Radioactivity of fission product and heavy nuclides deposited on soil in Fukushima Dai-Ichi Nuclear Power Plant accident

Abstract

Based on periodically performed radioactivity measurements on soil samples in the site of Fukushima Dai-Ichi Nuclear Power Station, activity ratios to ¹³⁷Cs of fission product and heavy nuclides were obtained for Sr, Nb, Mo, Tc, Ru, Ag, Te, I, Ba, La, Pu, Am, and Cm isotopes. By exponentially fitting or averaging, the activity ratios at the core shutdown were estimated. Using correlations of activity ratios of ¹³⁴Cs to ¹³⁷Cs, and ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu against fuel burnup, burnup of the fuel sourcing the deposited activity of the soil was estimated. The activity ratios to ¹³⁷Cs of each nuclide on the deposited activity were divided by those calculated on the fuel at the shutdown to obtain the deposited activity fraction of each nuclide as a relative value to ¹³⁷Cs, which also corresponds to the deposited fraction of each element as a relative value to Cs. The obtained deposited fractions relative to Cs are the orders of 10⁻⁴ to 10⁻² for Sr, 10⁻⁵ to 10⁻³ for Nb, 10⁻² to 10⁻¹ for Mo, 1 to 10 for I, 10⁻³ to 10⁻² for Ba, 10⁻² for La, 10⁻⁶ to 10⁻³ for Pu, 10⁻⁶ to 10⁻⁴ for Am, and 10⁻⁷ to 10⁻⁵ for Cm. The deposited fractions for Tc, Ag, and Te were not estimated due to the lack of the calculated inventories in the fuel for the relevant measured radioactive nuclides.

Keywords:

• Fukushima Dai-ichi NPP
• soil
• radioactivity measurement
• fission product nuclide
• heavy nuclide
• activity ratio to ¹³⁷Cs
• estimation of fuel burnup
• deposited fraction

1. Introduction

One of important part of severe accident analysis of nuclear reactors is to calculate the amount of radioactivity released from multilayered barriers such as a pressure vessel, a containment vessel, and a reactor building and deposited on the environment, which is called source term analysis. The analysis methods depend on various models treating complicated phenomena related to chemistry and physics, and their validations are crucial.

After the severe core damage of Fukushima Dai-Ichi Nuclear Power Station, radioactive material leaked from the reactor buildings. Measurement of radioactivity was periodically performed in various points inside and outside of the power station. The information of the released and deposited radioactivity is important to understand the process of the severe accident. Nishihara et al. [1] have reported a study of activity release ratios from the damaged core to stagnant water. The present study focuses on the measurement data of radioactivity on soil in the site, which have been performed by Tokyo Electric Power Company (TEPCO) since March 2011 and publically available [2]. The data include typical radioactive fission product (FP) nuclides such as Sr, Nb, Mo, Tc, Ru, Ag, Te, I, Cs, Ba, and La and heavy nuclides such as U, Pu, Am, and Cm. Summarizing the measured data in terms of relative activity ratios to that of ¹³⁷Cs, the activity ratios at the core shutdown date were analyzed by the decay correction for the nuclides of relatively short half lives. On the other hand, the radioactivity ratios of ¹³⁴Cs to ¹³⁷Cs, and those of ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu were obtained for the core shutdown date. Those ratios were used to estimate the burnup of the fuel sourcing the deposited radioactivity using correlations of these ratios against fuel burnup, which were obtained based on the previous calculations and measurement data [3]. The activity ratios to ¹³⁷Cs of each nuclide on the deposited activity were divided by those calculated on the fuel at the shutdown to obtain the deposited activity fraction of each nuclide as a relative value to ¹³⁷Cs, which also corresponds to the deposited fraction of each element as a relative value to Cs.

The first part of the present article describes the summary of radioactivity measurements on the soil samples, the second shows the deposited activity fraction, and the last conclusions.

2. Summary of radioactivity measurement on soil samples

As a part of radiation monitoring conducted by TEPCO in the site, soils were sampled at five places within 1 km from the common exhaust stack of the units 1 and 2 on 21 March, and the radioactivity was analyzed [2]. The results of the two places showed that the radioactivity ratios of ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu were 2.0 and 0.9, respectively, which indicated that the radioactivity came from the damaged core since the radioactivity ratios were far larger than those normally observed in the radioactivity of Pu isotopes in the soil in Japan. Gamma-ray spectroscopy was also applied to all the samples for the Pu analysis to indentify gamma-ray emitting nuclides, which were typically FP nuclides. After this observation, periodical sampling of soils at three fixed places in the site, and the radioactivity analysis have been conducted and are publically available from the web site of TEPCO [2]. The sampling places are shown in Figure 1 [2]. The places were selected about 500 m from the common exhaust stack of the units 1 and 2 and wide enough to take samples. Furthermore, the samples in the places 1 and 3 were taken from the surfaces which adjoined but did not overlap each other; the place 2 were in a wood for bird watching, and the samples were taken from the same surface but different depths until the radioactivity was not detected and then the sampling surface was moved to the next one, and so on. The information of the reports has the sampling place, sampling date, analysis date, analysis institute (the Japan Atomic Energy Agency or the Japan Chemical Analysis Center), nuclide, radioactivity in Bq/kg dry-soil and some comments. The activity was also reported in Bq/kg wet-soil for a small number of samples. The activity for the FP nuclides except Sr isotopes, Sr isotopes and heavy isotopes was reported in separate sheets. It is also mentioned in the comments that all samples for the analysis of Pu isotopes were analyzed by gamma-ray spectroscopy to determine the activity of gamma-ray emitting nuclides (the FP nuclides except Sr isotopes). The reported radioactivity is listed with the half lives and the numbers of measurement data for each place in Table 1. It should be noted that the measurement data are sparse for ⁹⁹Mo, ^99mTc, and ¹⁰⁶Ru. In addition to the nuclides in Table 1, the activity of ⁷Be (half life = 53.29 days) and ¹²⁵Sb (half life = 2.758 years) was reported once in the place 1. However, there was no other data so that these nuclides were not studied. The activity of uranium isotopes was also reported; however, the activity ratios were almost agree with those of natural uranium [4]. This indicates that the deposited activity of uranium isotopes originated from irradiated fuel of enriched uranium is far less than the activity of natural uranium. Appendix 1 describes decay chains to produce the relevant radioactive nuclides.

Figure 1. Locations of the three places for periodical radioactivity measurement in the site [2].

Table 1. Nuclides of radioactivity measurement on the soil samples in the site from 21 March 2011 to 28 November 2011 [2].

Nuclide	Half life	Number of measurement data			Nuclide	Half life	Number of measurement data
		Place 1	Place 2	Place 3			Place 1	Place 2	Place 3
^89Sr	50.53 days	6	5	6	^238Pu	87.7 years	46	1	34
^90Sr	28.79 years	6	5	6	^239Pu + ^240Pu	2.411E4^a + 6561 years	37	16	33
^95Nb	34.99 days	14	0	10	^241Am	432.6 years	6	0	4
^99Mo	2.75 days	1	0	1	^242Cm	162.94 days	9	2	6
^99mTc	6.02 h	2	0	2	^243Cm + ^244Cm	29.1 + 18.11 years	8	0	6
^106Ru	1.02 years	2	1	2
^110mAg	249.76 days	14	0	7
^129mTe	33.6 days	28	10	29
^132Te	3.20 days	8	4	7
^131I	8.03 days	27	24	24
^132I	2.30 h	3	2	3
^134Cs	2.07 years	50	49	49
^136Cs	13.16 days	26	10	25
^137Cs	30.08 years	50	49	49
^140Ba	12.75 days	4	1	1
^140La	1.68 days	3	1	2
Note: ^a2.411 × 10^4.

2.1. Fission product nuclides

The measured radioactivity of ¹³⁷Cs is plotted against the elapsed time in day after the shutdown of the reactors (hereafter referred to as the “shutdown”) as an example and shown in Figure 2. The measured activity varies with elapsed time for the places 1–3. This would be due to heterogeneity in deposited activity on the surface of soil. Changes in the activity in the place 2 are far larger and the activity level is lower than those in the places 1 and 3, which is attributed to the special sampling strategy as mentioned before. In order to extract effective information, measured activity for each nuclide was divided by that of ¹³⁷Cs for each sample (hereafter referred to as the “activity ratio to ¹³⁷Cs”). Figure 3 shows those plots for the places 1–3. In order to confirm the validity of data of the FP nuclides, decay constants were calculated by fifing the data by an exponential function of the elapsed time. The obtained decay constants in 1/day are listed in Table 2 and compared with nominal values. The nominal values are the decay constants of the specific nuclides minus that of ¹³⁷Cs. The decay constants based on the measurements are attached with fitting errors (1σ). Those without uncertainties are those obtained by connecting two measurement data. The decay constants based on the measurements for ^99mTc, ¹⁰⁶Ru, ¹³²I, and ¹⁴⁰La have considerably difference from the nominal values.

Figure 2. Measured activity of ¹³⁷Cs against elapsed time after the shutdown of the reactors.

Figure 3. Activity ratios to ¹³⁷Cs of FP nuclides against elapsed time after the shutdown. (a) Place 1, (b) place 2, and (c) place 3.

Table 2. Comparison between the decay constant of the measured activity ratio to ¹³⁷Cs and the nominal value defined by the decay constant of each nuclide minus that of ¹³⁷Cs.

Nuclide	Nominal decay constant (1/day)	Decay constant (1/day) based on measurement activity ratio to ^137Cs
		Place 1	Place 2	Place 3
^89Sr	0.0137	0.0171 ± 0.0016	0.0236 ± 0.0067	0.0160 ± 0.0030
^90Sr	2.83E-6	0.00298 ± 0.00154	0.0111 ± 0.0051	0.00256 ± 0.00261
^95Nb	0.0197	0.0136 ± 0.0029	–	0.0112 ± 0.0032
^99Mo	0.252	–	–	–
^99mTc	2.763	0.121^a	–	0.249^a
^106Ru	0.00180	0.129^a	–	0.262^a
^110mAg	0.00271	0.00329 ± 0.00166	–	0.00180 ± 0.00326
^129mTe	0.0206	0.0153 ± 0.0030	0.0139 ± 0.0112	0.0150 ± 0.0014
^132Te	0.217	0.222 ± 0.018	0.258 ± 0.038	0.217 ± 0.012
^131I	0.0863	0.0855 ± 0.0014	0.0804 ± 0.0054	0.0807 ± 0.0028
^132I	7.233	0.289^a ± 0.018	0.320^a	0.255^a ± 0.073
^134Cs	0.000854	0.00074 ± 0.00006	0.00081 ± 0.00010	0.00078 ± 0.00005
^136Cs	0.0526	0.0492 ± 0.0014	0.0485 ± 0.0047	0.0513 ± 0.0015
^137Cs	0 (Base)	–	–	–
^140Ba	0.0543	0.0845 ± 0.0102	–	–
^140La	0.413	0.134^a ± 0.033	–	0.134^a
Note: ^aSee Section 2.1.

The decay constants and relative activity of ^99mTc (half life = 6.02 h) are expected to be close to those of ⁹⁹Mo since ⁹⁹Mo is the mother nuclide of ^99mTc and has a much longer half life (2.75 days) and a radioactive balance is achieved. As expected, the decay constants and activity ratios based on the measurements are roughly comparable to those of ⁹⁹Mo. The large deviation of the decay constant of ¹⁰⁶Ru from the nominal value was observed. One of the reasons may be due to sparse data for obtaining the decay constant in the places 1 and 3. A concern on these data is sparseness for its relatively longer half life (1.02 years). Further study is necessary for the confirmation of the reliability of the data. The decay constant and activity of ¹³²I (half life = 2.30 h) are expected to be close to that of ¹³²Te (half life = 3.20 days) which is the mother nuclide of ¹³²I. In this point, the decay constants and activity ratios based on the measurements are comparable to those of ¹³²Te. The decay constant and relative activity of ¹⁴⁰La (half life = 1.68 days) are expected to be close to those of ¹⁴⁰Ba (half life = 12.75 days) because of the same reason. Even though deviations from the consistent values are relatively large, the measurement values were adopted in the present study.

By fitting the decay data of the activity ratios to ¹³⁷Cs by an exponential function, the activity ratios at the elapsed time = 0 (the shutdown) were determined for the FP nuclides. The obtained activity ratios to ¹³⁷Cs with fitting errors (1σ) are shown in Table 3. The values without errors are those obtained by connecting two measurement data. For ⁹⁹Mo and ¹⁰⁶Ru, which are shown for the place 1, a different processing of data was applied since the measurement data were sparse. In the case of ⁹⁹Mo, the two data at the places 1 and 3 were averaged for the activity and sampling date, and the nominal decay constant was applied to obtain the activity ratio at the shutdown. In the case of ¹⁰⁶Ru, five measured data at the places 1–3 and three data measured at three places other than the places 1–3 in the site [5] were averaged for the activity and sampling date, and the nominal decay constant was applied to obtain the activity ratio at the shutdown. As mentioned previously, further study is necessary for the confirmation of the reliability of the data of ¹⁰⁶Ru. Figure 4 illustrates the activity ratios to ¹³⁷Cs in Table 3. Here the values of ⁹⁹Mo and ¹⁰⁶Ru are shown as those of the place 1. The errors also attached to the value only at the plus side. The error is not shown for the nuclides that the errors were not assigned. Considerable differences of the activity ratios to ¹³⁷Cs between those of the places 1 and 3, and that of the place 2 are observed for Sr isotopes and ¹³¹I.

Figure 4. Activity ratios to ¹³⁷Cs at the shutdown for the places 1–3. (a) FP nuclides and (b) heavy nuclides.

Table 3. Activity ratios to ¹³⁷Cs of FP nuclides at the shutdown of the reactors for the deposited activity.

Nuclide	Half life	Activity ratio to ^137Cs
		Place 1	Place 2	Place 3
^89Sr	50.53 days	0.0153 ± 0.0047	0.101 ± 0.202	0.00570 ± 0.00380
^90Sr	28.79 years	0.00109 ± 0.00033	0.0107 ± 0.0138	0.000453 ± 0.000258
^95Nb	34.99 days	0.00788 ± 0.00371	–	0.00233 ± 0.00045
^99Mo	2.75 days	0.829 ± 0.624^a	←^a	←^a
^99mTc	6.02 h	0.227	–	0.417
^106Ru	1.02 years	0.0947 ± 0.0610^a	←^a	←^a
^110mAg	249.76 days	0.00598 ± 0.00080	–	0.00184 ± 0.00053
^129mTe	33.6 days	0.820 ± 0.198	0.873 ± 0.683	0.838 ± 0.099
^132Te	3.20 days	22.1 ± 11.4	39.5 ± 42.0	17.1 ± 6.0
^131I	8.03 days	31.6 ± 3.1	133 ± 54	12.0 ± 2.2
^132I	2.30 h	102 ± 55	144	25.5 ± 130
^134Cs	2.07 years	1.03 ± 0.01	1.00 ± 0.01	1.03 ± 0.01
^136Cs	13.16 days	0.217 ± 0.010	0.235 ± 0.047	0.228 ± 0.022
^137Cs	30.08 years	1.0 (Base)	1.0 (Base)	1.0 (Base)
^140Ba	12.75 days	0.0973 ± 0.0206	–	–
^140La	1.68 days	0.413 ± 0.268	–	0.182
Note: ^aSee Section 2.1.

2.2. Heavy nuclides

Activity ratios to ¹³⁷Cs are plotted for heavy nuclides including U isotopes and shown in Figure 5. The activity ratios among U isotopes for the places 1–3 are close to those of natural U as mentioned previously. The activity ratios scatter against samples. Average values through the samples are listed in Table 4 for Pu, Am, and Cm nuclides with the errors, which are standard deviations (1σ). The value without an error is that of single measurement. The data of ²⁴²Cm were expected to follow the specific decay constant, the decay constant of ²⁴²Cm minus that of ¹³⁷Cs; however, averaging was applied for simplicity. The errors are considerably large because of large scattering of the activity ratios to ¹³⁷Cs as shown in Figure 5. Figure 4 illustrates the average values. Considerable differences of the activity ratios to ¹³⁷Cs between those of the places 1 and 3, and that of the place 2 are observed for Pu isotopes. This would be related to the difference in the sampling strategies.

Figure 5. Activity ratios to ¹³⁷Cs of heavy nuclides against elapsed time after the shutdown for the places 1–3. (a) Place 1, (b) place 2, and (c) place 3.

Table 4. Average activity ratios to ¹³⁷Cs of heavy nuclides.

Nuclide	Half life	Activity ratio to ^137Cs
		Place 1	Place 2	Place 3
^238Pu	87.7 years	5.03E-7^a ± 5.55E-7	4.33E-6	9.99E-8 ± 1.31E-7
^239Pu + ^240Pu	2.411E4 + 6561 years	2.45E-7 ± 2.81E-7	1.24E-5 ± 2.75E-5	1.08E-8 ± 1.76E-7
^241Am	432.6 years	6.08E-8 ± 2.56E-8	–	2.05E-8 ± 8.99E-9
^242Cm	162.94 days	5.20E-6 ± 2.73E-6	3.99E-6 ± 5.04E-6	1.34E-6 ± 7.20E-7
^243Cm + ^244Cm	29.1 + 18.11 years	3.01E-7 ± 1.59E-7	–	4.75E-8 ± 1.73E-8
Note: ^a5.03 × 10^−7.

3. Deposited radioactivity fraction

One of the aims of the present study is to estimate how much specific element have been released from the reactor buildings and deposited on the ground (hereafter referred to as “deposited”) in terms of relative values to Cs. Here, N^X and N^Cs are the atomic number densities of elements X and Cs, respectively; A^Xi and A ^137Cs are the activity of an isotope in the element X and ¹³⁷ Cs, respectively. The bottom suffixes R and I means the atomic number densities of deposited atoms and atoms existed in the fuel at the shutdown. The fraction of the deposited atoms of X, , to that of Cs, , is defined by

Derivation of this equation is shown in Appendix 2. The values of the numerator of the right side in Equation (1) were obtained and are shown in Tables 3 and 4 for the FP and heavy nuclides. Now necessary values are the denominator of the right side.

3.1. Burnup of fuel sourcing deposited radioactivity

3.1.1. Activity ratios as burnup indicators

Some of the activity ratios between specific isotopes give information of burnup of irradiated fuel. In the present study, the activity ratios of ¹³⁴Cs to ¹³⁷Cs, and ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu were investigated. As shown in Appendix 1, in the chain of the mass number 134, short-lived FP nuclides decay to a stable nuclide ¹³⁴Xe; while direct production of ¹³⁴Cs by fission is negligibly small. Most atoms of ¹³⁴Cs are produced by neutron capture of stable isotopes ¹³³Cs (cumulative fission yield = 6.70% in ²³⁵U thermal fission, for example) during irradiation of fuel. Therefore, the production rate of ¹³⁴Cs mainly depends on the number density of ¹³³Cs, the microscopic capture cross-section of ¹³³Cs and the neutron flux. On the other hand, the production rates of ¹³⁷Cs (cumulative fission yield = 6.27% in ²³⁵U thermal fission, for example) and ¹³³Cs depend on the macroscopic fission cross-sections of fuel and the neutron flux. The radioactivity ratio (proportional to atomic density ratio) of ¹³⁴Cs to ¹³⁷Cs after an irradiation time is roughly proportional to the product of time and a neutron flux, which almost corresponds to the fuel burnup, as shown in Equation (2).

Here Y ₁₃₃(t) and Y ₁₃₇(t) are the cumulative fission yields of ¹³³Cs and ¹³⁷Cs, respectively, as a function of irradiation time t, and  Σ_f (t),  φ (t), and σ_c ¹³³(t) are the macroscopic fission cross-section of fuel, the neutron flux and the microscopic neutron capture cross-section of ¹³³Cs. The variables without (t) are time-independent values. In Equation (2), elimination of ¹³³Cs by neutron absorption and that of ¹³⁴Cs by decay are neglected for simplicity so that the activity of ¹³⁴Cs would be overestimated. The activity ratios of ¹³⁴Cs to ¹³⁷Cs at the shutdown are close to 1.0 as shown in Table 3. The author have reported that the ratios are 1.05 ± 0.02, 1.00 ± 0.02, and 1.05 ± 0.01 for the places 1, 2, and 3, respectively [6]. Those were obtained from the measurement data of the Japan Chemical Analysis Center. On the other hand, the present results are based on the whole data including the data of the Japan Atomic Energy Agency. The present and previous ratios are very similar. The ratios of the places 1–3 almost agree with each other within the errors. It is noted that the radioactivity ratio for the Chernobyl accident was reported to be about 0.5 [7], which represents relatively lower fuel burnup in the plant.

The production chain for ²³⁸Pu shown in Appendix 1 is a major one (more than 70%) in UO₂ fuel of light water reactors as discussed by Roque et al. [8]. The neutron capture process appears three, one, and two times in the chains for ²³⁸Pu, ²³⁹Pu, and ²⁴⁰Pu, respectively. Therefore, the ratios of ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu are roughly proportional to the burnup to the power of between one and two.

Figure 6 shows the activity of ²³⁸Pu and the sum of ²³⁹Pu and ²⁴⁰Pu, and the activity ratios of ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu. The data in the place 2 were not adopted since most of samples were reported as “not detected” for ²³⁸Pu which means less than detection limits typically 0.01 Bq/kg-dry soil. This is attributed to the special strategy in the sampling as mentioned before. The activity and radioactivity ratios fluctuate with the samples, which would be due to small signal-to-nose ratios in α-ray spectrometry for the determination of the radioactivity in the samples. The average values of the radioactivity ratios were determined to be 2.23 ± 0.44 and 2.24 ± 0.36 for the places 1 and 3, respectively. The errors of averaged values are shown in oneσ. In the averaging for the place 3, the data in the later period were excluded since a systematic irregularity appeared in the activity radio of ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu. This change in the trend should be further scrutinized. The authors have reported that the ratios are 2.23 ± 0.44 and 2.37 ± 0.27 for the places 1 and 3, respectively [6]. Those were obtained from the measurement data of the Japan Chemical Analysis Center. On the other hand, the present results were based on the whole data including the data of the Japan Atomic Energy Agency. The present and previous ratios are very similar.

Figure 6. Activity and activity ratio for ²³⁸Pu and the sum of ²³⁹Pu and ²⁴⁰Pu. (a) Place 1 and (b) place 3.

3.1.2. Activity ratio vs. fuel burnup

The correlations of the radioactivity ratios of Cs and Pu isotopes to fuel burnup were obtained from the available burnup calculation results [3] for the Cs and Pu isotopes, and from the experimental data [3,9] for the Pu isotopes. The referred calculation results were those for a lead use 9 × 9-9 fuel assembly which was loaded in the unit 1 of Fukushima Dai-Ni Nuclear Power Station (2F-1) and irradiated up to five cycles. Comparisons of major fuel specifications are shown in Table 5 and core specifications in Table A1 in Appendix 3. Major differences in the fuel assemblies specifications between the lead use 9 × 9-9 fuel assemblies of 2F-1 and 9 × 9 fuel assemblies of the units 1–3 of Fukushima Dai-Ichi Nuclear Power Station (1F-1 to 3) are: (1) the lattice type: a C-lattice for 2F-1, where the assembly pitches are the same (15.2 cm) for the control rod insertion sides and the opposite sides, and a D lattice (see the assembly pitch in Table A1) for 1F-1 to 3, for which a water channel location in the assembly is de-centering in the 9 × 9-9 fuel assembly, (3) assembly average enrichment: 3.6, 3.8, 3.8, and 3.4 wt% for 1F-1, 1F-2, 1F-3, and 2F-1, respectively, and (4) irradiation history. On the other hand, the core power densities, core average in-channel void fractions, fuel rod pitches, and fuel rod geometrical specifications are close. Since the present study is aimed at the first study on the burnup estimation of the fuel sourcing the activity, the burnup calculation results of the lead use 9 × 9-9 fuel assemblies of 2F-1 were adopted.

Table 5. Specifications of the 9 × 9 fuel assemblies of 1F-1 to 3 and the 9 × 9-9 lead use assembly of 2F-1.

Item	1F-1	1F-2, 3	2F-1
Inside of fuel channel (mm)	134	←	←
Fuel rod pitch (mm)	14.5/14.4^a	←	←
Number of fuel rods	72/74^a	←	←
Fuel cladding	Zry-2	←	←
Fuel cladding outer diameter (mm)	11.0/ 11.2^a	←	←
Fuel cladding inner diameter (mm)	9.6/9.8^a	←	←
Fuel pellet outer diameter (mm)	9.4/9.6^a	←	←
Pellet material	UO2, UO2-Gd2O3	←	←
Assembly avg. enrichment (wt%)	3.6	3.8	3.4
Note: ^aFor 9 × 9-9 fuel assembly/for 9 × 9–7 fuel assembly.

The burnup calculations had been performed using a continuous energy Monte Carlo code coupled with a depletion module, MVP-BURN [10,11] and a nuclear data library based on JENDL-3.3 [12]. A general purpose burnup chain model u4cm6fp104bp12T was used. It adopted heavy nuclides from ²³⁴U through ²⁴⁶Cm, 104 FP nuclides, and 12 burnable absorber nuclides [13], which was specially prepared for neutronics analyses of isotopic composition measurement data of irradiated fuel. The node average irradiation history was taken from the record of the core monitoring system of 2F-1 for power and in-channel fractions.

The original purpose of the calculations was to theoretically analyze measured isotopic inventories of six samples taken from the upper and lower part of the three selected fuel rods in the five-cycle-irradiated lead use assembly 2F1ZN3. The three rods were located in the inner, middle, and peripheral locations in the assembly, which had the maximum (4.9 wt% was assumed), middle, and minimum (2.1 wt% was assumed) enrichments, respectively, as shown in Figure 7 [3].

Figure 7. Fuel rod locations under burnup calculations for the five-cycle-irradiated lead use 9 × 9-9 assembly [3].

According to the comparison between the calculated and measured isotopic inventories of Pu and Cs isotopes, the calculations well reproduced the measured inventories of ¹³⁷Cs, ²³⁹Pu, and ²⁴⁰Pu; on the other hand, they systematically underestimated the inventories of ¹³⁴Cs and ²³⁸Pu by about 5 and 10%, respectively [3,14], This was attributed to the uncertainties in the nuclear data library JENDL-3.3. Therefore, these systematic biases were corrected for the following calculation-based correlation of the radioactivity ratios.

3.1.2.1. Activity ratio of ¹³⁴Cs to ¹³⁷Cs

The compiled correlations of the activity ratios of ¹³⁴Cs to ¹³⁷Cs based on the calculated isotopic inventories are shown in Figure 8 for the upper position of the assembly, which are at three-fourth from the bottom in the fuel effective part (hereafter referred to as the “upper core”). A dependency of the radioactivity ratios on enrichments are seen in the correlations. This reflects the differences in macroscopic cross-sections of the fuel with different enrichments and radial locations of the fuel rods, and the consequent differences in the neutron flux. This makes the slopes of higher enrichment rods lower than those of lower enrichment rods. Small disconnections on the slopes are also observed and attributed to core shutdown for refueling and other reasons. During the shutdown, atoms of ¹³⁴Cs decay at the half live of 2.07 years and the activity ratios decrease.

Figure 8. Calculation-based correlations of radioactivity ratios of ¹³⁴Cs to ¹³⁷Cs and radioactivity ratios for the places 1, 2, and 3.

In the figures, the radioactivity ratios of the places 1, 2, and 3 are also shown with the errors. The dotted boxes are an approximate overlapping region of the calculation-based correlations and the activity ratios to ¹³⁷Cs based on the measurements. The overlapped burnup ranges are from 18 to 29 GWd/t in the correlations. Endo et al. [15] has worked on the correlation for radioactivity ratios of ¹³⁴Cs to ¹³⁷Cs based on the measured radioactivity in the soils outside of the nuclear power station. He reported that the activity ratios were 0.996 ± 0.07 and the estimated average burnup was 17.1 ± 1.5 GWd/t. Okumura [16] also reported that the activity ratios obtained for contaminated water in the basements of the turbine buildings was from 0.92 to 1.0 and the estimated burnup was 20 GWd/t. Their estimation of burnup is lower than those in this study. Since their activity ratios are similar to the present study, the differences in the estimated burnup would be mainly attributed to the differences in the correlations used for the estimation of burnup. Their activity correlations were obtained by simple single fuel cell models and without considering the decrease in the activity ratios during the reactor shutdown for refueling and others.

3.1.2.2. Activity ratio of ²³⁸Pu to sum of ²³⁹Pu, and ²⁴⁰Pu

The compiled correlations of the radioactivity ratios of ²³⁸Pu and the sum of ²³⁹Pu, and ²⁴⁰Pu based on the calculated isotopic inventories are shown in Figure 9 for the upper core. In contrast to the radioactivity ratios of Cs isotopes, the correlations of the radioactivity ratios in Pu isotopes are less sensitive to the enrichments of fuel rods. The correlations reflect the differences in macroscopic cross-sections of the fuel and radial locations of the fuel rods, and the consequent differences in the neutron flux as those of the Cs correlations. In addition to that, higher enrichment rods tend to have steeper slopes due to that the origin of ²³⁸Pu is mainly ²³⁵U as mentioned before. In the figures, the radioactivity ratios of the places 1 and 3 are also shown with the errors. The dotted boxes are an approximate overlapping region of the calculation-based correlations and the radioactivity ratios based on the measurements. The overlapped burnup ranges are from 25 to 33 GWd/t in the correlations.

Figure 9. Calculation-based correlations of radioactivity ratios of ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu and radioactivity ratios for the places 1 and 3.

In addition to the calculation-based correlations, the experiment-based correlation was also compiled from the measured isotopic inventories of Pu isotopes for BWR fuels [3,9]. Figure 10 shows the obtained correlation. They included different types of BWR UO₂ fuels. The enrichments of the fuel samples are 3.9 and 3.4 wt% for the 8 × 8-1 fuel, 4.5 and 3.4 wt% for the 8 × 8-4 fuel, 4.4 and 3.4 wt% for the 9 × 9-7. Those of the 9 × 9-9 fuel are those of the above mentioned lead use 9 × 9-9 fuel assemblies of 2F-1. The data include the activity ratios based on the measured isotopic inventories for the fuel samples ranging from the lower to upper axial locations. The figure includes the radioactivity ratios of the places 1 and 3 with the errors. The dotted box shows the overlapping region of the experiment based correlations and the radioactivity ratios of the places 1 and 3 considering the errors. The overlapped burnup ranges are from 22.5 to 36 GWd/t in the experiment based correlation.

Table 6 shows the summary of the estimated burnup based on the activity ratios. It is observed that the estimated burnup based on the activity ratio of Pu isotopes was systematically larger than that on the activity ratio of Cs isotopes. However, the ranges of estimated burnup overlap each other. When the compiled correlations based on the calculated isotopic inventories for the lower position of the assembly (hereafter referred to as the “lower core”) were used, the estimated burnup was slightly larger by 3–5 GWd/t than that for the upper core as shown in Table 6. The calculation-based correlations for the lower core used in the present study are the same as those shown by the authors [6].

Table 6. Summary of estimated burnup.

Radioactivity ratio (correlation)	Burnup range (GWd/t)
Cs (upper core)	18–29
Pu (upper core)	25–33
Cs (lower core)	22.5–34
Pu (lower core)	27–37.5
Pu (experimental data)	22.5–36

3.2. Activity ratio to ¹³⁷Cs in fuel at shutdown

In order to estimate the ratio of A_I ^Xi to A_I ^137Cs in Equation (1) in the fuel sourcing the deposited activity at the shutdown, four sets of calculated inventories were selected as representing inventories: two sets for the upper core, (1) initial ²³⁵U enrichment 4.9 wt%, 30.5 GWd/t and (2) enrichment 2.1 wt%, 27.9 GWd/t, and two sets from the lower core, (3) initial ²³⁵U enrichment 4.9 wt%, 33.6 GWd/t, and (4) enrichment 2.1 wt%, 28.7 GWd/t. The enrichments were selected to cover the most range of fuel enrichments normally used in the 9 × 9 fuel assemblies in 1F-1 to 3. The fuel burnup was selected to be middle of the above mentioned burnup estimations and the available calculation points of fuel rods which were calculated under the inputs of assembly-node average burnup. The above fuel burnups correspond to the assembly-node average burnup 28.5 and 30.9 GWd/t for the upper and lower cores, respectively. The reliability of the referred inventory calculations for the 9 × 9 fuel assemblies have been confirmed through the comparison of the calculated results with measurement assay data on long-half-life and stable isotopes in FP nuclides in Nd, Cs, Eu, Sm, Gd, and Pm [3,14]. The comparison is also scheduled for FP nuclides of Mo, Tc, Ru, Rh, and Ag.

The activity ratio to ¹³⁷Cs of each isotope in the fuel at the shutdown is shown in Table 7 for the two selected sets of the calculated inventories of the upper core. The values of ⁸⁹Sr, ^99mTc, ^110mAg, ^129mTe, ¹³²Te, and ¹³²I are not shown, since the adopted burnup chain for FP nuclides in the burnup calculations did not include those nuclides. The ratio of the activity ratio to ¹³⁷Cs of each isotope in the deposited activity, , in Table 3 against that in the fuel at the shutdown, , was calculated and are shown in Table 7. The values also correspond to the ratios of the deposited fraction of each element, , against that of Cs, , as shown in Equation (1). The values of ⁹⁹Mo and ¹⁰⁶Ru are shown as those for the place 1, for which the values of were obtained by the special treatment as previously mentioned. The data in Figure 11 illustrate the values for the fuel condition of 4.9 wt% and 30.5 GWd/t in Table 7 as an example. The differences in between the two sets of inventories for the upper core are not significant for the FP nuclides, and Pu and Am isotopes; on the other hand, those of Cm isotopes are large. Table 8 shows the activity ratios to ¹³⁷Cs for the two selected sets of the calculated inventories of the lower core. Since the inventories of Pu, Am, and Cm nuclides are relatively smaller in the lower core than those in the upper core due to relatively lower conversion ratio caused by an axial distribution in a steam void, the activity ratio to ¹³⁷Cs in the fuel at the shutdown are smaller than those for the upper core for those nuclides. It makes larger the ratios of the activity ratios to ¹³⁷Cs of those nuclides in the deposited activity against those in the fuel at the shutdown. As shown in Tables 7 and 8, the orders of the deposited fraction of each element relative to Cs was estimated to be 10⁻⁴ to 10⁻² for Sr, 10⁻⁵ to 10⁻³ for Nb, 10⁻² to 10⁻¹ for Mo, 1 to 10 for I, 10⁻³ to 10⁻² for Ba, 10⁻² for La, 10⁻⁶ to 10⁻³ for Pu, 10⁻⁶ to 10⁻⁴ for Am, and 10⁻⁷ to 10⁻⁵ for Cm. That of Ru, which was estimated to be 10⁻³ to 10⁻², should be confirmed by further scrutiny.

Figure 10. Experiment-based correlations of radioactivity ratios of ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu and radioactivity ratios for the places 1 and 3.

Figure 11. Deposited activity fractions relative to ¹³⁷Cs in the fuel conditions of 4.9 wt% and 30.5 GWd/t for the places 1–3. (a) FP nuclide and (b) actinide nuclide.

Table 7. Ratio of activity ratio to ¹³⁷Cs of each isotope in the deposited activity, , against that in the fuel, , based on the upper core inventories at the shutdown.

		^a
Nuclide		Place 1	Place 2	Place 3
^90Sr	0.793	1.37E-3^b ± 4.16E-4	1.35E-2 ± 1.74E-2	5.71E-4 ± 3.25E-4
	0.637	1.71E-3 ± 5.18E-4	1.68E-2 ± 2.17E-2	7.11E-4 ± 4.05E-4
^95Nb	14.1	3.27E-4 ± 6.88E-5	–	1.65E-4 ± 3.19E-5
	12.1	3.81E-4 ± 8.02E-5	–	1.93E-4 ± 3.72E-5
^99Mo	17.6	4.71E-2 ± 3.55E-2	←^c	←^c
	17.0	4.88E-2 ± 3.67E-2	←^c	←^c
^106Ru^d	3.47	2.73E-2 ± 1.76E-2	←^c	←^c
	5.59	1.69E-2 ± 1.09E-2	←^c	←^c
^131I	9.16	3.45 ± 0.34	14.5 ± 5.9	1.31 ± 0.24
	9.37	3.37 ± 0.33	14.2 ± 5.8	1.28 ± 0.24
^134Cs	1.03	1.00 ± 0.01	0.971 ± 0.010	1.00 ± 0.01
	1.30	0.792 ± 0.008	0.769 ± 0.008	0.792 ± 0.008
^137Cs	1.0 (Base)	1.0 (Base)	1.0 (Base)	1.0 (Base)
^140Ba	17.2	5.66E-3 ± 1.20E-3	–	–
	16.1	6.04E-3 ± 1.28E-3	–	–
^140La	17.5	2.36E-2 ± 1.53E-2	–	1.04E-2
	16.5	2.50E-2 ± 1.62E-2	–	1.10E-2
^238Pu	1.63E-2	3.09E-5 ± 3.41E-5	2.66E-4	6.13E-6 ± 8.06E-6
	1.86E-2	2.71E-5 ± 2.99E-5	2.33E-4	5.37E-6 ± 7.06E-6
^239Pu +^240Pu	7.69E-3	3.18E-5 ± 3.66E-5	1.61E-3 ± 3.58E-3	1.41E-5 ± 2.28E-5
	9.17E-3	2.67E-5 ± 3.07E-5	1.35E-3 ± 3.00E-3	1.18E-5 ± 1.91E-5
^241Am	1.16E-3	5.24E-5 ± 2.21E-5	–	1.77E-5 ± 7.75E-6
	1.49E-3	4.08E-5 ± 1.72E-5	–	1.38E-5 ± 6.03E-6
^242Cm	2.60E-1	2.00E-5 ± 1.05E-5	1.54E-5 ± 1.94E-5	5.17E-6 ± 2.77E-6
	5.58E-1	9.33E-6 ± 4.89E-6	7.15E-6 ± 9.04E-6	2.41E-6 ± 1.29E-6
^243Cm +^244Cm	5.91E-3	5.10E-5 ± 2.69E-5	–	8.03E-6 ± 2.92E-6
	2.50E-2	1.21E-5 ± 6.35E-6	–	1.90E-6 ± 6.90E-7
Notes: Upper: fuel condition of 4.9 wt%, 30.5 GWd/t; lower: fuel condition of 2.1wt%, 27.9 GWd/t. ^aSee Appendix 2. ^b1.37 × 10^−3. ^cSee Section 3.2. ^dData should be confirmed by further study.

Table 8. Ratio of activity ratio to ¹³⁷Cs of each isotope in the deposited activity, , against that in the fuel, , based on the lower core inventories at the shutdown.

		^a
Nuclide		Place 1	Place 2	Place 3
^90Sr	0.814	1.34E-3^b ± 4.05E-4	1.31E-2 ± 1.70E-2	5.57E-4 ± 3.17E-4
	0.658	1.66E-3 ± 5.02E-4	1.63E-2 ± 2.10E-2	6.88E-4 ± 3.92E-4
^95Nb	11.4	4.04E-4 ± 8.51E-5	–	2.04E-4 ± 3.95E-5
	9.26	4.98E-4 ± 1.05E-4	–	2.52E-4 ± 4.86E-5
^99Mo	19.6	4.23E-2 ± 3.18E-2	←^c	←^c
	17.8	4.66E-2 ± 3.51E-2	←^c	←^c
^106Ru^d	3.31	2.86E-2 ± 1.84E-2	←^c	←^c
	5.37	1.76E-2 ± 1.14E-2	←^c	←^c
^131I	9.80	3.22 ± 0.32	13.6 ± 5.5	1.22 ± 0.22
	9.47	3.34 ± 0.33	14.0 ± 5.7	1.27 ± 0.23
^134Cs	0.954	1.08 ± 0.01	1.05 ± 0.01	1.00 ± 0.01
	1.20	0.858 ± 0.008	0.833 ± 0.008	0.858 ± 0.008
^137Cs	1.0 (Base)	1.0 (Base)	1.0 (Base)	1.0 (Base)
^140Ba	16.9	5.76E-3 ± 1.22E-3	–	–
	14.8	6.57E-3 ± 1.39E-3	–	–
^140La	17.0	2.43E-2 ± 1.58E-2	–	1.07E-2
	15.1	2.74E-2 ± 1.77E-2	–	1.21E-2
^238Pu	1.19E-2	4.23E-5 ± 4.67E-5	3.64E-4	8.40E-6 ± 1.10E-5
	1.43E-2	3.52E-5 ± 3.88E-5	3.03E-4	6.99E-6 ± 9.19E-6
^239Pu + ^240Pu	6.07E-3	4.03E-5 ± 4.64E-5	2.03E-3 ± 4.53E-3	1.79E-5 ± 2.89E-5
	7.80E-3	3.14E-5 ± 3.61E-5	1.53E-3 ± 3.53E-3	1.39E-5 ± 2.25E-5
^241Am	9.10E-4	6.68E-5 ± 2.82E-5	–	2.26E-5 ± 9.88E-6
	1.08E-3	5.63E-5 ± 2.37E-5	–	1.90E-5 ± 8.32E-6
^242Cm	1.78E-1	2.92E-5 ± 1.53E-5	2.24E-5 ± 2.83E-5	7.55E-6 ± 4.05E-6
	3.58E-1	1.45E-5 ± 7.62E-6	1.12E-5 ± 1.41E-5	3.75E-6 ± 2.01E-6
^243Cm + ^244Cm	4.42E-3	6.82E-5 ± 3.59E-5	–	1.07E-5 ± 3.90E-6
	1.90E-2	1.59E-5 ± 8.36E-6	–	2.50E-6 ± 9.08E-7
Notes: Upper: fuel condition of 4.9 wt%, 33.6 GWd/t; lower: fuel condition of 2.1wt%, 28.7 GWd/t. ^aSee Appendix 2. ^b1.34 × 10^−3. ^cSee Section 3.2. ^dData should be confirmed by further study.

4. Conclusions

Based on the radioactivity measurements on the soil samples in the site of Fukushima Dai-Ichi Nuclear Power Station, the study to investigate the deposited activity fraction of the FP and heavy nuclides was performed. Using correlations of the activity ratios of ¹³⁴Cs to ¹³⁷Cs, and ²³⁸Pu to the sum of ²³⁹Pu and ²⁴⁰Pu against fuel burnup, the burnup of the fuel sourcing the deposited activity was estimated to be about 30 GWd/t. In this study, the activity in the fuel at the shutdown was obtained by the inventory calculations for the 9 × 9 fuel assembly using the estimated burnup. The fraction of activity deposited on the soil was obtained as the relative value to that of ¹³⁷Cs. The obtained deposited fractions relative to Cs are the orders of 10⁻⁴ to 10⁻² for Sr, 10⁻⁵ to 10⁻³ for Nb, 10⁻² to 10⁻¹ for Mo, 1 to 10 for I, 10⁻³ to 10⁻² for Ba, 10⁻² for La, 10⁻⁶ to 10⁻³ for Pu, 10⁻⁶ to 10⁻⁴ for Am, and 10⁻⁷ to 10⁻⁵ for Cm. That of Ru, which was estimated to be 10⁻³ to 10⁻², should be confirmed by further study. The deposited fractions for Tc, Ag, and Te were not estimated due to the lack of the calculated inventories in the fuel for the relevant measured radioactive nuclides.

Figure A1. Decay chains of FP and heavy nuclides under activity measurement with half lives and cumulative fission yields of thermal fission of ²³⁵U in % (Y).

Table A1. Major core specifications of 1F-1, 2, 3, and 2F-1.

Item	1F-1	1F-2, 3	2F-1
Core thermal power (MWt)	1380	2381	3293
Core flow rate (t/h)	21.8 × 10^3	33.3 × 10^3	48.3 × 10^3
Core pressure (MPa [gage])	6.89	6.93	6.93
Core inlet temperature (°C)	285	286	286
Number of fuel assemblies	400	548	764
Assembly pitch (cm)	15.7/14.8^a	15.7/14.8^a	15.2
Core effective height (m)	3.66	3.71	3.71
Core equivalent diameter (m)	3.44	4.03	4.75
Core power density (kW/l)	40.6	50.4	50.0
U weight (t)	68	94/95^b	132/131^b
Core average in-channel void fraction (%)	33/34^b	41/42^b	43^b
Notes: ^aControl rod insertion sides/the opposite sides. ^bCore for 9 × 9-9 fuel assemblies/that for 9 × 9–7 fuel assemblies (see also Table 5).

Appendix 1: Decay chain of measured activity

The decay chains in Figure A1 show a major chain to be produced the relevant FP and heavy isotopes (highlighted by a dark color). The cumulative fission yields in thermal neutron fission of ²³⁵U are also shown as “Y” for the FP nuclides [17].

Appendix 2: Derivation of relative deposited fraction to that of Cs

Here A^Xi and A ^137Cs are the activities of an isotope in the element X and ¹³⁷ Cs, respectively. They are obtained by

Here N^X and N^Cs are the atomic number densities of elements X and Cs, respectively, f^Xi and f ^137Cs are the isotopic abundances of X_i and ¹³⁷Cs, respectively, and  λ ^X and  λ  ^137Cs are decay constants of X_i and ¹³⁷Cs, respectively, and the bottom suffixes R and I mean the values of the deposited material and the fuel at the shutdown, respectively. Therefore the ratios of the activity of X_i to ¹³⁷Cs are expressed by

The ratio is

Therefore

Appendix 3: Major core specifications of units 1, 2, and 3 of Fukushima Dai-Ichi Nuclear Power Station, and unit 1 of Fukushima Dai-Ni Nuclear Power Station.

Table A1 shows major core specifications of Units 1, 2, and 3 of Fukushima Dai-Ichi Nuclear Power Station, and Unit 1 of Fukushima Dai-Ni Nuclear Power Station [18].