ML23331A692

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Appendix 4, Ujv Report Z-1172, MCP Calculation of Cask Criticality for Atabor Internals of Thickness 4 Mm, March 2004
ML23331A692
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Issue date: 03/31/2004
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Text

Ústav jaderného výzkumu ez a.s.

Divize reaktorových sluzeb

ÚJV Report: Z - 1172 MCNP Calculation of Cask Criticality for ATABOR Internals of Thickness 4 mm Prepared by:

Stanislav Flíbor Department Manager:

Ing. Milan Marek, CSc.

DRS Manager:

Ing. Jan Kysela, CSc.

ez, March 2004

ABSTRACT This Report deals with the behaviour of transport and storage cask for spent fuel from research reactors with respect to criticality. The calculations are performed for fuels IRT-2M 80%, IRT-2M 36%, IRT-3M 36%, IRT-3M 19,5% U-Mo, IRT-4M 19,7% and fuel EK-10.

For fuel EK-10 also the option has been calculated that the fuel element was disassembled to individual rods and these are closed in a stainless steel sheath.

3 / 58

1.

Table of Contents

1.

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

2.

Introduction........................................................................................................................ 4

3.

Material composition.......................................................................................................... 4

4.

Calculation......................................................................................................................... 5

5.

Determination of the resulting value keff............................................................................ 6

6.

Fuel IRT-2M with 36% enrichment of 235U...................................................................... 7

7.

Fuel IRT-2M with 80% 235U............................................................................................ 14

8.

Fuel IRT-3M with 36% enrichment of 235U..................................................................... 21

9.

Fuel IRT-3M U-Mo with 19.5% enrichment of 235U....................................................... 28

10.

Fuel IRT-4M with 19.7% enrichment of 235U.............................................................. 35

11.

Fuel EK-10 with 10% enrichment of 235U................................................................... 42

12.

Fuel EK-10 with 10% enrichment of 235U in stainless steel sheath............................. 49

13.

Summary...................................................................................................................... 56

14.

References.................................................................................................................... 56

15.

Appendix 1 - Dependence of keff on water density.................................................... 57

16.

Appendix 2 - Dependence of keff on the height of flooding a cask with water........... 58

píloha 4Azákladní-kritinost.doc 4 / 58

2. Introduction This Report includes calculation documentation of the behaviour of a transport and storage cask for spent fuel from research reactors with respect to maintaining the subcriticality of the entire system.

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

A 3D model of the whole cask was made for the calculations according to -KODA JS a.s.

documentation:

Ae30340P (Ae 006 057 resp.) -VPVR cask Ae30942P (Ae 006 058 resp.) - Basket

3. Material composition Chemical composition of used materials and used libraries of effective cross-sections are indicated in Table 1.

Table 1: Chemical composition of used materials Material Element Library Weight part

[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 B

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 element cladding 2,7 g.cm-3 Al 13027.60c 100

píloha 4Azákladní-kritinost.doc 5 / 58 Material Element Library Weight part

[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

4. Calculation The calculations are carried out for fresh fuel using a mode for the calculation of the system criticality - KCODE. 50 non-active cycles of calculation (keff is not calculated) were used for the calculation of the initial distribution of points to start the calculation. A total number of 500 cycles with 500 starting points in each cycle were used to determine the calculated value of keff. The calculations were performed for the following options:
1. Filling of the free space inside the cask with water of density from interval

<0, 0.998> g.cm-3

2. Step-by-step flooding of the cask with water (zero water level corresponds to the cask bottom)
3. Calculations for temperature states as indicated in [1]
4. Calculations for specified tolerances of B concentrations in ATABOR
5. Calculations for specified tolerances of ATABOR internals thickness
6. Calculations for specified tolerances of the total weight of U in fuel
7. Calculations for tolerances of 235U enrichment in fuel
8. Calculations for specified tolerances of matrix in fuel
9. Calculations for the change of element position in the cask
10. Calculations for specified tolerances of fuel active length Calculations for the change of ATABOR internals rack pitch have not been performed as the tests of deformation of a cask with internals did not prove it. The lower tolerance of B content in material (1,2 %) and the lower tolerance of the ATABOR internals thickness (3,6 mm) is always considered in the calculations. Check calculations are also performed with the upper limits of tolerances.

píloha 4Azákladní-kritinost.doc 6 / 58

5. Determination of the resulting value keff The resulting value keff was determined as follows:

i i

stat vyp k

k k

2

vyp k

calculated value keff stat

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

k systematic method error i

error of the systematic method error, differences of vyp k

and of calculated values for individual tolerances In order to determine the systematic error, such errors have been chosen from the set of benchmark experiments indicated in [4] which approximate as much as possible the examined issue with respect to the type of fuel, 235U concentration, rack and moderator. Selected experiments and calculated values keff are indicated in Table 2. The value of in this way determined systematic method error is as follows k

= 0,006 0,015 Table 2: Benchmark experiments Enrichment keff 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 [2]

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 [3]

17 %

0,9956 0,0007

píloha 4Azákladní-kritinost.doc 7 / 58

6. Fuel IRT-2M with 36% enrichment of 235U 6.1 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%

8016.60c 235U weight 230.00 g 238U weight 408.89 g Al weight 483.44 g O weight 86.27 g Total 1208.61 g Active part length 60 cm Fuel volume 284.1281 cm3 U density 2.2486 g.cm-3 Fuel density 4.2537 g.cm-3 U atomic density 5.7146E+21 at.cm-3 Fuel atomic density 5.5120E+22 at.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

píloha 4Azákladní-kritinost.doc 8 / 58 Fig. 1: Model of a basic cell with fuel IRT-2M 36%

Fig. 2: Cross section of a cask with fuel IRT-2M 36%

píloha 4Azákladní-kritinost.doc 9 / 58 Fig. 3: Longitudinal section of a cask with fuel IRT-2M 36%

píloha 4Azákladní-kritinost.doc 10 / 58 6.2 Results of calculations for the change of water density Water density

[g.cm-3]

keff error 2

Water density

[g.cm-3]

keff error 2

0.001161 0.0584 0.0003 0.5 0.4221 0.0026 0.025 0.0996 0.0008 0.525 0.4360 0.0026 0.05 0.1282 0.0009 0.55 0.4482 0.0025 0.075 0.1502 0.0010 0.575 0.4624 0.0026 0.1 0.1684 0.0011 0.6 0.4746 0.0027 0.125 0.1854 0.0012 0.625 0.4863 0.0027 0.15 0.2031 0.0014 0.65 0.5026 0.0028 0.175 0.2177 0.0014 0.675 0.5156 0.0028 0.2 0.2335 0.0016 0.7 0.5225 0.0029 0.225 0.2504 0.0017 0.725 0.5385 0.0028 0.25 0.2676 0.0019 0.75 0.5476 0.0030 0.275 0.2830 0.0019 0.775 0.5567 0.0028 0.3 0.2995 0.0019 0.8 0.5699 0.0029 0.325 0.3152 0.0021 0.825 0.5785 0.0028 0.35 0.3307 0.0022 0.85 0.5885 0.0031 0.375 0.3458 0.0021 0.875 0.5996 0.0029 0.4 0.3609 0.0021 0.9 0.6098 0.0030 0.425 0.3749 0.0024 0.925 0.6159 0.0030 0.45 0.3910 0.0023 0.95 0.6262 0.0029 0.475 0.4055 0.0025 0.975 0.6340 0.0029 0.998203 0.6439 0.0031

píloha 4Azákladní-kritinost.doc 11 / 58 6.3 Results of calculations for flooding a cask with water Water level in a cask

[cm]

keff error 2

-5.75 0.0586 0.0003 4.25 0.0665 0.0005 9.25 0.0754 0.0007 14.25 0.1844 0.0017 19.25 0.3338 0.0022 24.25 0.4312 0.0026 34.25 0.5358 0.0027 44.25 0.5885 0.0028 54.25 0.6183 0.0028 64.25 0.6367 0.0030 74.25 0.6434 0.0031 84.25 0.6419 0.0030 94.25 0.6431 0.0031 (zero water level corresponds to the cask bottom)

píloha 4Azákladní-kritinost.doc 12 / 58 6.4 Results of calculations for individual tolerances keff error 2

Calculations for individual temperature states of a cask 95,3°C - option 1 acc. to Ae 10622/Dok Rev.1 0.6413 0.0029 132,4°C - option 2a acc. to Ae 10622/Dok Rev.1 0.6420 0.0031 103,6°C - option 2b acc. to Ae 10622/Dok Rev.1 0.6423 0.0030 88,4°C - option 3a acc. to Ae 10622/Dok Rev.1 0.6401 0.0028 103,9°C - option 3b acc. to Ae 10622/Dok Rev.1 0.6454 0.0031 232°C - option 4 acc. to Ae 10622/Dok Rev.1 0.6399 0.0031 Calculations for B concentrations in ATABOR 1,2 %

0.6439 0.0031 1,6%

0.6022 0.0031 Calculations for tolerances of ATABOR internals thickness 3,6 mm 0.6439 0.0031 4,0 mm 0.6290 0.0030 Calculations for tolerances of total U weight in fuel

-5%

0.6278 0.0029

+5%

0.6534 0.0031 Calculations for enrichment tolerances

-1%

0.6433 0.0030

+1 0.6415 0.0030 Calculations for specified tolerances of matrix contents 36% portion of Al 0.6422 0.0030 44% portion of Al 0.6422 0.0030 Calculations for displacement of elements inside the rack Cask resting on its side 0.6433 0.0031 Aggregation of elements 0.6434 0.0031 Calculations for tolerances of fuel active part length 58 cm 0.6486 0.0029 62 cm 0.6336 0.0032

píloha 4Azákladní-kritinost.doc 13 / 58 6.5 Conclusion With respect to criticality the transport and storage cask for spent fuel from research reactors for fuel IRT-2M with 36% enrichment of 235U satisfies the requirement for subcriticality according to §7 of the SÚJB Decree No. 106/1998 Col.

keff = 0.671 The resulting value of keff was determined according to the formula indicated in Chapter 5.

píloha 4Azákladní-kritinost.doc 14 / 58

7. Fuel IRT-2M with 80% 235U 7.1 Material composition of fuel Enrichment 80.00%

Used library of effective cross-sections 235U weight portion 28.00%

92235.60c 238U weight portion 7.00%

92238.60c Al weight portion 65.00%

13027.60c 235U weight 171.00 g 238U weight 42.75 g Al weight 396.96 g Total 610.71 g Active part length 60 cm Fuel volume 162.3589 cm3 U density 1.3165 g.cm-3 Fuel density 3.7615 g.cm-3 U atomic density 3.3646E+21 at.cm-3 Fuel atomic density 5.7935E+22 at.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

píloha 4Azákladní-kritinost.doc 15 / 58 Fig. 4: Model of a basic cell with fuel IRT-2M 80%

Fig. 5: Cross section of a cask with fuel IRT-2M 80%

píloha 4Azákladní-kritinost.doc 16 / 58 Fig. 6: Longitudinal section of a cask with fuel IRT-2M 80%

píloha 4Azákladní-kritinost.doc 17 / 58 7.2 Results of calculations for the change of water density Water density

[g.cm-3]

keff error 2

Water density

[g.cm-3]

keff error 2

0.001161 0.0405 0.0002 0.5 0.3639 0.0016 0.025 0.0758 0.0005 0.525 0.3776 0.0016 0.05 0.1002 0.0006 0.55 0.3894 0.0016 0.075 0.1188 0.0006 0.575 0.4031 0.0017 0.1 0.1348 0.0007 0.6 0.4151 0.0018 0.125 0.1498 0.0008 0.625 0.4286 0.0018 0.15 0.1641 0.0008 0.65 0.4382 0.0018 0.175 0.1791 0.0009 0.675 0.4509 0.0018 0.2 0.1933 0.0010 0.7 0.4607 0.0018 0.225 0.2085 0.0010 0.725 0.4737 0.0019 0.25 0.2237 0.0011 0.75 0.4847 0.0018 0.275 0.2378 0.0012 0.775 0.4947 0.0019 0.3 0.2522 0.0013 0.8 0.5032 0.0019 0.325 0.2679 0.0014 0.825 0.5127 0.0019 0.35 0.2811 0.0014 0.85 0.5229 0.0020 0.375 0.2965 0.0013 0.875 0.5327 0.0020 0.4 0.3096 0.0015 0.9 0.5399 0.0019 0.425 0.3243 0.0015 0.925 0.5502 0.0020 0.45 0.3389 0.0015 0.95 0.5579 0.0019 0.475 0.3497 0.0016 0.975 0.5663 0.0020 0.998203 0.5742 0.0020

píloha 4Azákladní-kritinost.doc 18 / 58 7.3 Results of calculations for flooding a cask with water Water level in a cask

[cm]

keff error 2

-5.75 0.0406 0.0002 4.25 0.0479 0.0003 9.25 0.0563 0.0004 14.25 0.1513 0.0010 19.25 0.2862 0.0015 24.25 0.3787 0.0017 34.25 0.4762 0.0019 44.25 0.5220 0.0020 54.25 0.5504 0.0020 64.25 0.5671 0.0020 74.25 0.5746 0.0020 84.25 0.5719 0.0020 94.25 0.5721 0.0020 (zero water level corresponds to the cask bottom)

píloha 4Azákladní-kritinost.doc 19 / 58 7.4 Results of calculations for individual tolerances keff error 2

Calculations for individual temperature states of a casks 95,3°C - option 1 acc. to Ae 10622/Dok Rev.1 0.5709 0.0028 132,4°C - option 2a acc. to Ae 10622/Dok Rev.1 0.5709 0.0030 103,6°C - option 2b acc. to Ae 10622/Dok Rev.1 0.5711 0.0027 88,4°C - option 3a acc. to Ae 10622/Dok Rev.1 0.5719 0.0028 103,9°C - option 3b acc. to Ae 10622/Dok Rev.1 0.5711 0.0028 232°C - option 4 acc. to Ae 10622/Dok Rev.1 0.5709 0.0028 Calculations for B concentration in ATABOR 1,2 %

0.5742 0.0020 1,6%

0.5407 0.0028 Calculations for tolerances of ATABOR internals thickness 3,6 mm 0.5742 0.0020 4,0 mm 0.5598 0.0019 Calculations for tolerances of total U weight in fuel

-5%

0.5615 0.0027

+5%

0.5878 0.0028 Calculations for enrichment tolerances

-1%

0.5722 0.0028

+1 0.5753 0.0027 Calculations for specified tolerances of matrix contents 60% portion of Al 0.5722 0.0029 70% portion of Al 0.5722 0.0029 Calculations for displacement of elements inside the rack Cask resting on its side 0.5745 0.0028 Aggregation of elements 0.5746 0.0028 Calculations for tolerances of fuel active part length 58 cm 0.5802 0.0019 62 cm 0.5660 0.0019

píloha 4Azákladní-kritinost.doc 20 / 58 7.5 Conclusion With respect to criticality the transport and storage cask for spent fuel from research reactors for fuel IRT-2M with 80% enrichment of 235U satisfies the requirements for subcriticality according to §7 of the SÚJB Decree No. 106/1998 Col.

keff = 0.603 The resulting value of keff was determined according to the formula indicated in Chapter 5.

píloha 4Azákladní-kritinost.doc 21 / 58

8. Fuel IRT-3M with 36% enrichment of 235U 8.1 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%

8016.60c 235U weight 352.00 g 238U weight 625.78 g Al weight 739.88 g O weight 132.04 g Total 1849.69 g Active part length 60 cm Fuel volume 389.9286 cm3 U density 2.5076 g.cm-3 Fuel density 4.7437 g.cm-3 U atomic density 6.3728E+21 at.cm-3 Fuel atomic density 6.1469E+22 at.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

píloha 4Azákladní-kritinost.doc 22 / 58 Fig. 7: Model of a basic cell with fuel IRT-3M 36%

Fig. 8: Cross section of a cask with fuel IRT-3M 36%

píloha 4Azákladní-kritinost.doc 23 / 58 Fig. 9: Longitudinal section of a cask with fuel IRT-3M 36%

píloha 4Azákladní-kritinost.doc 24 / 58 8.2 Results of calculations for the change of water density Water density

[g.cm-3]

keff error 2

Water density

[g.cm-3]

keff error 2

0.001161 0.0893 0.0005 0.5 0.4909 0.0027 0.025 0.1417 0.0010 0.525 0.5043 0.0027 0.05 0.1776 0.0012 0.55 0.5173 0.0026 0.075 0.2043 0.0013 0.575 0.5309 0.0028 0.1 0.2264 0.0014 0.6 0.5417 0.0029 0.125 0.2457 0.0015 0.625 0.5577 0.0028 0.15 0.2656 0.0015 0.65 0.5712 0.0029 0.175 0.2818 0.0017 0.675 0.5826 0.0029 0.2 0.2983 0.0017 0.7 0.5941 0.0031 0.225 0.3171 0.0019 0.725 0.6066 0.0029 0.25 0.3323 0.0019 0.75 0.6196 0.0032 0.275 0.3518 0.0021 0.775 0.6315 0.0032 0.3 0.3647 0.0022 0.8 0.6402 0.0032 0.325 0.3804 0.0023 0.825 0.6516 0.0033 0.35 0.3989 0.0024 0.85 0.6625 0.0031 0.375 0.4151 0.0025 0.875 0.6756 0.0033 0.4 0.4298 0.0025 0.9 0.6843 0.0032 0.425 0.4452 0.0025 0.925 0.6966 0.0032 0.45 0.4610 0.0027 0.95 0.7068 0.0033 0.475 0.4748 0.0025 0.975 0.7177 0.0035 0.998203 0.7231 0.0032

píloha 4Azákladní-kritinost.doc 25 / 58 8.3 Results of calculations for flooding a cask with water Water level in a cask

[cm]

keff error 2

-5.75 0.0893 0.0005 4.25 0.0982 0.0007 9.25 0.1080 0.0008 14.25 0.2240 0.0018 19.25 0.3822 0.0027 24.25 0.4878 0.0030 34.25 0.6059 0.0030 44.25 0.6649 0.0032 54.25 0.6954 0.0031 64.25 0.7153 0.0033 74.25 0.7237 0.0032 84.25 0.7215 0.0033 94.25 0.7207 0.0032 (zero water level corresponds to the cask bottom)

píloha 4Azákladní-kritinost.doc 26 / 58 8.4 Results of calculations for individual tolerances keff error 2

Calculations for individual temperature states of a casks 95,3°C - option 1 acc. to Ae 10622/Dok Rev.1 0.7193 0.0033 132,4°C - option 2a acc. to Ae 10622/Dok Rev.1 0.7200 0.0032 103,6°C - option 2b acc. to Ae 10622/Dok Rev.1 0.7220 0.0031 88,4°C - option 3a acc. to Ae 10622/Dok Rev.1 0.7192 0.0031 103,9°C - option 3b acc. to Ae 10622/Dok Rev.1 0.7243 0.0032 232°C - option 4 acc. to Ae 10622/Dok Rev.1 0.7254 0.0031 Calculations for B concentration in ATABOR 1,2 %

0.7231 0.0032 1,6%

0.6742 0.0032 Calculations for tolerances of ATABOR internals thickness 3,6 mm 0.7231 0.0032 4,0 mm 0.7089 0.0035 Calculations for tolerances of total U weight in fuel

-5%

0.7090 0.0031

+5%

0.7335 0.0033 Calculations for enrichment tolerances

-1%

0.7240 0.0031

+1 0.7238 0.0033 Calculations for specified tolerances of matrix contents 36% portion of Al 0.7206 0.0033 44% portion of Al 0.7231 0.0034 Calculations for displacement of elements inside the rack Cask resting on its side 0.7128 0.0033 Aggregation of elements 0.7129 0.0033 Calculations for tolerances of fuel active part length 58 cm 0.7265 0.0030 62 cm 0.7164 0.0031

píloha 4Azákladní-kritinost.doc 27 / 58 8.5 Conclusion With respect to criticality the transport and storage cask for spent fuel from research reactors for fuel IRT-3M with 36% enrichment of 235U satisfies the requirement for subcriticality according to §7 of the SÚJB Decree No. 106/1998 Col.

keff = 0.751 The resulting value of keff was determined according to the formula indicated in Chapter 5.

píloha 4Azákladní-kritinost.doc 28 / 58

9. Fuel IRT-3M U-Mo with 19.5% enrichment of 235U 9.1 Material composition of fuel Enrichment 19.50%

Used library of effective cross-sections 235U weight portion 15.64%

92235.60c 238U weight portion 64.56%

92238.60c Mo weight portion 9.00%

42000.60c O weight portion 10.81%

8016.60c 235U weight 400.00 g 238U weight 1651.28 g Mo weight 230.21 g O weight 276.42 g Total 2557.92 g Active part length 60 cm Fuel volume 389.9286 cm3 U density 5.2607 g.cm-3 Fuel density 6.5600 g.cm-3 U atomic density 1.3341E+22 at.cm-3 Fuel atomic density 4.3730E+22 at.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Mo mol. weight 95.9400 g.mol-1 O mol. weight 15.9994 g.mol-1

píloha 4Azákladní-kritinost.doc 29 / 58 Fig. 10: Model of a basic cell with fuel IRT-3M 19.5% U-Mo Fig. 11: Cross section of a cask with fuel IRT-3M 19.5% U-Mo

píloha 4Azákladní-kritinost.doc 30 / 58 Fig. 12: Longitudinal section of a cask with fuel IRT-3M 19.5% U-Mo

píloha 4Azákladní-kritinost.doc 31 / 58 9.2 Results of calculations for the change of water density Water density

[g.cm-3]

keff error 2

Water density

[g.cm-3]

keff error 2

0.001161 0.1107 0.0006 0.5 0.5012 0.0027 0.025 0.1602 0.0009 0.525 0.5139 0.0029 0.05 0.1959 0.0011 0.55 0.5271 0.0028 0.075 0.2219 0.0012 0.575 0.5422 0.0029 0.1 0.2442 0.0014 0.6 0.5557 0.0030 0.125 0.2631 0.0015 0.625 0.5689 0.0029 0.15 0.2807 0.0016 0.65 0.5817 0.0027 0.175 0.2981 0.0016 0.675 0.5926 0.0029 0.2 0.3165 0.0018 0.7 0.6071 0.0028 0.225 0.3323 0.0019 0.725 0.6189 0.0030 0.25 0.3495 0.0020 0.75 0.6263 0.0031 0.275 0.3649 0.0021 0.775 0.6411 0.0031 0.3 0.3814 0.0022 0.8 0.6520 0.0030 0.325 0.3978 0.0023 0.825 0.6625 0.0032 0.35 0.4124 0.0024 0.85 0.6727 0.0031 0.375 0.4298 0.0022 0.875 0.6843 0.0031 0.4 0.4428 0.0025 0.9 0.6923 0.0030 0.425 0.4551 0.0023 0.925 0.7027 0.0031 0.45 0.4725 0.0025 0.95 0.7102 0.0031 0.475 0.4854 0.0026 0.975 0.7215 0.0032 0.998203 0.7305 0.0032

píloha 4Azákladní-kritinost.doc 32 / 58 9.3 Results of calculations for flooding a cask with water Water level in a cask

[cm]

keff error 2

-5.75 0.1115 0.0005 4.25 0.1187 0.0007 9.25 0.1276 0.0009 14.25 0.2377 0.0018 19.25 0.3945 0.0024 24.25 0.4988 0.0028 34.25 0.6158 0.0029 44.25 0.6724 0.0031 54.25 0.7013 0.0031 64.25 0.7251 0.0033 74.25 0.7289 0.0033 84.25 0.7328 0.0031 94.25 0.7300 0.0032 (zero water level corresponds to the cask bottom)

píloha 4Azákladní-kritinost.doc 33 / 58 9.4 Results of calculations for individual tolerances keff error 2

Calculations for individual temperature states of a casks 95,3°C - option 1 acc. to Ae 10622/Dok Rev.1 0.7288 0.0031 132,4°C - option 2a acc. to Ae 10622/Dok Rev.1 0.7277 0.0033 103,6°C - option 2b acc. to Ae 10622/Dok Rev.1 0.7275 0.0031 88,4°C - option 3a acc. to Ae 10622/Dok Rev.1 0.7335 0.0032 103,9°C - option 3b acc. to Ae 10622/Dok Rev.1 0.7328 0.0034 232°C - option 4 acc. to Ae 10622/Dok Rev.1 0.7298 0.0034 Calculations for B concentration in ATABOR 1,2 %

0.7305 0.0032 1,6%

0.6878 0.0031 Calculations for tolerances of ATABOR internals thickness 3,6 mm 0.7305 0.0032 4,0 mm 0.7171 0.0031 Calculations for tolerances of total U weight in fuel

-5%

0.7195 0.0033

+5%

0.7410 0.0031 Calculations for enrichment tolerances

-1%

0.7284 0.0031

+1 0.7327 0.0031 Calculations for specified tolerances of matrix contents 8.1% portion of Mo 0.7290 0.0032 9.9% portion of Mo 0.7310 0.0030 Calculations for displacement of elements inside the rack Cask resting on its side 0.7221 0.0032 Aggregation of elements 0.7211 0.0032 Calculations for tolerances of fuel active part length 58 cm 0.7336 0.0032 62 cm 0.7267 0.0033

píloha 4Azákladní-kritinost.doc 34 / 58 9.5 Conclusion With respect to criticality the transport and storage cask for spent fuel from research reactors for fuel IRT-3M U-Mo with 19.5 % enrichment of 235U satisfies the requirement for subcriticality according to §7 of the SÚJB Decree No. 106/1998 Col.

keff = 0.759 The resulting value of keff was determined according to the formula indicated in Chapter 5.

píloha 4Azákladní-kritinost.doc 35 / 58

10. Fuel IRT-4M with 19.7% enrichment of 235U 10.1 Material composition of fuel Enrichment 19.70%

Used library of effective cross-sections 235U weight portion 10.42%

92235.60c 238U weight portion 42.46%

92238.60c Al weight portion 40.00%

13027.60c O weight portion 7.13%

8016.60c 235U weight 300.00 g 238U weight 1222.84 g Al weight 1152.04 g O weight 205.22 g Total 2880.10 g Active part length 60 cm Fuel volume 387.6995 cm3 U density 3.9279 g.cm-3 Fuel density 7.4287 g.cm-3 U atomic density 9.9617E+21 at.cm-3 Fuel atomic density 9.6207E+22 at.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

píloha 4Azákladní-kritinost.doc 36 / 58 Fig. 13: Model of a basic cell with fuel IRT-4M 19.7%

Fig. 14: Cross section of a cask with fuel IRT-4M 19.7%

píloha 4Azákladní-kritinost.doc 37 / 58 Fig. 15: Longitudinal section of a cask with fuel IRT-4M 19.7%

píloha 4Azákladní-kritinost.doc 38 / 58 10.2 Results of calculations for the change of water density Water density

[g.cm-3]

keff error 2

Water density

[g.cm-3]

keff error 2

0.001161 0.0897 0.0005 0.5 0.4346 0.0025 0.025 0.1344 0.0009 0.525 0.4475 0.0024 0.05 0.1642 0.0010 0.55 0.4598 0.0025 0.075 0.1870 0.0012 0.575 0.4722 0.0025 0.1 0.2054 0.0013 0.6 0.4823 0.0026 0.125 0.2211 0.0013 0.625 0.4976 0.0027 0.15 0.2382 0.0014 0.65 0.5076 0.0025 0.175 0.2540 0.0015 0.675 0.5181 0.0027 0.2 0.2682 0.0016 0.7 0.5321 0.0030 0.225 0.2822 0.0016 0.725 0.5396 0.0031 0.25 0.2972 0.0017 0.75 0.5507 0.0030 0.275 0.3101 0.0018 0.775 0.5604 0.0030 0.3 0.3251 0.0020 0.8 0.5708 0.0029 0.325 0.3395 0.0020 0.825 0.5808 0.0029 0.35 0.3526 0.0020 0.85 0.5947 0.0028 0.375 0.3669 0.0021 0.875 0.6016 0.0031 0.4 0.3800 0.0023 0.9 0.6108 0.0030 0.425 0.3953 0.0024 0.925 0.6218 0.0031 0.45 0.4083 0.0024 0.95 0.6298 0.0030 0.475 0.4210 0.0024 0.975 0.6365 0.0031 0.998203 0.6463 0.0029

píloha 4Azákladní-kritinost.doc 39 / 58 10.3 Results of calculations for flooding a cask with water Water level in a cask

[cm]

keff error 2

-5.75 0.0896 0.0005 4.25 0.0964 0.0006 9.25 0.1042 0.0007 14.25 0.1982 0.0016 19.25 0.3398 0.0024 24.25 0.4348 0.0026 34.25 0.5408 0.0026 44.25 0.5935 0.0030 54.25 0.6215 0.0029 64.25 0.6385 0.0028 74.25 0.6462 0.0030 84.25 0.6466 0.0030 94.25 0.6471 0.0030 (zero water level corresponds to the cask bottom)

píloha 4Azákladní-kritinost.doc 40 / 58 10.4 Results of calculations for individual tolerances keff error 2

Calculations for individual temperature states of a casks 95,3°C - option 1 acc. to Ae 10622/Dok Rev.1 0.6477 0.0030 132,4°C - option 2a acc. to Ae 10622/Dok Rev.1 0.6487 0.0030 103,6°C - option 2b acc. to Ae 10622/Dok Rev.1 0.6450 0.0030 88,4°C - option 3a acc. to Ae 10622/Dok Rev.1 0.6475 0.0031 103,9°C - option 3b acc. to Ae 10622/Dok Rev.1 0.6504 0.0030 232°C - option 4 acc. to Ae 10622/Dok Rev.1 0.6474 0.0030 Calculations for B concentration in ATABOR 1,2 %

0.6463 0.0029 1,6%

0.6030 0.0028 Calculations for tolerances of ATABOR internals thickness 3,6 mm 0.6463 0.0029 4,0 mm 0.6331 0.0029 Calculations for tolerances of total U weight in fuel

-5%

0.6348 0.0030

+5%

0.6572 0.0029 Calculations for enrichment tolerances

-1%

0.6470 0.0030

+1 0.6499 0.0031 Calculations for specified tolerances of matrix contents 36% portion of Al 0.6486 0.0030 44% portion of Al 0.6470 0.0031 Calculations for displacement of elements inside the rack Cask resting on its side 0.6418 0.0031 Aggregation of elements 0.6419 0.0031 Calculations for tolerances of fuel active part length 58 cm 0.6536 0.0032 62 cm 0.6444 0.0031

píloha 4Azákladní-kritinost.doc 41 / 58 10.5 Conclusion With respect to criticality the transport and storage cask for spent fuel from research reactors for fuel IRT-4M with 19.7 % enrichment of 235U satisfies the requirement for subcriticality according to §7 of the SÚJB Decree No. 106/1998 Col.

keff = 0.676 The resulting value of keff was determined according to the formula indicated in Chapter 5.

píloha 4Azákladní-kritinost.doc 42 / 58

11. Fuel EK-10 with 10% enrichment of 235U 11.1 Material composition of fuel Enrichment 10.00%

Used library of effective cross-sections 235U weight portion 7.67%

92235.60c 238U weight portion 69.01%

92238.60c Mg weight portion 13.00%

12000.60c O weight portion 10.32%

8016.60c 235U weight 128.80 g 238U weight 1159.20 g Mg weight 218.36 g O weight 173.35 g Total 1679.72 g Active part length 50 cm Fuel volume 307.8761 cm3 U density 4.1835 g.cm-3 Fuel density 5.4558 g.cm-3 U atomic density 1.0597E+22 at.cm-3 Fuel atomic density 4.9364E+22 at.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Mg mol. weight 24.3050 g.mol-1 O mol. weight 15.9994 g.mol-1

píloha 4Azákladní-kritinost.doc 43 / 58 Fig. 16: Model of a basic cell with fuel EK-10 10%

Fig. 17: Cross section of a cask with fuel EK-10 10%

píloha 4Azákladní-kritinost.doc 44 / 58 Fig. 18: Longitudinal section of a cask with fuel EK-10 10%

píloha 4Azákladní-kritinost.doc 45 / 58 11.2 Results of calculations for the change of water density Water density

[g.cm-3]

keff error 2

Water density

[g.cm-3]

keff error 2

0.001161 0.0543 0.0003 0.5 0.2961 0.0020 0.025 0.0776 0.0005 0.525 0.3082 0.0021 0.05 0.0938 0.0006 0.55 0.3184 0.0021 0.075 0.1065 0.0007 0.575 0.3305 0.0022 0.1 0.1185 0.0008 0.6 0.3391 0.0022 0.125 0.1282 0.0009 0.625 0.3467 0.0022 0.15 0.1402 0.0011 0.65 0.3588 0.0023 0.175 0.1513 0.0011 0.675 0.3663 0.0024 0.2 0.1607 0.0012 0.7 0.3774 0.0024 0.225 0.1737 0.0014 0.725 0.3885 0.0024 0.25 0.1837 0.0014 0.75 0.3964 0.0024 0.275 0.1956 0.0015 0.775 0.4058 0.0025 0.3 0.2071 0.0016 0.8 0.4144 0.0025 0.325 0.2178 0.0017 0.825 0.4216 0.0026 0.35 0.2290 0.0018 0.85 0.4302 0.0025 0.375 0.2421 0.0017 0.875 0.4375 0.0026 0.4 0.2518 0.0018 0.9 0.4434 0.0025 0.425 0.2644 0.0020 0.925 0.4533 0.0027 0.45 0.2749 0.0019 0.95 0.4591 0.0025 0.475 0.2864 0.0019 0.975 0.4675 0.0026 0.998203 0.4728 0.0027

píloha 4Azákladní-kritinost.doc 46 / 58 11.3 Results of calculations for flooding a cask with water Water level in a cask

[cm]

keff error 2

-5.75 0.0543 0.0003 4.25 0.0587 0.0004 9.25 0.0630 0.0005 14.25 0.1081 0.0010 19.25 0.2208 0.0018 24.25 0.3032 0.0022 34.25 0.3934 0.0026 44.25 0.4395 0.0026 54.25 0.4593 0.0025 64.25 0.4734 0.0027 74.25 0.4739 0.0027 84.25 0.4727 0.0027 94.25 0.4737 0.0026 (zero water level corresponds to the cask bottom)

píloha 4Azákladní-kritinost.doc 47 / 58 11.4 Results of calculations for individual tolerances keff error 2

Calculations for individual temperature states of a casks 95,3°C - option 1 acc. to Ae 10622/Dok Rev.1 0.4715 0.0027 132,4°C - option 2a acc. to Ae 10622/Dok Rev.1 0.4736 0.0027 103,6°C - option 2b acc. to Ae 10622/Dok Rev.1 0.4725 0.0026 88,4°C - option 3a acc. to Ae 10622/Dok Rev.1 0.4744 0.0027 103,9°C - option 3b acc. to Ae 10622/Dok Rev.1 0.4745 0.0025 232°C - option 4 acc. to Ae 10622/Dok Rev.1 0.4697 0.0026 Calculations for B concentration in ATABOR 1,2 %

0.4728 0.0027 1,6%

0.4449 0.0025 Calculations for tolerances of ATABOR internals thickness 3,6 mm 0.4728 0.0027 4,0 mm 0.4611 0.0025 Calculations for tolerances of total U weight in fuel

-5%

0.4641 0.0025

+5%

0.4804 0.0027 Calculations for enrichment tolerances

-1%

0.4762 0.0026

+1 0.4737 0.0026 Calculations for specified tolerances of matrix contents 11.7 % portion of Mg 0.4745 0.0026 14.3 % portion of Mg 0.4758 0.0027 Calculations for displacement of elements inside the rack Cask resting on its side 0.4720 0.0027 Aggregation of elements 0.4730 0.0017 Calculations for tolerances of fuel active part length 48 cm 0.4782 0.0027 52 cm 0.4670 0.0026

píloha 4Azákladní-kritinost.doc 48 / 58 11.5 Conclusion With respect to criticality the transport and storage cask for spent fuel from research reactors for fuel EK-10 with 10 % enrichment of 235U satisfies the requirement for subcriticality according to §7 of the SÚJB Decree No. 106/1998 Col.

keff = 0.500 The resulting value of keff was determined according to the formula indicated in Chapter 5.

píloha 4Azákladní-kritinost.doc 49 / 58

12.

Fuel EK-10 with 10% enrichment of 235U in stainless steel sheath 12.1 Material composition of fuel Enrichment 10.00%

Used library of effective cross-sections 235U weight portion 7.67%

92235.60c 238U weight portion 69.01%

92238.60c Mg weight portion 13.00%

12000.60c O weight portion 10.32%

8016.60c 235U weight 128.80 g 238U weight 1159.20 g Mg weight 218.36 g O weight 173.35 g Total 1679.72 g Active part length 50 cm Fuel volume 307.8761 cm3 U density 4.1835 g.cm-3 Fuel density 5.4558 g.cm-3 U atomic density 1.0597E+22 at.cm-3 Fuel atomic density 4.9364E+22 at.cm-3 235U mol. weight 235.0439 g.mol-1 238U mol. weight 238.0508 g.mol-1 Mg mol. weight 24.3050 g.mol-1 O mol. weight 15.9994 g.mol-1

píloha 4Azákladní-kritinost.doc 50 / 58 Fig. 19: Model of a basic cell with fuel EK-10 10% in a stainless steel sheath Fig. 20: Cross section of a cask with fuel EK-10 10% in a stainless steel sheath

píloha 4Azákladní-kritinost.doc 51 / 58 Fig. 21: Longitudinal section of a cask with fuel EK-10 10% in a stainless steel sheath

píloha 4Azákladní-kritinost.doc 52 / 58 12.2 Results of calculations for the change of water density Water density

[g.cm-3]

keff error 2

Water density

[g.cm-3]

keff error 2

0.001161 0.0678 0.0003 0.5 0.2596 0.0020 0.025 0.0934 0.0006 0.525 0.2634 0.0020 0.05 0.1111 0.0007 0.55 0.2702 0.0021 0.075 0.1247 0.0008 0.575 0.2760 0.0021 0.1 0.1358 0.0009 0.6 0.2811 0.0020 0.125 0.1449 0.0009 0.625 0.2859 0.0022 0.15 0.1550 0.0011 0.65 0.2900 0.0022 0.175 0.1649 0.0012 0.675 0.2966 0.0021 0.2 0.1719 0.0013 0.7 0.3004 0.0022 0.225 0.1808 0.0012 0.725 0.3043 0.0023 0.25 0.1904 0.0014 0.75 0.3085 0.0023 0.275 0.1963 0.0015 0.775 0.3148 0.0022 0.3 0.2048 0.0016 0.8 0.3176 0.0023 0.325 0.2122 0.0015 0.825 0.3211 0.0024 0.35 0.2204 0.0017 0.85 0.3248 0.0022 0.375 0.2261 0.0017 0.875 0.3318 0.0024 0.4 0.2331 0.0018 0.9 0.3326 0.0025 0.425 0.2391 0.0017 0.925 0.3342 0.0025 0.45 0.2467 0.0019 0.95 0.3369 0.0024 0.475 0.2530 0.0019 0.975 0.3450 0.0025 0.998203 0.3456 0.0024

píloha 4Azákladní-kritinost.doc 53 / 58 12.3 Results of calculations for flooding a cask with water Water level in a cask

[cm]

keff error 2

-5.75 0.0676 0.0003 4.25 0.0855 0.0007 9.25 0.1471 0.0013 14.25 0.2113 0.0018 19.25 0.2530 0.0021 24.25 0.2787 0.0021 34.25 0.3163 0.0024 44.25 0.3349 0.0024 54.25 0.3463 0.0024 64.25 0.3449 0.0024 74.25 0.3458 0.0025 84.25 0.3447 0.0024 94.25 0.3436 0.0025 (zero water level corresponds to the cask bottom)

píloha 4Azákladní-kritinost.doc 54 / 58 12.4 Results of calculations for individual tolerances keff error 2

Calculations for individual temperature states of a casks 95,3°C - option 1 acc. to Ae 10622/Dok Rev.1 0.3457 0.0024 132,4°C - option 2a acc. to Ae 10622/Dok Rev.1 0.3442 0.0023 103,6°C - option 2b acc. to Ae 10622/Dok Rev.1 0.3443 0.0023 88,4°C - option 3a acc. to Ae 10622/Dok Rev.1 0.3451 0.0025 103,9°C - option 3b acc. to Ae 10622/Dok Rev.1 0.3440 0.0024 232°C - option 4 acc. to Ae 10622/Dok Rev.1 0.3457 0.0023 Calculations for B concentration in ATABOR 1,2 %

0.3456 0.0024 1,6%

0.3268 0.0023 Calculations for tolerances of ATABOR internals thickness 3,6 mm 0.3456 0.0024 4,0 mm 0.3401 0.0024 Calculations for tolerances of total U weight in fuel

-5%

0.3389 0.0025

+5%

0.3539 0.0025 Calculations for enrichment tolerances

-1%

0.3446 0.0024

+1 0.3439 0.0025 Calculations for specified tolerances of matrix contents 11.7 % portion of Mg 0.3434 0.0024 14.3 % portion of Mg 0.3438 0.0024 Calculations for displacement of elements inside the rack Cask resting on its side 0.3399 0.0022 Aggregation of elements 0.3389 0.0022 Calculations for tolerances of fuel active part length 48 cm 0.3492 0.0025 52 cm 0.3414 0.0025

píloha 4Azákladní-kritinost.doc 55 / 58 12.5 Conclusion With respect to criticality the transport and storage cask for spent fuel from research reactors for fuel EK-10 with 10 % enrichment of 235U in stainless steel sheath satisfies the requirement for subcriticality according to §7 of the SÚJB Decree No. 106/1998 Col.

keff = 0.372 The resulting value of keff was determined according to the formula indicated in Chapter 5.

píloha 4Azákladní-kritinost.doc 56 / 58

13. 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 36% enrichment of 235U 0.671 IRT-2M with 80% enrichment of 235U 0.603 IRT-3M with 36% enrichment of 235U 0.751 IRT-3M U-Mo with 19.5% enrichment of 235U 0.759 IRT-4M with 19.7% enrichment of 235U 0.676 EK-10 with 10% enrichment of 235U 0.500 EK-10 with 10% enrichment of 235U in stainless steel sheath 0.372

14. References
1. J.-ik, P Friedl: Transport and Storage Cask for Spent Fuel from Research Reactors -

Calculation of Temperatures, Ae 10622/Dok Rev. 1, Plze February 2004

2. Russell D. Mosteller: LATTICES OF ORALLOY CUBES IN WATER, NEA/NSC/DOC(95)03/II, Volume II, HEU-MET-FAST-006, September 2002
3. 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
4. International Handbook Of Evaluated Criticality Safety Benchmark Experiments, NEA, September 2002

57 / 58

15. Appendix 1 - Dependence of keff on water density 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Hustota vody [g/cm3]

keff IRT-2M 80%

IRT-2M 36%

IRT-3M 36%

IRT-3M 19.5% U-Mo IRT-4M 19.7%

EK-10 EK-10 v pouzde

píloha 4Azákladní-kritinost.doc 58 / 58

16. Appendix 2 - Dependence of keff on the height of flooding a cask with water 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-10 0

10 20 30 40 50 60 70 80 90 10 Výka zaplavení kontejneru [cm]

keff IRT-2M 80%

IRT-2M 36%

IRT-3M 36%

IRT-3M 19.5% U-Mo IRT-4M 19.7%

EK-10 EK-10 v pouzde

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