Experimental Method for Verification of Calculated ¹³⁷Cs Content in Nuclear Fuel Assemblies

Figures & data

TABLE I Parameters of the Measured Fuel Assemblies

ID	Reactor	Burnable Absorber	Burnup (MWd/tU)^a	Cooling Time Between Discharge from Reactor and Time of Measurement (Year)
PWR01	R2	No	52,7	7.5
PWR02	R2	No	49,7	7.4
PWR03	R3	No	48,1	16.3
PWR04	R4	Yes	46,9	8.3
PWR05	R4	Yes	46,9	8.4
PWR06	R3	No	45,8	17.3
PWR07	R4	No	44,5	9.3
PWR08	R4	No	44,4	28.2
PWR09	R2	No	45,8	9.3
PWR10	R3	No	43,4	18.3
PWR11	R3	Yes	43,3	16.3
PWR12	R4	No	43,0	28.2
PWR13	R2	No	40,7	29.5
PWR14	R3	Yes	40,7	19.3
PWR15	R4	No	40,0	29.1
PWR16	R3	Yes	40,2	20.3
PWR17	R4	No	40,4	17.2
PWR18	R3	Yes	39,6	21.3
PWR19	R2	No	35,0	31.5
PWR20	R3	No	34,0	30.3
PWR21	R3	No	33,6	30.3
PWR22	R4	No	31,0	30.2
PWR23	R3	Yes	28,4	20.3
PWR24	R3	No	23,0	21.3
PWR25	R3	No	19,6	32.5

^aThe tU in the burnup column stands for metric tonne of U.

Fig. 1. Schematic illustration of the geometry used in the Geant4 model displaying a PWR 17 × 17 fuel assembly placed in the water pool along the blue z-axis. The conical collimator slit through the pool wall at the Clab is directed along the red x-axis. Reused with permission from Ref. 6.

TABLE II In-Data and Results for the Measurement of ¹³⁷Cs Activity

ID	$I_i$ (s^−1)	$\epsilon$ (s^−1∙Bq^−1)	${\kappa }_i$	$A_i$ (Bq)	${\sigma }_{A_i}$ (Bq^2)
PWR01	10 361.6	3.5932E−06	1.8095E−06	1.59E+15	3.33E+13
PWR02	9 980.3	3.5932E−06	1.8095E−06	1.54E+15	3.21E+13
PWR03	8 520.0	3.6044E−06	1.7904E−06	1.32E+15	2.75E+13
PWR04	9 346.6	3.6018E−06	1.7904E−06	1.45E+15	3.03E+13
PWR05	9 225.3	3.5932E−06	1.7904E−06	1.43E+15	3.00E+13
PWR06	7 665.1	3.6044E−06	1.7904E−06	1.19E+15	2.48E+13
PWR07	8 750.7	3.6018E−06	1.7904E−06	1.36E+15	2.83E+13
PWR08	5 861.3	3.5932E−06	1.7904E−06	9.11E+14	1.90E+13
PWR09	9 050.2	3.5932E−06	1.8095E−06	1.39E+15	2.91E+13
PWR10	7 307.9	3.6018E−06	1.7904E−06	1.13E+15	2.37E+13
PWR11	7 074.6	3.6018E−06	1.7904E−06	1.10E+15	2.29E+13
PWR12	5 829.4	3.5932E−06	1.7904E−06	9.06E+14	1.89E+13
PWR13	5 045.1	3.5932E−06	1.8095E−06	7.76E+14	1.62E+13
PWR14	6 500.2	3.6018E−06	1.7904E−06	1.01E+15	2.10E+13
PWR15	5 416.1	3.6018E−06	1.7904E−06	8.40E+14	1.75E+13
PWR16	6 446.4	3.6018E−06	1.7904E−06	1.00E+15	2.09E+13
PWR17	6 708.7	3.5932E−06	1.7904E−06	1.04E+15	2.18E+13
PWR18	5 874.7	3.6018E−06	1.7904E−06	9.11E+14	1.90E+13
PWR19	4 169.1	3.5932E−06	1.8095E−06	6.41E+14	1.34E+13
PWR20	4 408.9	3.5932E−06	1.7904E−06	6.85E+14	1.43E+13
PWR21	4 331.5	3.6018E−06	1.7904E−06	6.72E+14	1.40E+13
PWR22	3 954.5	3.5932E−06	1.7904E−06	6.15E+14	1.28E+13
PWR23	4 512.1	3.6018E−06	1.7904E−06	7.00E+14	1.46E+13
PWR24	2 941.7	3.6018E−06	1.7904E−06	4.56E+14	9.52E+12
PWR25	2 382.6	3.5932E−06	1.7904E−06	3.70E+14	7.74E+12

Fig. 2. Measured versus calculated ¹³⁷Cs activity for PWR01 to PWR25.

TABLE III Calculated Activity of ¹³⁷Cs for Fuel Assemblies PWR01 to PWR25

ID	$A_i$ (Bq)
PWR01	2.36E+15
PWR02	2.20E+15
PWR03	1.75E+15
PWR04	2.06E+15
PWR05	2.05E+15
PWR06	1.59E+15
PWR07	1.92E+15
PWR08	1.24E+15
PWR09	1.94E+15
PWR10	1.51E+15
PWR11	1.50E+15
PWR12	1.21E+15
PWR13	1.03E+15
PWR14	1.37E+15
PWR15	1.10E+15
PWR16	1.32E+15
PWR17	1.44E+15
PWR18	1.23E+15
PWR19	8.37E+14
PWR20	9.26E+14
PWR21	8.91E+14
PWR22	8.38E+14
PWR23	9.53E+14
PWR24	6.26E+14
PWR25	5.27E+14

TABLE IV Relative Difference Between the Measured and Calculated ¹³⁷Cs Activities*

ID	$\frac{A_i\left(Calc\right)}{\left[A_i\left(Mea\right)\times 1.390\right]}$	Uncertainty (%)
PWR01	1.06	2.89
PWR02	1.03	2.89
PWR03	0.95	2.89
PWR04	1.02	2.89
PWR05	1.03	2.89
PWR06	0.96	2.89
PWR07	1.02	2.89
PWR08	0.98	2.89
PWR09	1.00	2.89
PWR10	0.96	2.89
PWR11	0.98	2.89
PWR12	0.96	2.89
PWR13	0.95	2.89
PWR14	0.98	2.89
PWR15	0.94	2.89
PWR16	0.95	2.89
PWR17	0.99	2.89
PWR18	0.97	2.89
PWR19	0.94	2.89
PWR20	0.97	2.89
PWR21	0.95	2.89
PWR22	0.98	2.89
PWR23	0.98	2.89
PWR24	0.99	2.89
PWR25	1.02	2.89

*Measured activities multiplied with the constant 1.390.

Fig. 3. Ratio between calculated and measured ¹³⁷Cs activity for PWR01 to PWR25. All the measured ¹³⁷Cs activities are multiplied by the constant 1.390.

P. JANSSON, “Kappa Factors,” SKB Document ID 1878149, Version 1.0, SKB (Feb. 2020).

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