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Novel method for estimation of the indoor-to-outdoor airborne radioactivity ratio following the Fukushima Daiichi Nuclear Power Plant accident Yanliang Tan a,⁎, Tetsuo Ishikawa b, Miroslaw Janik c, Shinji Tokonami d, Masahiro Hosoda e, Atsuyuki Sorimachi b, Kimberlee Kearfott f a
College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, Hunan Province, China Fukushima Medical University, 1 Hikariga-oka, Fukushima, Japan c Regulatory Science Research Program, National Institute of Radiological Sciences, Chiba, Japan d Department of Radiation Physics, Institute of Radiation Emergency Medicine, Hirosaki University, Hirosaki, Aomori, Japan e Hirosaki University Graduate School of Health Science, Hirosaki, Aomori, Japan f Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI, United States b
H I G H L I G H T S
G R A P H I C A L
A B S T R A C T
• Actual ASF of the dwells is very important to estimate the inhalation dose. • A simple model is developed to describe ASF. • The key parameter of ASF is obtained from the measurement of NIRS. • The ASF of any dwellings can be obtained by our model and relatively parameters.
a r t i c l e
i n f o
Article history: Received 6 May 2015 Received in revised form 5 July 2015 Accepted 6 July 2015 Available online xxxx Editor: D. Barcelo Keywords: Airborne sheltering factor Air exchange rate Indoor airborne deposition velocity ⁎ Corresponding author. E-mail address: [email protected] (Y. Tan).
a b s t r a c t The accident at the Fukushima Daiichi Nuclear Power Plant (FDNPP) in Japan resulted in signiﬁcant releases of ﬁssion products. While substantial data exist concerning outdoor air radioactivity following the accident, the resulting indoor radioactivity remains pure speculation without a proper method for estimating the ratio of the indoor to outdoor airborne radioactivity, termed the airborne sheltering factor (ASF). Lacking a meaningful value of the ASF, it is difﬁcult to assess the inhalation doses to residents and evacuees even when outdoor radionuclide concentrations are available. A simple model was developed and the key parameters needed to estimate the ASF were obtained through data ﬁtting of selected indoor and outdoor airborne radioactivity measurement data obtained following the accident at a single location. Using the new model with values of the air exchange rate, interior air volume, and the inner surface area of the dwellings, the ASF can be estimated for a variety of dwelling types. Assessment of the inhalation dose to
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1. Introduction The accident at the Fukushima Daiichi Nuclear Power Plant (FDNPP) in Japan resulted in a signiﬁcant release of ﬁssion products that were dispersed worldwide (Wai and Yu, 2015). An abundance of environmental radiation monitoring data exists (Tazoe et al., 2012; Amano et al., 2012; Hosoda et al., 2011, 2013a). In addition, whole body counter (WBC) and thyroid probe measurements of residents and evacuees were conducted (Hosoda et al., 2013b; Tokonami et al., 2012), revealing intakes of Cs-137 and I-131. It is important to estimate the inhalation doses to potentially exposed individuals, especially those who may not have undergone thyroid or WBC measurements. While most available airborne radioactivity monitoring data were obtained outdoors, it is reasonable to assume that the residents near FDNPP sheltered indoors prior to evacuation following the accident and appropriately reduced building ventilation. Generally, researchers utilized what is termed by some the “air decontamination factor” or the indoor-to-outdoor air radioactivity ratio to obtain the indoor radioactivity from outdoor radioactivity. This paper introduces more descriptive nomenclature, namely the airborne sheltering factor (ASF), to refer to an estimated or assumed indoor-to-outdoor airborne radioactivity factor. The protective effect of the ASF simply arises from the reduction by the building on airborne radionuclide concentrations. This clearly distinguishes it from reductions in concentrations caused by active interventions such as ﬁltering or cleanup operations, a meaning often engendered by the term “decontamination”. The term ASF is also useful in differentiating between direct measurements of both indoor and outdoor radionuclide air concentrations which, when divided, would most precisely be referred to as indoor-to-outdoor concentration ratios. The ASF depends upon several parameters, such as the air exchange rate of a building, the deposition rate of the radionuclides onto the inner surface of the building, the indoor re-suspension rate, and the nature of the radioactive materials, in particular the radioactive aerosol's size, half-life, and chemical form (Price and Jayaraman, 2006). Because of differences in all of those factors, the values of ASF will be different even for buildings having the same types of construction and building materials. According to the ofﬁcial statistics of Japan in 2008, only 60% of Japanese dwellings are wooden and other buildings are constructed of different materials, which is likely to cause changes in the ASF compared with other building types. It would be highly desirable to have a means for estimating the ASF for buildings of different types that would depend upon parameters that can be reasonably assumed or estimated for speciﬁc buildings of interest for which indoor-to-outdoor airborne activity ratios are not available but for which information may exist for outdoor radionuclide concentrations. In this work, a simple model to estimate the ASF for any building based upon knowledge of the net indoor-to-outdoor air exchange rate and the building's inner surface area and air volume is proposed. The model depends upon a number of additional variables that are not speciﬁc to the building type, but that are more dependent upon the aerosol size, radionuclide half-life and chemical form. The simple model reduces those variables to two simple model parameters that could be generally determined for a given type of release from measurements of temporally varying data about the outdoor and indoor air concentrations for a known building or set of buildings. Once those non-building speciﬁc parameters have been determined, the ASF could then be computed with the model adjusting for the building-dependent characteristics for other buildings exposed to similar aerosols under comparable conditions. Finally, the inhalation doses of residents and evacuees could be estimated based upon the
ASF of their building, their building occupancy factor, and the measured radioactivity data in outdoor air. 2. Material and methods 2.1. ASF calculation method Radionuclide concentrations in indoor and outdoor air were measured simultaneously after the FDNPP accident at the National Institute of Radiological Sciences (NIRS) in Chiba Prefecture, Japan, located about 220 km south-southwest of the FDNPP (Ishikawa et al., 2014). The researchers captured the indoor-to-outdoor concentration ratios for I-131 and Cs-137 for the readily characterizable concrete buildings they instrumented. Those data were utilized to determine the generalized parameters for the simple model developed for this work. The ASF for buildings of any type exposed to radionuclide-bearing aerosols similar in physical and chemical form to those measured at NIRS can be obtained using the model with the data-derived generalized parameters and three building speciﬁc parameters: the building air exchange rate, the inner surface area for the structure, and the indoor air volume. Ishikawa et al. (2014) deployed two sets of air sampling equipment after the FDNPP accident. The ﬁrst set placed 1 m above the roof of a ﬁve-story concrete building at NIRS, and the second was located on a ﬁfth-ﬂoor room of the same building, approximately 2 m above the ﬂoor. Windows of the room were maintained closed for the duration of the data collection. The sampling ﬁlters were analyzed with a high-purity germanium detector (HPGe) of NIRS that had been inter-compared with Hirosaki University. Table 1 lists the data from Ishikawa et al. (2014). The integrated measured indoor-to-outdoor concentrations of I-131 and Cs-131 were estimated as:
ASF I131 ¼
C ID131 ð jÞT j
, 27 X
ASF Cs137 ¼
C OD131 ð jÞT j ¼ 0:44
27 X 1
C ID137 ð jÞT j
, 27 X
C OD137 ð jÞT j ¼ 0:58
where COD131( j) and CID131( j) are the outdoor and indoor concentrations of I-131 for the jth sampling period, COD137(j) and CID137(j) are the corresponding Cs-137 concentrations, and Tj is the duration of the jth sampling period. Ishikawa et al. (2014) used the measured values in all available sampling periods, resulting in values of 0.48 and 0.72. The different sampling periods account for the difference between Ishikawa's and the results for this work, with the sampling period here chosen to correspond closely with data employed for development of the model. The diurnal sampling periods were about 9 h and 15 h. Because the radionuclides accumulate on the sampling ﬁlter continuously, information about temporal variations within the sampling periods are lost, and the measurements represent averages. Smaller sampling periods would have been desirable from the viewpoint of time resolution for studying indoor-to-outdoor concentration ratio dynamics, but longer sample collection times were chosen, appropriately, to reduce measurement statistical uncertainty under circumstances for which radioactivity concentrations were unpredictable. The uncertainties of these data in Table 1 are less than 0.07 Bq m− 3 for I-131 and 0.03 Bq m− 3 for Cs-137.
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Table 1 Measured indoor concentrations of outdoor and indoor of I-131 and Cs-137 for a single concrete building in NIRS in March, 2011. Period no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Average 20% of the average
Long sampling period is the reason why the indoor concentration is higher than the outdoor in many sampling periods, and the mechanism of this phenomenon will be illustrated by the model in Section 2.3. 2.2. The model for the kinetic relationship between indoor and outdoor airborne activities Air is exchanged between the indoors and outdoors, resulting in an exchange of airborne radionuclides. Within the building radionuclides may settle on surfaces and may be re-suspended into the indoor air from those surfaces. If the concentrations of radionuclides are high and the re-suspension effect is neglected, which will be discussed in greater detail later, then, the change of the ith radionuclide concentration in indoor air as a function of time can be described as: dC IDi ðt Þ L C ðt Þvdi S ¼ ½C ODi ðt Þ−C IDi ðt Þ−λi C IDi ðt Þ− IDi dt V V
where CIDi(t) is the indoor concentration of the ith radionuclide at time t; CODi(t) is the outdoor concentration of the ith radionuclide, which is predominantly determined by the accident source term and prevailing environmental conditions; λi is the decay constant of the ith radionuclide; vdi is the indoor deposition velocity of the ith radionuclide; L is the air ﬂow exchange rate between the room and the outside; V is the air volume of the room; and S is the inner surface area of the room which is available for the deposition of radionuclides from room air. S may be assumed to be equal to the surface area of the walls in the room. Eq. (3) represents a simple mass-balance equation for a given radionuclide in indoor air. In that equation, VL ½C ODi ðtÞ−C IDi ðtÞ represents the net increase in indoor radionuclide concentration caused by entrance of air from the outside, λiCIDi(t) mathematically captures the losses from radiological decay,
di S models and C IDi ðtÞv V
of radionuclide on the room surfaces. For ease of analysis, this equation can be rewritten as: dC IDi ðt Þ ¼ AC ODi ðt Þ−BC IDi ðt Þ dt
L v S þ λi þ di V V
where A is the fractional air entrance rate into the room from the outside, and B represents the fractional losses of radionuclides from the indoor air due to all causes. It is noted that the air entrance and regress rates from the room may be due to active ventilation due to heating or cooling, or entrance through windows and cracks in the walls themselves. If the radionuclide concentration in indoor air reaches a steady state, then the rate of change of the radionuclide concentration in the indoor ðtÞ ¼ 0, so that: air becomes zero, namely: dC IDi dt
ASF i ¼ A=Bi ¼ C IDi ðt Þ=C ODi ðt Þ
where ASFi is the ASF of the ith radionuclide. In terms of the physical parameters, it is noted that the steady state or fully equilibrated value of the ASF is, as a result of combining Eqs. (5)–(7):
ASF i ðsteady stateÞ ¼
L V L S þ λi þ vdi V V
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Integrating both sides of Eq. (4) for the time period from t1 to t2 yields: Z C IDi ðt 2 Þ−C IDi ðt 1 Þ ¼ A
Z C ODi ðt Þdt−Bi
C IDi ðt Þdt
Eq. (7) corresponds with the ASF for a steady state situation, while Eq. (9) represents the ASF for a situation in which radionuclide concentrations are changing. 2.3. The mechanism led abnormal ratio of radionuclide concentration in indoor air to outdoor air Because the sampling period is long, most disturbances of the radionuclide concentration in outdoor air will be reﬂected as changes in the indoor radionuclide concentration during the same sampling period. Only those disturbances that are near the end of a sampling period would lead to an abnormal ratio of radionuclide concentration in outdoor and indoor air. Fig. 1 shows the effect of a rectangular disturbance at the end of a sampling period obtained from Eq. (4). Based on this sampling principle, the outdoor radionuclide concentration in the previous sampling period includes the rectangular disturbance, but the most inﬂuence on indoor air will be reﬂected in the next sampling period, e.g. the I-131 concentration in the 1st and 13th sampling periods and the Cs-137 concentration in the 11th sampling period. These sampling period numbers are deﬁned in Table 1. If the rectangular disturbance is much narrow and high, the inﬂuence on ratio of radionuclide concentration of indoor air to outdoor air will be notable. In extreme cases, the radionuclide concentration of indoor air can be higher than that of outdoor air in the next period, e.g. the I-131 in the 12th sampling period and Cs-137 concentrations in the 10th, 12th and 13th sampling periods.
the change of indoor concentrations is slower than that of outdoor concentration, it is suitable to assume that the indoor concentration changes immediately at the beginning of nth sampling period and maintain that value until the ending of that period. This model does not regard the effect of re-suspension. However, but the re-suspension contribution to indoor radionuclides concentration is signiﬁcant when the quantity of radionuclides settled on surfaces is great and the indoor airborne radionuclide concentrations are low. Due to this fact, only those indoor measurement data higher than 20% of the average indoor concentrations were selected for analysis. From the mechanism led abnormal ratio of radionuclide concentration in indoor air to outdoor air, only those disturbances which are near the end of a sampling period lead to abnormal indoor to outdoor air radionuclide concentrations ratios. In such cases, data from, neighboring sampling periods were combined so that the disturbances of the outdoor air radionuclide concentrations in would be reﬂected in the indoor radionuclide concentrations. In this circumstance, Eq. (9) can be rewritten as: ½C IDi ð jÞ−C IDi ð j−1Þ=T j ¼ AC ODi ð jÞ−BC IDi ð jÞ
where Tj is the time of jth sampling period, and CIDi( j) and CODi( j) are the ith radionuclide concentration in indoor and outdoor in the jth sample period, respectively. Table 2 lists all the data selected and combined in this manner from Table 1. According to the least squares method with Eq. (10), there is a chi-square function, X2 ¼
2 C IDI ð jÞ−C IDI ð j−1Þ T j ½C ODI ð jÞ þ C IDI ð jÞ −AC ODI ð jÞ þ BI−131 C IDI ð jÞ Tj 2 X C IDCs ð jÞ−C IDCs ð j−1Þ þ T j ½C ODCs ð jÞ þ C IDCs ð jÞ −AC ODCs ð jÞ þ BCs−137 C IDCs ð jÞ Tj
2.4. Abstraction method to obtain key parameters If both the indoor and outdoor radionuclide concentrations are known as functions of time, then a set of equations of the form of Eqs. (3) and (4) exists, with one equation for each time point. It would be possible to determine through mathematical best ﬁt practices the values of the parameters A and B i . Unfortunately, the existing data represent integrations of concentrations over signiﬁcant time periods relative to the expected values of the kinetics parameters. Because the measured concentrations of I-131 and Cs-137 on the ﬁlter are the equivalent average concentrations in the sampling period, and the evolution detail of radionuclide concentration in any sampling period is unknown, the matching time for the concentration also cannot be obtained. In this fact, it is not a bad choice to assume that the outdoor or indoor concentrations are constant in any sampling period. Because
where CIDI( j) and CODI( j) are the I-131 concentrations in indoor and outdoor during the jth sample period, respectively. CIDCs( j) and CODCs( j) are the Cs-137 concentrations in indoor and outdoor for the jth sample period, respectively. Tj[CODI( j) + CIDI( j)] and Tj[CODCs( j) + CIDCs( j)] are the corresponding sampling time period duration weighted values. Substituting all the data from Table 2 into Eq. (11), commercially available mathematical programming software (Mathematica 8.0) may then be used to ﬁnd the suitable values of A, BI − 131 and BCs − 137 for which the value of the chi-square function is minimized. 3. Results and discussion 3.1. The air exchange rate and the indoor deposition velocity of I-131 and Cs-137 The values of A, BI − 131 and BCs − 137 were determined to be 0.15 h−1, 0.28 h−1 and 0.25 h−1, respectively. The inner wall area of the room was 125.4 m2, with a corresponding room volume equal to 87.7 m3. Because the air exchange rate from the outdoor wall is far larger than the decay constants of I-131 and Cs-137, Eq. (6) can be simpliﬁed
Fig. 1. The inﬂuence on the radionuclide concentration of indoor air from a rectangular disturbance of outdoor air at the end of a sampling period. (The low curve is the reﬂection of the rectangular outdoor radionuclide concentration in indoor air. Rectangular disturbance in outdoor air: width, 1 h; height, 10 Bq m−3; A = 0.15 h−1, B = 0.3 h−1).
as Bi ¼ VL þ vVdi S (10). From Eq. (10), the indoor deposition velocity of I-131 was determined to be 0.09 m h−1, while the indoor deposition velocity for Cs-137 was 0.07 m h−1. ASF obtained from Eq. (8) for the data was 0.54 and 0.60 for airborne I-131 and Cs-137, respectively. The sources of error in ASF values are the changes of air exchange rate, which depended on the changes of the temperature and the air pressure, and the changes of airborne size in all measurement periods. According to the results of Eqs. (1) and (2), the errors for ASFI-131 and ASFCs-137 are about 23% and 3%, respectively. This amount of error is acceptable.
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Table 2 Selected and combined data from Table 1. Period no.
2 10 11,12,13 14 15 17 18 19 25,26 IDI ð j−1Þ ¼ C IDI ð jÞ−C ; * ΔCT IDI Tj j
IDI ð j−1Þ ΔC IDCs IDCS ð j−1Þ In the combined periods, the concentrations of uncombined periods are used to calculate the ΔCT IDI ¼ C IDI ð jÞ−C ; T j ¼ C IDCs ð jÞ−C : Tj Tj j
Because the natural characteristics of I-131 and Cs-137 are different, the ability of these radionuclides to attach to different sizes of aerosols is different. Thus, the difference of the indoor deposition velocity may arise from aerosol size differences. 3.2. The effect of re-suspension There exists substantial theoretical and experimental research on the effects of re-suspension on airborne radionuclide concentrations (Raja et al., 2010; Barth et al., 2014; Zhang et al., 2013; Goldasteh et al., 2013). If the effect of re-suspension is considered for Eq. (4), the model presented here can be rewritten as dC IDi ðt Þ ¼ AC ODi ðt Þ−BC IDi ðt Þ þ si Atotali =V dt
A s C ðt Þ þ i Atotali =V: B B ODi
dC IDi ðt Þ L ¼ ½C oDi ðt Þ−C IDi ðt Þ−λi C IDi ðt Þ: dt V
The half-life of I-131 is 8.1 days. Fig. 2 shows the decontamination effect of the dwellings. If the doors and windows are open when the I-131 concentration in outdoor air is low, the gaseous I-131 concentration in indoor air should decrease quickly. Then, the decontamination effect of the dwellings may be useful to reduce the dose from gaseous I-131. Of course, it is also useful to reduce the dose from airborne radioactivity. While the ASF is used to estimate indoorto-outdoor airborne radioactivity factor, it cannot be used to estimate the gaseous iodine concentration.
ð12Þ 3.4. The effect of the air conditioner and the heater
where si is the re-suspension rate of the ith kind of radionuclide; Atotali is the accumulation activity of the ith kind of radionuclide on the inner surface of the building. When the concentrations of the ith radionuclide in outdoor and indoor air are steady, C IDi ðtÞ ¼ AB C ODi ðtÞ þ sBi Atotali =V , Eq. (12) can be simpliﬁed as
C IDi ðt Þ ¼
For gaseous I-131, Eq. (3) can be rewritten as
From the published literature, Sehmel (1980) had found that re-suspension rates range over six orders of magnitude from 10−12 to 10−4 s−1. After the nuclear accident, it was likely that people remained relatively stationary indoors, and thus the re-suspension rate for this case should be small. So, the effect of re-suspension can be ignored when the radionuclides in the indoor air are very high. In this calculation, only the data in one peak is used to obtain the key parameters, thus re-suspension is negligible for the simple model.
The deposition velocity of radioactivity airborne in indoor air depends on the natural characteristics and the airﬂow in the dwelling. March is spring and the temperature in Japan is still low. Most families near FDNPP had to use the gas, fuel, or electric heaters. With heating, the indoor air velocity will be accelerated resulting in an increased airborne radioactivity deposition velocity. The effects of air conditioning are very complex. There are two kinds of air conditioners: the traditional type that does not exchange air with outdoor environment, and a new type that does exchange air activity. If the new type conditioners are used in some dwellings, the air exchange rates must be measured while operating those new systems. In the room these measurements were performed in NIRS, the air conditioner is a traditional type manufactured in 2003 and was in continuous operation. The indoor air velocity will be accelerated by air conditioner resulting in an increased airborne radionuclide deposition
3.3. The decontamination effect of the dwellings to the gaseous I-131 No statistical data have been reported for chemical forms of iodine released by the FDNPP accident. From the data of the Chernobyl accident (Noguchi and Murata, 1988), gaseous iodine is the main component of I-131. Generally, researchers think that there would be almost no effect of decontamination for gaseous iodine (Ishikawa et al., 2014). It is reasonable when the gaseous I-131 concentration in outdoor air always is high in a long term. However, we ﬁnd that the I-131 concentration in NIRS is ﬂuctuant, and the range of each signiﬁcant peak is less than two days.
Fig. 2. Gaseous I-131 concentration in outdoor air and indoor air. The low curve is the gaseous I-131 concentration in indoor air, air exchange rate equals 0.15.
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velocity. Because all the measured data are from that room, the radioactivity airborne deposition velocity may not accurately reﬂect those in room with operational heaters. Because there is no method of obtaining the deposition velocity in rooms with a heater, using measurement data may be better than making assumptions. The basic principle of air conditioner is that the indoor air is pumped into the heat exchanger and then return to the room. In this case, the radioactivity airborne will also be pumped into the heat exchanger, and it will deposit on the inner surface of the air path in the conditioner. The air conditioner is a buffer, it will adsorb the radioactivity airborne on its inner surface when the radioactivity airborne concentration in indoor air is high and it also will release the radioactivity airborne when the radioactivity airborne concentration in indoor air is low until the balance of deposition effect and re-suspension effect. Fortunately, the inner surface area in the air conditioner is very small and the air speed in the air conditioner is very high for the narrow pipe leads strong re-suspension effect. So, the air conditioning is a buffer for airborne radioactivity, but it is only a very small buffer, and the inﬂuence on the radioactivity airborne concentration in indoor air is negligible. 4. Conclusions A suitable ASF of the dwellings of the residents around FDNPP is very important for the estimation of the inhalation doses of residents and evacuees. A simple model was developed to obtain the indoor airborne deposition velocities of I-131 and Cs-137 from the measurement data of NIRS after FDNPP accident. With the measurement of the air exchange rate, volume and the inner surface area of any dwelling, the ASF and the inhalation rate can be obtained from the model and the indoor airborne deposition velocity of I-131 and Cs-137. Acknowledgments This project is supported by the National Natural Science Foundation of China (grant no. 11075049, 11375058), the Excellent Talents Program of Hengyang Normal University of China, the Hunan Provincial Applied Basic Research Base of Optoelectronic Information Technology and the construct program of the key discipline in Hunan province. The GTX780 used for this research was donated by the NVIDIA Corporation.
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Novel method for estimation of the indoor-to-outdoor airborne radioactivity ratio following the Fukushima Daiichi Nuclear Power Plant accident.
The accident at the Fukushima Daiichi Nuclear Power Plant (FDNPP) in Japan resulted in significant releases of fission products. While substantial dat...