagram 32: Dependence of keff on the level height inside the cask

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99 / 159 12.3.4 Results of calculations for individual tolerances(temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 42: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. toAe 11540/Dok Rev. 0 149.10 °C 0.0499 0.0001 179.36 °C 0.0498 0.0002 120.51 °C 0.0497 0.0001 152.07 °C 0.0498 0.0001 293.3 °C 0.0498 0.0002 Calculations for B concentrations in ATABOR 1.2 %

0.0498 0.0001 1.6%

0.0488 0.0001 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0498 0.0001 4.0 mm 0.0499 0.0001 Calculations for tolerances of total U weight in fuel

-5%

0.0477 0.0002

+5%

0.0519 0.0001 Calculations for 235U enrichment tolerances

-1%

0.0500 0.0002

+1 0.0496 0.0001 Calculations for specified tolerances of matrix content

-10%

0.0493 0.0002

+10%

0.0504 0.0001 Calculations for rods displacement inside the lattice Grouping of rods 0.0503 0.0002 Calculations for tolerances of active fuel part length

-2 cm 0.0504 0.0001

+2 cm 0.0493 0.0002

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100 / 159 12.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 43: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0516 0.0002 2

0.0502 0.0001 4

0.0500 0.0001 6

0.0499 0.0002 8

0.0498 0.0001 10 0.0497 0.0002 Diagram 33: keff dependence on the distance between the casks under normal transport conditions

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101 / 159 12.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 44: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.5453 0.0015 2

0.5463 0.0015 4

0.5444 0.0015 6

0.5453 0.0015 8

0.5450 0.0015 10 0.5445 0.0015 Diagram 34: keff dependence on the distance between the casks under transport accident conditions

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102 / 159 12.6 Conclusion 12.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.5460 stat calculated keff value error 0.0022 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C 0.00007 calculations for cask temperature states - 179.36 °C 0.00003 calculations for cask temperature states - 120.51 °C

-0.00013 calculations for cask temperature states - 152.07 °C 0.00000 calculations for cask temperature states - 293.3 °C 0.00002 Calculations for B concentrations in ATABOR - 1.2% B 0.00000 Calculations for B concentrations in ATABOR - 1.6% B

-0.00098 Calculations for ATABOR internals thickness tolerances-3.6mm 0.00000 Calculations for ATABOR internals thickness tolerances - 4 mm 0.00006 decrease of total U weight in fuel (-5% U)

-0.00207 increase of total U weight in fuel (+5% U) 0.00210 decrease of U enrichment (-1% 235U) 0.00020 increase of U enrichment (+1% 235U)

-0.00024 reduction of matrix content in fuel (-10%)

-0.00046 increase of matrix content in fuel (+10%)

0.00058 calculations of grouping of rods 0.00048 reduction of active length of fuel (-2 cm) 0.00065 increase of active length of fuel (+2 cm)

-0.00054 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) v 12.3.2 - Calculation results for flooding a standing cask, 12.3.3 - Calculation results for flooding a cask resting on its side for point ii) v 12.3.4 - Calculation results for individual tolerances for point iii) v 12.3.4 - Calculation results for individual tolerances, for point iv) v 12.3.4 - Calculation results for individual tolerances for point v) v 12.3.1 - Results of calculations for the change of water density inside the

cask, and a

12.3.2 - Calculation results for flooding a standing cask, 12.3.3 - Calculation results for flooding a cask resting on its side for point vi) v 12.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.5696 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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103 / 159 12.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0516 stat calculated keff value error 0.0002 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.0728 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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104 / 159 12.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.5463 stat calculated keff value error 0.0015 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.5689 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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105 / 159

13. VVR-M5 fuel with 90% enrichment of 235U 13.1 Material composition of fuel Enrichment 90.00%

Used library of effective cross sections 235U weight portion 31.50%

92235.60c 238U weight portion 3.50%

92238.60c Al weight portion 65.00%

13027.60c 235U weight 66.00 g

238U weight 7.33 g

Al weight 136.19 g

Total 209.52 g

Active part length 50 cm Fuel volume 106.03 cm3 U density 0.6916 g.cm-3 Fuel density 1.9760 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1

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106 / 159 13.2 Model of a cask with fuel Fig. 24: Model of VVR-M5 fuel with 90% enrichment of 235U - cross section Fig. 25: Cask with VVR-M5 fuel with 90% enrichment of 235U - cross section

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107 / 159 Fig. 26: Cask with VVR-M5 fuel with 90% enrichment of 235U - longitudinal section

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108 / 159 13.3 Cask criticality calculation results 13.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 45: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0481 0.0001 0.15 0.1812 0.0007 0.01 0.0642 0.0002 0.16 0.1876 0.0007 0.02 0.0792 0.0003 0.17 0.1940 0.0007 0.03 0.0918 0.0004 0.18 0.2003 0.0010 0.04 0.1024 0.0004 0.19 0.2059 0.0011 0.05 0.1116 0.0004 0.2 0.2119 0.0012 0.06 0.1204 0.0005 0.3 0.2742 0.0015 0.07 0.1283 0.0005 0.4 0.3318 0.0016 0.08 0.1355 0.0005 0.5 0.3836 0.0017 0.09 0.1427 0.0005 0.6 0.4367 0.0019 0.1 0.1487 0.0006 0.7 0.4782 0.0020 0.11 0.1561 0.0006 0.8 0.5192 0.0020 0.12 0.1619 0.0006 0.9 0.5526 0.0021 0.13 0.1684 0.0006 0.998203 0.5847 0.0022 0.14 0.1747 0.0007 Check calc.

0.5854 0.0002

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109 / 159 Diagram 35: Dependence of keff on water density inside the cask

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110 / 159 13.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 46: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0480 0.0002 50 0.5339 0.0023 5

0.0498 0.0003 55 0.5514 0.0022 10 0.0512 0.0003 60 0.5660 0.0023 15 0.0577 0.0004 65 0.5770 0.0022 20 0.0901 0.0007 70 0.5812 0.0022 25 0.2369 0.0014 75 0.5810 0.0022 30 0.3536 0.0018 80 0.5842 0.0023 35 0.4247 0.0019 85 0.5815 0.0021 40 0.4737 0.0020 90 0.5838 0.0022 45 0.5094 0.0021 Diagram 36: Dependence of keff on the level height inside the cask

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111 / 159 13.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 47: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0482 0.0002 32.5 0.5314 0.0022 2.5 0.0582 0.0004 35 0.5365 0.0023 5

0.1003 0.0008 37.5 0.5420 0.0024 7.5 0.1998 0.0013 40 0.5525 0.0022 10 0.2908 0.0016 42.5 0.5622 0.0021 12.5 0.3169 0.0017 45 0.5646 0.0023 15 0.3622 0.0020 47.5 0.5716 0.0023 17.5 0.4150 0.0020 50 0.5783 0.0021 20 0.4387 0.0019 52.5 0.5783 0.0022 22.5 0.4599 0.0021 55 0.5796 0.0023 25 0.4935 0.0021 57.5 0.5835 0.0021 27.5 0.5075 0.0021 60 0.5809 0.0022 30 0.5149 0.0022 Diagram 37: Dependence of keff on the level height inside the cask

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112 / 159 13.3.4 Results of calculations for individual tolerances(temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 48: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. toAe 11540/Dok Rev. 0 149.10 °C 0.0483 0.0001 179.36 °C 0.0482 0.0002 120.51 °C 0.0485 0.0001 152.07 °C 0.0483 0.0001 293.3 °C 0.0484 0.0002 Calculations for B concentrations in ATABOR 1.2 %

0.0481 0.0001 1.6%

0.0469 0.0001 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0481 0.0001 4.0 mm 0.0495 0.0001 Calculations for tolerances of total U weight in fuel

-5%

0.0451 0.0002

+5%

0.0512 0.0001 Calculations for 235U enrichment tolerances

-1%

0.0482 0.0002

+1 0.0482 0.0001 Calculations for specified tolerances of matrix content

-10%

0.0477 0.0002

+10%

0.0491 0.0001 Calculations for rods displacement inside the lattice Grouping of rods 0.0489 0.0002 Calculations for tolerances of active fuel part length

-2 cm 0.0493 0.0001

+2 cm 0.0473 0.0002

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113 / 159 13.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 49: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0498 0.0002 2

0.0485 0.0002 4

0.0483 0.0002 6

0.0482 0.0002 8

0.0480 0.0002 10 0.0479 0.0002 Diagram 38: keff dependence on the distance between the casks under normal transport conditions

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114 / 159 13.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 50: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.5815 0.0023 2

0.5821 0.0021 4

0.5810 0.0022 6

0.5815 0.0022 8

0.5817 0.0023 10 0.5807 0.0021 Diagram 39: keff dependence on the distance between the casks under transport accident conditions

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115 / 159 13.6 Conclusion 13.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.5847 stat calculated keff value error 0.0024 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C 0.00016 calculations for cask temperature states - 179.36 °C 0.00011 calculations for cask temperature states - 120.51 °C 0.00039 calculations for cask temperature states - 152.07 °C 0.00020 calculations for cask temperature states - 293.3 °C 0.00029 calculations for B concentrations in ATABOR - 1.2% B 0.00000 calculations for B concentrations in ATABOR - 1.6% B

-0.00117 calculations for ATABOR internals thickness tolerances-3.6mm 0.00000 calculations for ATABOR internals thickness tolerances - 4 mm 0.00141 decrease of total U weight in fuel (-5% U)

-0.00296 increase of total U weight in fuel (+5% U) 0.00312 decrease of U enrichment (-1% 235U) 0.00015 increase of U enrichment (+1% 235U) 0.00011 reduction of matrix content in fuel (-10%)

-0.00037 increase of matrix content in fuel (+10%)

0.00099 calculations of grouping of rods 0.00084 reduction of active length of fuel (-2 cm) 0.00125 increase of active length of fuel (+2 cm)

-0.00082 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) v 13.3.2 - Calculation results for flooding a standing cask, 13.3.3 - Calculation results for flooding a cask resting on its side for point ii) v 13.3.4 - Calculation results for individual tolerances for point iii) v 13.3.4 - Calculation results for individual tolerances, for point iv) v 13.3.4 - Calculation results for individual tolerances for point v) v 13.3.1 - Results of calculations for the change of water density inside the

cask, and 13.3.2 - Calculation results for flooding a standing cask, 13.3.3 - Calculation results for flooding a cask resting on its side for point vi) v 13.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.6089 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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116 / 159 13.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0498 stat calculated keff value error 0.0002 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.0710 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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117 / 159 13.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.5821 stat calculated keff value error 0.0023 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.6055 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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118 / 159

14. VVR-M7 fuel with 90% enrichment of 235U 14.1 Material composition of fuel Enrichment 90.00%

Used library of effective cross sections 235U weight portion 27.73%

92235.60c 238U weight portion 3.08%

92238.60c Al weight portion 65.00%

13027.60c O weight portion 4.19%

235U weight 66.00 g

238U weight 7.33 g

Al weight 136.19 g

O weight 9.97 Total 209.52 g

Active part length 50 cm Fuel volume 106.03 cm3 U density 0.6916 g.cm-3 Fuel density 1.9760 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1 O mol. weight 15.9994

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119 / 159 14.2 Model of a cask with fuel Fig. 27: Model of VVR-M7 fuel with 90% enrichment of 235U - cross section Fig. 28: Cask with VVR-M7 fuel with 90% enrichment of 235U - cross section

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120 / 159 Fig. 29: Cask with VVR-M7 fuel with 90% enrichment of 235U - longitudinal section

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121 / 159 14.3 Cask criticality calculation results 14.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 51: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0484 0.0002 0.15 0.1823 0.0010 0.01 0.0648 0.0004 0.16 0.1889 0.0010 0.02 0.0798 0.0004 0.17 0.1951 0.0011 0.03 0.0929 0.0005 0.18 0.2009 0.0010 0.04 0.1033 0.0006 0.19 0.2063 0.0011 0.05 0.1130 0.0006 0.2 0.2136 0.0011 0.06 0.1212 0.0007 0.3 0.2737 0.0014 0.07 0.1290 0.0007 0.4 0.3338 0.0017 0.08 0.1363 0.0007 0.5 0.3855 0.0019 0.09 0.1436 0.0008 0.6 0.4348 0.0019 0.1 0.1496 0.0009 0.7 0.4793 0.0019 0.11 0.1574 0.0008 0.8 0.5184 0.0020 0.12 0.1629 0.0009 0.9 0.5526 0.0022 0.13 0.1695 0.0009 0.998203 0.5816 0.0023 0.14 0.1763 0.0009 Check calc.

0.5814 0.0002

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122 / 159 Diagram 40: Dependence of keff on water density inside the cask

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123 / 159 14.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 52: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0483 0.0002 50 0.5333 0.0021 5

0.0501 0.0003 55 0.5511 0.0022 10 0.0515 0.0003 60 0.5654 0.0022 15 0.0581 0.0004 65 0.5764 0.0022 20 0.0912 0.0007 70 0.5849 0.0022 25 0.2366 0.0014 75 0.5830 0.0022 30 0.3534 0.0017 80 0.5840 0.0022 35 0.4265 0.0020 85 0.5817 0.0021 40 0.4753 0.0020 90 0.5817 0.0022 45 0.5112 0.0021 Diagram 41: Dependence of keff on the level height inside the cask

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124 / 159 14.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 53: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0486 0.0002 32.5 0.5309 0.0021 2.5 0.0586 0.0004 35 0.5380 0.0021 5

0.1009 0.0007 37.5 0.5432 0.0022 7.5 0.1996 0.0013 40 0.5540 0.0022 10 0.2929 0.0017 42.5 0.5637 0.0022 12.5 0.3185 0.0018 45 0.5650 0.0021 15 0.3645 0.0018 47.5 0.5716 0.0022 17.5 0.4168 0.0020 50 0.5781 0.0022 20 0.4350 0.0019 52.5 0.5778 0.0023 22.5 0.4595 0.0020 55 0.5818 0.0022 25 0.4945 0.0022 57.5 0.5837 0.0023 27.5 0.5090 0.0021 60 0.5819 0.0022 30 0.5191 0.0022 Diagram 42: Dependence of keff on the level height inside the cask

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125 / 159 14.3.4 Results of calculations for individual tolerances(temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 54: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. toAe 11540/Dok Rev. 0 149.10 °C 0.0483 0.0002 179.36 °C 0.0484 0.0002 120.51 °C 0.0484 0.0002 152.07 °C 0.0484 0.0002 293.3 °C 0.0485 0.0002 Calculations for B concentrations in ATABOR 1.2 %

0.0484 0.0002 1.6%

0.0475 0.0002 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0484 0.0002 4.0 mm 0.0490 0.0002 Calculations for tolerances of total U weight in fuel

-5%

0.0466 0.0002

+5%

0.0504 0.0002 Calculations for 235U enrichment tolerances

-1%

0.0485 0.0002

+1 0.0485 0.0002 Calculations for specified tolerances of matrix content

-10%

0.0483 0.0002

+10%

0.0488 0.0002 Calculations for rods displacement inside the lattice Grouping of rods 0.0490 0.0002 Calculations for tolerances of active fuel part length

-2 cm 0.0490 0.0002

+2 cm 0.0480 0.0002

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126 / 159 14.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 55: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0503 0.0002 2

0.0489 0.0002 4

0.0485 0.0002 6

0.0484 0.0002 8

0.0486 0.0002 10 0.0485 0.0002 Diagram 43: keff dependence on the distance between the casks under normal transport conditions

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127 / 159 14.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 56: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.5833 0.0022 2

0.5830 0.0023 4

0.5831 0.0023 6

0.5825 0.0022 8

0.5839 0.0022 10 0.5838 0.0021 Diagram 44: keff dependence on the distance between the casks under transport accident conditions

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128 / 159 14.6 Conclusion 14.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.5849 stat calculated keff value error 0.0023 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C

-0.00010 calculations for cask temperature states - 179.36 °C

-0.00003 calculations for cask temperature states - 120.51 °C

-0.00002 calculations for cask temperature states - 152.07 °C

-0.00005 calculations for cask temperature states - 293.3 °C 0.00002 Calculations for B concentrations in ATABOR - 1.2% B 0.00000 Calculations for B concentrations in ATABOR - 1.6% B

-0.00095 Calculations for ATABOR internals thickness tolerances-3.6mm 0.00000 Calculations for ATABOR internals thickness tolerances - 4 mm 0.00060 decrease of total U weight in fuel (-5% U)

-0.00183 increase of total U weight in fuel (+5% U) 0.00191 decrease of U enrichment (-1% 235U) 0.00002 increase of U enrichment (+1% 235U) 0.00005 reduction of matrix content in fuel (-10%)

-0.00011 increase of matrix content in fuel (+10%)

0.00032 calculations of grouping of rods 0.00059 reduction of active length of fuel (-2 cm) 0.00057 increase of active length of fuel (+2 cm)

-0.00042 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) v 14.3.2 - Calculation results for flooding a standing cask, 14.3.3 - Calculation results for flooding a cask resting on its side for point ii) v 14.3.4 - Calculation results for individual tolerances for point iii) v 14.3.4 - Calculation results for individual tolerances, for point iv) v 14.3.4 - Calculation results for individual tolerances for point v) v 14.3.1 - Results of calculations for the change of water density inside the

cask, and 14.3.2 - Calculation results for flooding a standing cask, 14.3.3 - Calculation results for flooding a cask resting on its side for point vi) v 14.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.6085 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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129 / 159 14.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0503 stat calculated keff value error 0.0002 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.0715 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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130 / 159 14.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.5839 stat calculated keff value error 0.0023 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.6072 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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131 / 159

15. TVR-S fuel with 2% enrichment of 235U 15.1 Material composition of fuel Enrichment 2.00%

Used library of effective cross sections 235U weight portion 2.00%

92235.60c 238U weight portion 98.00%

92238.60c 235U weight 7.60 g

238U weight 372.40 g

Total 380.00 g

Active part length 10 cm Fuel volume 20.73 cm3 U density 18.3296 g.cm-3 Fuel density 18.3269 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1

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132 / 159 15.2 Model of a cask with fuel Fig. 30: Model of TVR-S fuel with 2% enrichment of 235U - cross section Fig. 31: Cask with TVR-S fuel with 2% enrichment of 235U - cross section

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133 / 159 Fig. 32: Cask with TVR-S fuel with 2% enrichment of 235U - longitudinal section

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134 / 159 15.3 Cask criticality calculation results 15.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 57: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0794 0.0002 0.15 0.1299 0.0004 0.01 0.0849 0.0002 0.16 0.1324 0.0004 0.02 0.0901 0.0002 0.17 0.1355 0.0004 0.03 0.0947 0.0002 0.18 0.1382 0.0004 0.04 0.0985 0.0002 0.19 0.1410 0.0004 0.05 0.1020 0.0002 0.2 0.1442 0.0004 0.06 0.1053 0.0003 0.3 0.1723 0.0005 0.07 0.1083 0.0003 0.4 0.2008 0.0006 0.08 0.1112 0.0003 0.5 0.2272 0.0007 0.09 0.1138 0.0003 0.6 0.2520 0.0008 0.1 0.1163 0.0003 0.7 0.2740 0.0009 0.11 0.1192 0.0003 0.8 0.2945 0.0009 0.12 0.1219 0.0003 0.9 0.3108 0.0009 0.13 0.1243 0.0003 0.998203 0.3249 0.0010 0.14 0.1270 0.0003 Check calc.

0.3246 0.0003

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135 / 159 Diagram 45: Dependence of keff on water density inside the cask

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136 / 159 15.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 58: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0794 0.0002 50 0.3161 0.0009 5

0.1333 0.0005 55 0.3194 0.0009 10 0.2053 0.0007 60 0.3222 0.0010 15 0.2404 0.0008 65 0.3233 0.0009 20 0.2652 0.0008 70 0.3245 0.0036 25 0.2808 0.0009 75 0.3255 0.0009 30 0.2930 0.0009 80 0.3244 0.0009 35 0.3014 0.0009 85 0.3254 0.0009 40 0.3070 0.0009 90 0.3243 0.0009 45 0.3131 0.0009 Diagram 46: Dependence of keff on the level height inside the cask

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137 / 159 15.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 59: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0794 0.0003 32.5 0.2993 0.0013 2.5 0.0821 0.0003 35 0.3030 0.0013 5

0.0948 0.0004 37.5 0.3037 0.0013 7.5 0.1324 0.0007 40 0.3111 0.0013 10 0.1830 0.0009 42.5 0.3157 0.0013 12.5 0.1915 0.0010 45 0.3153 0.0013 15 0.2113 0.0011 47.5 0.3185 0.0014 17.5 0.2454 0.0012 50 0.3240 0.0014 20 0.2530 0.0011 52.5 0.3217 0.0013 22.5 0.2614 0.0012 55 0.3241 0.0013 25 0.2831 0.0012 57.5 0.3263 0.0013 27.5 0.2894 0.0012 60 0.3253 0.0014 30 0.2909 0.0012 Diagram 47: Dependence of keff on the level height inside the cask

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138 / 159 15.3.4 Results of calculations for individual tolerances(temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 60: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. to Ae 11540/Dok Rev. 0 149.10 °C 0.0793 0.0002 179.36 °C 0.0794 0.0002 120.51 °C 0.0794 0.0002 152.07 °C 0.0794 0.0002 293.3 °C 0.0794 0.0002 Calculations for B concentrations in ATABOR 1.2 %

0.0794 0.0002 1.6%

0.0785 0.0002 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0794 0.0002 4.0 mm 0.0800 0.0002 Calculations for tolerances of total U weight in fuel

-5%

0.0776 0.0002

+5%

0.0813 0.0002 Calculations for 235U enrichment tolerances

-1%

0.0794 0.0002

+1 0.0795 0.0002 Calculations for rods displacement inside the lattice Grouping of rods 0.0800 0.0002 Calculations for tolerances of active fuel part length

-1 cm 0.0800 0.0002

-1 cm 0.0790 0.0002

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139 / 159 15.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 61: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0802 0.0003 2

0.0796 0.0003 4

0.0795 0.0003 6

0.0796 0.0003 8

0.0794 0.0003 10 0.0793 0.0003 Diagram 48: keff dependence on the distance between the casks under normal transport conditions

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140 / 159 15.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 62: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.3249 0.0014 2

0.3242 0.0013 4

0.3243 0.0013 6

0.3252 0.0013 8

0.3251 0.0013 10 0.3244 0.0014 Diagram 49: keff dependence on the distance between the casks under transport accident conditions

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141 / 159 15.6 Conclusion 15.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.3263 stat calculated keff value error 0.0036 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C

-0.00010 calculations for cask temperature states - 179.36 °C

-0.00003 calculations for cask temperature states - 120.51 °C

-0.00002 calculations for cask temperature states - 152.07 °C

-0.00005 calculations for cask temperature states - 293.3 °C 0.00002 calculations for B concentrations in ATABOR - 1.2% B 0.00000 calculations for B concentrations in ATABOR - 1.6% B

-0.00095 calculations for ATABOR internals thickness tolerances - 3.6mm 0.00000 calculations for ATABOR internals thickness tolerances - 4 mm 0.00060 decrease of total U weight in fuel (-5% U)

-0.00183 increase of total U weight in fuel (+5% U) 0.00191 decrease of U enrichment (-1% 235U) 0.00002 increase of U enrichment (+1% 235U) 0.00005 calculations of grouping of rods 0.00059 reduction of active length of fuel (-1 cm) 0.00057 increase of active length of fuel (+1 cm)

-0.00042 The subcriticality was demonstrated for cases according to the Decree 317/2002Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) v 15.3.2 - Calculation results for flooding a standing cask, 15.3.3 - Calculation results for flooding a cask resting on its side for point ii) v 15.3.4 - Calculation results for individual tolerances for point iii) v 15.3.4 - Calculation results for individual tolerances, for point iv) v 15.3.4 - Calculation results for individual tolerances for point v) v 15.3.1 - Results of calculations for the change of water density inside the

cask, and 15.3.2 - Calculation results for flooding a standing cask, 15.3.3 - Calculation results for flooding a cask resting on its side for point vi) v 15.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.3512 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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142 / 159 15.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0802 stat calculated keff value error 0.0003 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.1015 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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143 / 159 15.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.3252 stat calculated keff value error 0.0014 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.3476 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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144 / 159

16. TVR-S fuel with 80% enrichment of 235U 16.1 Material composition of fuel Enrichment 80.00%

Used library of effective cross sections 235U weight portion 24.65%

92235.60c 238U weight portion 6.16%

92238.60c Al weight portion 65.00%

13027.60c O weight portion 4.18%

235U weight 8.00 g

238U weight 2.00 g

Al weight 21.09 g

O weight 1.36 Total 32.45 g

Active part length 10 cm Fuel volume 20.73 cm3 U density 0.4823 g.cm-3 Fuel density 1.5651 g.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Al mol. weight 26.9815 g.mol-1 O mol. weight 15.9994

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145 / 159 16.2 Model of a cask with fuel Fig. 33: Model of TVR-S fuel with 80% enrichment of 235U - cross section Fig. 34: Cask with TVR-S fuel with 80% enrichment of 235U - cross section

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146 / 159 Fig. 35: Cask with TVR-S fuel with 80% enrichment of 235U - longitudinal section

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147 / 159 16.3 Cask criticality calculation results 16.3.1 Results of calculations for the change of water density inside the cask (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with air or water of density from the interval of <0.01; 0.998203> g.cm-3.

Tab. 63: Calculations of keff for the change of water density inside the cask Density keff Error Density keff Error

[g/cm³]

2

[g/cm³]

2 0.001161 0.0236 0.0001 0.15 0.0989 0.0006 0.01 0.0326 0.0002 0.16 0.1025 0.0006 0.02 0.0408 0.0003 0.17 0.1063 0.0007 0.03 0.0478 0.0003 0.18 0.1108 0.0007 0.04 0.0536 0.0003 0.19 0.1140 0.0007 0.05 0.0592 0.0004 0.2 0.1177 0.0007 0.06 0.0639 0.0004 0.3 0.1548 0.0009 0.07 0.0683 0.0004 0.4 0.1917 0.0011 0.08 0.0721 0.0004 0.5 0.2251 0.0012 0.09 0.0765 0.0005 0.6 0.2546 0.0014 0.1 0.0801 0.0005 0.7 0.2811 0.0014 0.11 0.0843 0.0005 0.8 0.3050 0.0015 0.12 0.0880 0.0005 0.9 0.3255 0.0016 0.13 0.0913 0.0005 0.998203 0.3457 0.0016 0.14 0.0953 0.0006 Check calc.

0.3451 0.0003

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148 / 159 Diagram 50: Dependence of keff on water density inside the cask

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149 / 159 16.3.2 Results of calculations for flooding a standing cask with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the cask inside bottom - see Fig. 1).

Tab. 64: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0236 0.0001 50 0.3328 0.0015 5

0.1069 0.0006 55 0.3359 0.0016 10 0.1978 0.0009 60 0.3399 0.0016 15 0.2412 0.0009 65 0.3428 0.0016 20 0.2719 0.0010 70 0.3445 0.0077 25 0.2918 0.0010 75 0.3435 0.0011 30 0.3049 0.0011 80 0.3443 0.0017 35 0.3153 0.0010 85 0.3442 0.0011 40 0.3223 0.0016 90 0.3444 0.0012 45 0.3303 0.0016 Diagram 51: Dependence of keff on the level height inside the cask

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150 / 159 16.3.3 Results of calculations for flooding a cask resting on its side with water (temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is gradually flooded with water (the level of 0 cm corresponds to the inside cask wall - see Fig. 2).

Tab. 65: Calculations of keff when flooding the cask Level keff Error Level keff Error

[cm]

2

[cm]

2 0

0.0237 0.0001 32.5 0.3118 0.0015 2.5 0.0286 0.0002 35 0.3190 0.0015 5

0.0515 0.0005 37.5 0.3198 0.0015 7.5 0.1078 0.0008 40 0.3272 0.0015 10 0.1714 0.0012 42.5 0.3312 0.0015 12.5 0.1840 0.0011 45 0.3334 0.0015 15 0.2068 0.0013 47.5 0.3357 0.0016 17.5 0.2470 0.0013 50 0.3426 0.0016 20 0.2558 0.0014 52.5 0.3421 0.0015 22.5 0.2662 0.0014 55 0.3422 0.0015 25 0.2921 0.0014 57.5 0.3455 0.0016 27.5 0.3002 0.0015 60 0.3445 0.0016 30 0.3041 0.0015 Diagram 52: Dependence of keff on the level height inside the cask

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151 / 159 16.3.4 Results of calculations for individual tolerances(temperature 27 °C)

The cask is surrounded by ~ 30 cm of water, the cask internal space is filled with dry air.

Tab. 66: Calculations of keff for individual tolerances keff Error 2

Calculations for individual temperature states of a cask acc. to Ae 11540/Dok Rev. 0 149.10 °C 0.0235 0.0001 179.36 °C 0.0236 0.0001 120.51 °C 0.0236 0.0001 152.07 °C 0.0236 0.0001 293.3 °C 0.0237 0.0001 Calculations for B concentrations in ATABOR 1.2 %

0.0236 0.0001 1.6%

0.0227 0.0001 Calculations for ATABOR internals thickness tolerances 3.6 mm 0.0236 0.0001 4.0 mm 0.0242 0.0001 Calculations for tolerances of total U weight in fuel

-5%

0.0218 0.0001

+5%

0.0255 0.0001 Calculations for 235U enrichment tolerances

-1%

0.0237 0.0001

+1 0.0237 0.0001 Calculations for specified tolerances of matrix content

-10%

0.0233 0.0001

+10%

0.0246 0.0001 Calculations for rods displacement inside the lattice Grouping of rods 0.0242 0.0001 Calculations for tolerances of active fuel part length

-1 cm 0.0242 0.0001

+1 cm 0.0232 0.0001

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152 / 159 16.4 Results of calculations for a group of casks under normal transport conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 87, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with dry air. Ambient temperature is 27 °C.

Tab. 67: keff dependence on the distance between the casks under normal transport conditions Distance keff Error

[cm]

2 0

0.0245 0.0001 2

0.0239 0.0001 4

0.0236 0.0001 6

0.0236 0.0001 8

0.0237 0.0001 10 0.0236 0.0001 Diagram 53: keff dependence on the distance between the casks under normal transport conditions

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153 / 159 16.5 Results of calculations for a group of casks under transport accident conditions According to the Decree 317/2002 Col., Appendix 1, Part I, Sec. 88, letter a) for the purpose of calculations the infinite number of casks is surrounded from above and from below by ~ 30 cm of water, there is a gap between the casks in the interval of <0; 10> cm filled with water. The space inside the cask is filled with water. Ambient temperature is 27 °C.

Tab. 68: keff dependence on the distance between the casks under transport accident conditions Distance keff Error

[cm]

2 0

0.3440 0.0016 2

0.3442 0.0016 4

0.3447 0.0015 6

0.3436 0.0017 8

0.3454 0.0016 10 0.3449 0.0016 Diagram 54: keff dependence on the distance between the casks under transport accident conditions

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154 / 159 16.6 Conclusion 16.6.1 Evaluation of an individual isolated cask According to a formula indicated in Chap. 5 the resulting keff value was determined at 95%/95% level of probability/reliability, as follows:

kvyp maximum calculated keff value 0.3457 stat calculated keff value error 0.0077 k

systematic method error 0.006 i

error of a systematic method error 0.015 calculations for cask temperature states - 149.10 °C

-0.00010 calculations for cask temperature states - 179.36 °C

-0.00004 calculations for cask temperature states - 120.51 °C

-0.00002 calculations for cask temperature states - 152.07 °C

-0.00006 calculations for cask temperature states - 293.3 °C 0.00002 Calculations for B concentrations in ATABOR - 1.2% B 0.00000 Calculations for B concentrations in ATABOR - 1.6% B

-0.00090 Calculations for ATABOR internals thickness tolerances-3.6mm 0.00000 Calculations for ATABOR internals thickness tolerances - 4 mm 0.00060 decrease of total U weight in fuel (-5% U)

-0.00183 increase of total U weight in fuel (+5% U) 0.00191 decrease of U enrichment (-1% 235U) 0.00002 increase of U enrichment (+1% 235U) 0.00005 reduction of matrix content in fuel (-10%)

-0.00037 increase of matrix content in fuel (+10%)

0.00099 calculations of grouping of rods 0.00059 reduction of active length of fuel (-1 cm) 0.00058 increase of active length of fuel (+1 cm)

-0.00042 The subcriticality was demonstrated for cases according to the Decree 317/2002 Col.,

Appendix 1, Part I, Sec. 77, letter a),

for point i) in 16.3.2 - Calculation results for flooding a standing cask, 16.3.3 - Calculation results for flooding a cask resting on its side for point ii) in 16.3.4 - Calculation results for individual tolerances for point iii) in 16.3.4 - Calculation results for individual tolerances, for point iv) in 16.3.4 - Calculation results for individual tolerances for point v) in 16.3.1 - Results of calculations for the change of water density inside the

cask, and 16.3.2 - Calculation results for flooding a standing cask, 16.3.3 - Calculation results for flooding a cask resting on its side for point vi) in 16.3.4 - Calculation results for individual tolerances The resulting keff value determined according to the formula indicated in Chap. 5 is keff = 0.3747 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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155 / 159 16.6.2 Assessment of a group of casks under normal transport conditions The subcriticality of a group of casks under normal conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 87, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, there is no water inside the cask. Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.0245 stat calculated keff value error 0.0001 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows keff = 0.0456 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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156 / 159 16.6.3 Assessment of a group of casks under transport accident conditions The subcriticality of a group of casks under transport accident conditions was demonstrated according to the Decree 317/2002 Col, Appendix 1, Part I, Sec. 88, letter a).

A number of casks for which the value of subcriticality was determined, was chosen as N = (i.e. an infinite number of casks put one next to the other in a square lattice), the group of casks is surrounded by ~ 30 cm of water from above and from below, there is a gap between the casks filled with water, water has penetrated inside the cask.

Under these conditions the resulting keff value was determined according to the formula indicated in Chap. 5, considering the components indicated in the following Table:

kvyp maximum calculated keff value 0.3454 stat calculated keff value error 0.0017 k

systematic method error 0.006 i

error of a systematic method error 0.015 The resulting keff value was determined according to the formula indicated in Chapter 5 at 95%/95% level of probability/reliability, as follows:

keff = 0.3681 With respect to criticality the transport cask satisfies the requirement for subcriticality according to §47 of the SÚJB Decree 195/1999 Col.

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157 / 159

17. Summary The following Table summarizes the results of determination of multiplication coefficient for the studied types of fuel Type of fuel keff IRT-2M with 90% enrichment of 235U 0.6053 IRT-3M with 90% enrichment of 235U 0.7331 S-36 with 36% enrichment of 235U 0.5559 S-36 with 36% enrichment of 235U in a stainless steel sheath 0.5316 VVR-M with 36% enrichment of 235U 0.5216 VVR-M2 with 36% enrichment of 235U 0.4832 VVR-M5 with 36% enrichment of 235U 0.5696 VVR-M5 with 90% enrichment of 235U 0.6089 VVR-M7 with 90% enrichment of 235U 0.6085 TVR-S with 2% enrichment of 235U in a stainless steel sheath 0.3512 TVR-S with 80% enrichment of 235U in a stainless steel sheath 0.3747

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18. References

1. Russell D.

Mosteller:

LATTICES OF ORALLOY CUBES IN

WATER, NEA/NSC/DOC(95)03/II, Volume II, HEU-MET-FAST-006, September 2002

2. Anatoli Tsiboulia, Yevgeniy Rozhikhin, Vladimir Lependin: WATER-MODERATED U(17)O2 ANNULAR FUEL RODS WITHOUT ABSORBER AND WITH GADOLINIUM OR CADMIUM ABSORBERS IN 6.8-CM-PITCH HEXAGONAL LATTICES AT DIFFERENT TEMPERATURES, NEA/NSC/DOC/(95)03/III, Volume III, IEU-COMP-THERM-002, September 2002

3. International Handbook Of Evaluated Criticality Safety Benchmark Experiments, NEA, September 2002

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Ústav jaderného výzkumu ez a.s.

159 / 159

19. Appendix 1: VPVR Cask