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Consequence calculation for relocation after nuclear accidents
Nuclear Engineering and Design 208 (2001) 235– 244 www.elsevier.com/locate/nucengdes
Consequence calculation for relocation after nuclear accidents J. Qu Institute of Nuclear Energy Technology, Tsinghua Uni6ersity, Beijing 100084, People’s Republic of China Received 31 July 2000; received in revised form 26 February 2001; accepted 28 February 2001
Abstract This paper presents the results of dose and cost calculation for relocation after nuclear accidents. In order to quantify the relationship between radiation dose and relevant parameters defining protective actions, well-designed calculations have been performed and the results analyzed. On the basis of this, some dependencies between the important parameters describing the features of relocation and decontamination have been mathematically formulated. The similar has also been done for some economic costs as a result of implementing the countermeasures considered in this paper. © 2001 Elsevier Science B.V. All rights reserved.
1. Introduction In the event of an accidental release from a nuclear installation, the population living around the facility may be affected by the harmful radiological exposure from the radioactive materials released. To protect the general public from this impact, implementation of some protective actions may be required. However, protective measures aimed to avoid or reduce the exposure to the public may also bring some hazards with it to the population and the society. Therefore, the decision making on the implementation of protective actions shall be based on principles of protection and optimization. Meanwhile, every effort should be made to prevent serious deterministic health effects among the public from happening (ICRP, 1990; IAEA, 1991). E-mail address: [email protected] (J. Qu).
Relevant quantitative assessment is usually required in the process of identifying an optimized strategy to implement protective actions. Radiation dose and the economic cost as a result of taking countermeasures are examples of this kind of quantities. This paper presents the results of dose and cost calculation for relocation after an accidental release. In order to quantify the relationship between radiation dose and important parameters defining protective actions, relevant modeling has been performed and the calculations analyzed. On the basis of this, some dependencies between the important parameters describing the features of relocation and decontamination have been mathematically formulated. The similar has also been done for some economic costs as a result of implementing relocation and decontamination. It is clear that there would be more costs than we have defined in this paper.
0029-5493/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 9 - 5 4 9 3 ( 0 1 ) 0 0 3 6 5 - X
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J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
However, because of the limitation of relevant data available at the time we were conducting this work, we have only discussed part of the costs that may eventually emerge. Several models for predicting the economic impact of nuclear accidents have been developed both in Europe and in the United States (USNRC, 1990; Haywood et al., 1991; Faude, 1992). Generally speaking, these models could not find general applications because of national economic differences. In this paper we have predicted the economic impact of an accidental release in the territory of Germany. The modeling of economic consequences and relevant data we used for this purpose have been developed by Karlsruhe Research Center, Germany (Faude, 1992). All calculations done in this paper have been performed using the European accident consequence assessment code package COSYMA (KfK and NRPB, 1991). The work presented in this paper is part of a comprehensive effort where consequences and optimization of relocation using cost/benefit analysis technique has been studied (Qu and Ehrhardt, 1998).
2. Modeling of protective actions Relocation is one of the countermeasures that may be introduced to protect the public, should an accident occur. The main purpose of this protective action is to avoid or reduce the high radiological exposure as a result of deposition of radionuclides onto the ground (from ground to people and animals and water). In this paper,
relocation has been considered as a measure to avoid or reduce the external exposure from nuclides deposited. The intervention level of dose for initiating it has been defined as the individual effective dose integrated over the first year following an accidental release from this exposure pathway. The nuclides deposited will gradually attenuate with time due to radioactive decay and weathering. When the radiation dose via this pathway decreases to a level below a certain value defined in advance, the population relocated can return to where they were before the relocation. This preset value of radiation dose has been defined as the projected individual effective dose in the next year, and called as the dose level for resettlement in this paper. Decontamination has been taken as a measure to reduce the possible duration of relocation. The reduction of relocation duration by decontamination has been modeled by a decontaminating factor. This factor is defined as the ratio of the projected dose before decontamination to that thereafter. The modeling of the protective actions considered in this study is illustrated in Fig. 1. IL and DF stands for the intervention level of dose for relocation and decontaminating factor, respectively. In this paper IL is defined as the potential individual dose in open air. D G 1 represents the projected individual dose in the first year following an accident due to ground external exposure in the open air. D G T indicates the dose over the Tth year from the same exposure pathway. ILback is the dose level for resettlement. It has been defined as IL·Cback, where Cback is less than or equal to one. The time period that a relocation
Fig. 1. Illustration of the modeling of the protective actions considered.
J. Qu / Nuclear Engineering and Design 208 (2001) 235–244 Table 1 Principal data used in the calculation of cost as a result of relocationa Cost category
Transport (private, public) Accommodation Loss in income Loss in capital service Buildings Equipment Private property
Unit cost
50 DM/cap
Depreciation rate (1/a)
237
parameters used to calculate economic costs are given in Table 1 (Qu, 1991).
3. Source term and other assumptions
–
3000 DM/cap–yr 28 800 DM/cap–yr
78 500 DM/cap 0.03 17 100 DM/cap 0.11 24 000 DM/cap 0.15
a General assumption for all cost categories: interest rate: 0.07/a; discount rate: 0.05/a. Note: Current exchange rate from DM to US$ is about 2:1.
may take depends on the relocating speed given and the area affected. The relocating speed assumed in this paper is 100 km2 d − 1. Once the individual dose decreases to a level below ILback, resettlement of the relocated population will start. Because the implementation of ground decontamination needs some time for technical preparation, it has been assumed in this paper that decontamination will be only operable from the second year following an accident. The relevant
The source term assumed in the calculations is the source term F3b-DE of German risk study DRS-B (GRS, 1990). This source term can be described as follows. The containment is bypassed due to steam generator heating pipe leak. As a result of this, the primary side pressure relief opens. Up to the melting through of the reactor pressure vessel there still exists 12 m water supply in the defected steam generator. Under this source term the distance range of taking relocation will not exceed 150 km under all the weather conditions considered in this paper when IL is set at a level of 50 mSv. This is also the distance range in which we take relocation as a practicable protective measure. The important radionuclides and their release fractions as well as time dependence of this source term are given in Table 2. Mainly because German economic data have been applied in the calculation of economic costs, the nuclides inventories given in German risk study DRS-A (GRS, 1979) have been used in this paper. Other principal parameters of this source term are the following: physical release height: 10 m; thermal energy discharge rate: 0 kJ h − 1;
Table 2 Time-dependent activity release of radionuclides Nuclide group
Release fraction
Kr–Xe
1.7E−01
I
2.5E−02
Cs
2.5E−02
Te
1.5E−02
a
Nuclide
Kr-88 Xe-133 Xe-135 I-131 I-132 I-133 I-135 Cs-134 Cs-137 Te-129m Te-132
Activity release (1015 Bq) T= 9 h (l h)a
T= 10 h (l h)a
328.10 7523.20 2921.00 35.20 48.98 56.75 27.50 2.65 2.81 0.11 3.13
0.00 0.00 0.00 53.31 73.86 83.88 38.38 3.96 4.21 2.42 69.00
T stands for delay of release. The value in the parentheses is release duration.
Total release (1015 Bq)
328.10 7523.20 2921.00 88.51 122.85 140.63 65.89 6.61 7.02 2.53 72.13
J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
238
Fig. 2. The 99% percentiles of individual dose in function of distance from release point.
release duration: 1 h; cross-sectional area of reactor building: 40 m×40 m. In all the calculations done in this paper 288 weather sequences have been used. They have been selected using stratified sampling technique (Panitz et al., 1989) from the database of the atmospheric dispersion parameters collected from the meteorological tower at the Karlsrune Research Center, Germany. The population distribution data around the Biblis Nuclear Power Plant, Germany has been adopted in the calculation of collective dose. The shielding factor to external exposure from radioactive plume and deposited nuclides has been assumed to be 0.3 and 0.2, respectively. No shielding effect has been taken into account in the calculation of internal exposure due to inhalation of radioactive materials. The integration time period for dose calculation has been assumed to be 70 yr.
4. Calculation results
4.1. Indi6idual dose 6ersus IL Fig. 2 shows the 99% percentiles of residual individual dose (ID99) in function of distance at
various ILs. A percentile here has been defined as the probability that the quantity under consideration will not exceed a certain value. For example, the 99% percentiles presented in Fig. 2 indicate that in 99% of all cases the residual individual dose at different distances will not exceed its corresponding value presented on the ordinate. The potential individual doses without countermeasures as well as the sum of the external exposure from radioactive plume and the internal exposure due to inhalation of nuclides in the plume are also included. The value of Cback and DF has been assumed to be 0.5 and 3, respectively. In this paper relocation has been assumed to be implemented after the passage of radioactive plume. Therefore, it has no effect both on the external exposure from the passing plume and internal exposure from inhalation of radionuclides in the plume. Finally, the total potential dose from all exposure pathways may at most be reduced to the level of dose contributed from those two pathways. It is clearly shown that the averted dose (DD) increases as IL decreases. The averted dose is defined as the difference between the projected dose and the residual dose. Suppose that Se be the shortest distance range within which relocation is effective in reducing dose. Then it increases with
J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
decreasing IL. It is also indicated that DD increases with decreasing distance given an IL. Because of this, introducing relocation can significantly reduce the potential dose in the near range where high individual dose usually occurs.
4.2. Collecti6e dose 6ersus IL In Fig. 3 the expectation of collective dose in function of IL is presented. In the calculation of collective dose a distance range of 150 km has been used. This has also been assumed to be the distance range in which relocation is considered. Meanwhile, the potential collective dose without protective actions is also illustrated in this figure. It is obviously shown that the reduction of collective dose will be very limited when relocation is taken at a level above about 500 mSv. The explanation of this is that the collective dose contributed from population groups with high individual doses is considerably low. The collective dose decreases substantially with decreasing IL when IL is below about 200 mSv. Fig. 4 presents the collective dose averted in function of distance from release location. The shape, e.g.
239
peaks and valleys, of the curves mainly reflects the feature of the distribution of population in function of distance assumed in this paper.
4.3. Economic costs 6ersus IL The economic cost considered in this paper as a result of implementing countermeasures is dependent upon the number of people affected and the duration of the actions taken. The results of our study have shown that the number of people affected by relocation is approximately inversely proportional to IL. Obviously, the duration of the relocation depends on the potential individual dose at the time relocation starts and the dose level for resettlement. Fig. 5 presents the economic cost as a result of relocation in function of IL. It can be seen that the total cost for relocation and the loss in income increases significantly with decreasing IL for ILs below a level of about 200 mSv. This is determined by the fact that the number of people affected by relocation will increase substantially with decreasing IL when IL locates in that range. It has been found that the economic cost as a
Fig. 3. Expectation of collective dose in function of intervention level of dose for relocation.
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J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
Fig. 4. Collective dose averted in function of distance from release point.
result of relocation is mainly composed of the loss in income and loss in property. (The loss in power plant generation of electricity was not included in this paper.)
4.4. Indi6idual dose 6ersus ILback As presented above, in this paper the dose level for resettlement of relocated population has been defined as the product of intervention level for relocation IL and the factor Cback. For individuals whose potential dose is far greater than the IL applied, radiation dose will be significantly reduced by means of relocation. However, the reduction in exposure will be considerably limited in case the potential individual dose is close to the IL used. It will be particularly this case when IL does not differ from ILback significantly. The results of calculations done have shown that the effect of ILback on the residual individual dose after relocation is very limited, especially when Cback 00.1. It has been found that the averted dose by relocation will be greater than the residual dose when the following relationship is satisfied:
Cback B
1 PD , 2 IL
(1)
where PD represents the potential individual dose in the first year following an accidental release due to external exposure from radionuclides deposited on the ground.
4.5. Collecti6e dose 6ersus ILback The results of the present study have shown that the collective dose varies with ILback very gently. The dependency of the collective dose on ILback decreases gradually with increasing IL. For example, when IL is set at 50 mSv, the collective dose can be reduced only by about 10% of its potential value as Cback decreases from 1 to 0.3. This can be explained as follows. Although the individual dose in high dose ranges can be reduced significantly by relocation, it does not vary substantially with Cback. On the other hand, in dose ranges close to IL used Cback does not contribute much to the reduction of collective dose although the reduction of individual dose depends on Cback to a greater extent.
J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
4.6. Economic costs 6ersus ILback The number of people affected by relocation is merely dependent on IL. It has nothing to do with ILback. Usually, in the early phase of an accidental release the external exposure rate resulting from the radionuclides deposited decreases quickly. In case that Cs-137 dominates the external exposure in the longer term, the exposure rate with time can be approximately described by an exponential function (Kevin et al., 1990). In this case, the duration of relocation (Td) can be formulated as follows: Td =
1 PD ln u DF·Cback·IL
,
(2)
where u is the combined effective attenuation constant of radioactive decay and weathering. The other parameters in the equation have the same meaning as defined above. For relocation with longer duration the economic cost is approximately proportional to its duration. Furthermore, both theoretical analysis
241
and the results of calculations have shown that the relationship between the cost of implementing relocation (KOrel) and the factor Cback can be described as follows: KOrel 8 ln
1 . Cback
(3)
4.7. Radiation dose 6ersus DF Radiation dose averted by relocation is basically determined by the relative difference between the potential individual dose and the dose level for resettlement. The population relocated can return to where they were before the relocation earlier by means of decontamination. Although decontamination can reduce the possible duration of relocation, it has little effect on the radiation dose finally averted because of the strategy of implementing relocation and decontamination considered in this paper. This has also been demonstrated by the results of calculations performed in the present work.
Fig. 5. Cost for relocation versus intervention level of dose for relocation.
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J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
Fig. 6. Economic cost as a result of implementing protective actions.
4.8. Economic cost 6ersus DF As discussed above, decontamination can reduce the duration of relocation and hence the economic cost as a result of relocation. On the other hand, however, decontamination itself brings some economical cost with it. From Eq. (2), the maximum reduction in the duration of relocation as a result of decontamination (DTmax) can be expressed as follows: 1 DTmax = ln DF. u
(4)
As mentioned above, loss in income is the main component of the economic cost that may emerge as a result of carrying out relocation. It is approximately proportional to the time period relocation may last. The economic cost resulting from the implementation of decontamination (KOde) depends upon the area affected by decontamination and the cost of decontaminating a unit of area, i.e., KOde = Fde·f(DF),
(5)
where Fde and f(DF) stands for the area affected by decontamination and the cost of decontaminating a unit of area, respectively. Clearly, f(DF) is a function of DF. In this study, f(DF) has been assumed to be 7.0, 18.6 and 42.0 DM m − 2 for DF = 3, 5 and 10, respectively (Qu, 1991). The economic cost as a result of taking relocation as well as decontamination in function of DF is presented in Fig. 6. It can be seen that the economic cost for relocation decreases with increasing DF while the cost for decontamination shows an approximately linear increase with increasing DF. The 99th percentiles of relocation cost and decontamination cost show a stronger dependence on DF than their mean values does. As shown in Fig. 7, the total economic cost of taking relocation and decontamination increases with time in form of a power function approximately. The indicator d or a behind the numbers in the parentheses on the time axis represents days or years after the introduction of relocation, respectively. From Fig. 7 it can be seen that in the early phase the cost as a result of relocation increases rapidly with time. The cost will finally
J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
approach to a defined value. This is essentially decided by the fact that the majority of the population relocated will be able to return to their homes after a certain time period following an accidental release.
243
potential difficulties in the implementation of this protective action, we have not included this action in this paper.
5. Conclusions
4.9. Influence of source terms For the source term given in Table 2 the projected individual dose in the first year following an accident will mainly come from the external exposure from radioactive isotopes of iodine and cesium. This exposure will be dominated by the exposure from the isotopes of cesium (mainly 134 Cs and 137Cs) when the release fractions of important isotopes of iodine and 132Te are similar to that of cesium. However, the exposure from iodine will contribute a lot to the total dose occurred in the first year if the release fractions of iodine isotopes are significantly greater than that of cesium. Therefore, the area affected by relocation and hence the economic cost resulting from relocation will also increase considerably accordingly. Obviously, administration of stable iodine can usually be a useful measure in reducing the internal exposure due to inhalation. Considering
For a densely populated area with active industrial and commercial business as the reference site considered in this paper, the economic cost as a result of taking relocation depends significantly on the intervention level of dose for relocation. It increases substantially with decreasing intervention levels when the intervention level locates in a range below about 200 mSv. In general, the individual dose averted by relocation increases as the intervention level for introducing this measure decreases. Especially, implementing relocation can significantly reduce the individual dose projected in the near range where high individual dose usually occurs. So far as the collective dose is concerned, the reduction in collective dose will be very limited when relocation is taken at a level above about 500 mSv. The reason behind this is that the collective dose is dominantly contributed from area with a large
Fig. 7. Economic cost as a result of taking countermeasures in function of relocation duration.
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J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
amount of people and relatively low individual doses. However, the collective dose decreases substantially with decreasing intervention level for relocation below about 200 mSv. On the other hand, both the individual dose and the collective dose show a week dependency on the dose level for resettlement. Because of this, it would not be a wise approach to using dose level for resettlement far below the intervention level for relocation for it would result in longer duration of relocation and hence higher economic cost. Decontamination does not significantly affect the radiation dose that may finally be averted when it is implemented as a measure to reduce the possible duration of relocation. As the decontaminating factor increases, the cost of taking relocation decreases while the cost resulting from decontamination increases. The total cost as a result of implementing the two protective measures will reach to a minimum value when the decontaminating factor locates in the range between about 2 and 3.
References IAEA, 1991. Assessment of Radiological Consequences and Evaluation of Protective Measures, The International Chernobyl Project – Technical Report, International Atomic Energy Agency. ICRP, 1990. Recommendations of the International Commis-
sion on Radiological Protection, ICRP Publication 60, International Commission on Radiological Protection, Pergamon Press, Oxford. Faude, D., 1992. COSYMA Modeling of Economic Consequences, KfK-4336. GRS, 1979. Deutsche Risikostudie Kernkraftwerke (Phase A), Eine Untersuchung zu dem durch Stoerfaelle in Kernkraftwerkn Verurachten Risiko, Gesellschaft fuer Reaktorsicherheit (GRS) mbH, Verlag TUEV Rheinland, Koeln. GRS, 1990. Deutsche Risikostudie Kernkraftwerke (Phase B), Gesellschaft fuer Reaktorsicherheit (GRS) mbH, Verlag TUEV Rheinland, Koeln. Haywood, S.M., Robinson, C.A., Heady, C., 1991. COCO-1: Model for Assessing the Cost of Offsite Consequences of Accidental Releases of Radioactivity, NRPB-R243. Kevin, M.M., John, L.K., Irene, K.H., 1990. Cs-137 fallout depth distribution in forest versus field sites: implications for external gamma dose rates. Journal of Environmental Radioactivity 23 (12), 23 – 47. KfK and NRPB, 1991. Kernforschungszentrum Karlsruhe GmbH and National Radiological Protection Board, COSYMA: A New Program Package for Accident Consequence Assessment, EUR-13028EN. Panitz, H.J., Matzerath, C., Paesler-Sauer, J., 1989. UFOMOD: Atmospheric Dispersion and Deposition, Report KfK-4332. Qu, J., 1991. Konsequenzen und Wirksamkeit von Umsiedlungsmassnahmen nach kerntechnischen Unfaellen, Report KfK-4990. Qu, J., Ehrhardt, J., 1998. Dose and cost considerations for relocation after nuclear accidents. Heath Physics 75 (2), 130 – 135. USNRC, 1990. MELCOR Accident Consequence Code System (MACCS), NUREG/CR-4691, vol. 2, U.S. Nuclear Regulatory Commission.
Consequence calculation for relocation after nuclear accidents J. Qu Institute of Nuclear Energy Technology, Tsinghua Uni6ersity, Beijing 100084, People’s Republic of China Received 31 July 2000; received in revised form 26 February 2001; accepted 28 February 2001
Abstract This paper presents the results of dose and cost calculation for relocation after nuclear accidents. In order to quantify the relationship between radiation dose and relevant parameters defining protective actions, well-designed calculations have been performed and the results analyzed. On the basis of this, some dependencies between the important parameters describing the features of relocation and decontamination have been mathematically formulated. The similar has also been done for some economic costs as a result of implementing the countermeasures considered in this paper. © 2001 Elsevier Science B.V. All rights reserved.
1. Introduction In the event of an accidental release from a nuclear installation, the population living around the facility may be affected by the harmful radiological exposure from the radioactive materials released. To protect the general public from this impact, implementation of some protective actions may be required. However, protective measures aimed to avoid or reduce the exposure to the public may also bring some hazards with it to the population and the society. Therefore, the decision making on the implementation of protective actions shall be based on principles of protection and optimization. Meanwhile, every effort should be made to prevent serious deterministic health effects among the public from happening (ICRP, 1990; IAEA, 1991). E-mail address: [email protected] (J. Qu).
Relevant quantitative assessment is usually required in the process of identifying an optimized strategy to implement protective actions. Radiation dose and the economic cost as a result of taking countermeasures are examples of this kind of quantities. This paper presents the results of dose and cost calculation for relocation after an accidental release. In order to quantify the relationship between radiation dose and important parameters defining protective actions, relevant modeling has been performed and the calculations analyzed. On the basis of this, some dependencies between the important parameters describing the features of relocation and decontamination have been mathematically formulated. The similar has also been done for some economic costs as a result of implementing relocation and decontamination. It is clear that there would be more costs than we have defined in this paper.
0029-5493/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 9 - 5 4 9 3 ( 0 1 ) 0 0 3 6 5 - X
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J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
However, because of the limitation of relevant data available at the time we were conducting this work, we have only discussed part of the costs that may eventually emerge. Several models for predicting the economic impact of nuclear accidents have been developed both in Europe and in the United States (USNRC, 1990; Haywood et al., 1991; Faude, 1992). Generally speaking, these models could not find general applications because of national economic differences. In this paper we have predicted the economic impact of an accidental release in the territory of Germany. The modeling of economic consequences and relevant data we used for this purpose have been developed by Karlsruhe Research Center, Germany (Faude, 1992). All calculations done in this paper have been performed using the European accident consequence assessment code package COSYMA (KfK and NRPB, 1991). The work presented in this paper is part of a comprehensive effort where consequences and optimization of relocation using cost/benefit analysis technique has been studied (Qu and Ehrhardt, 1998).
2. Modeling of protective actions Relocation is one of the countermeasures that may be introduced to protect the public, should an accident occur. The main purpose of this protective action is to avoid or reduce the high radiological exposure as a result of deposition of radionuclides onto the ground (from ground to people and animals and water). In this paper,
relocation has been considered as a measure to avoid or reduce the external exposure from nuclides deposited. The intervention level of dose for initiating it has been defined as the individual effective dose integrated over the first year following an accidental release from this exposure pathway. The nuclides deposited will gradually attenuate with time due to radioactive decay and weathering. When the radiation dose via this pathway decreases to a level below a certain value defined in advance, the population relocated can return to where they were before the relocation. This preset value of radiation dose has been defined as the projected individual effective dose in the next year, and called as the dose level for resettlement in this paper. Decontamination has been taken as a measure to reduce the possible duration of relocation. The reduction of relocation duration by decontamination has been modeled by a decontaminating factor. This factor is defined as the ratio of the projected dose before decontamination to that thereafter. The modeling of the protective actions considered in this study is illustrated in Fig. 1. IL and DF stands for the intervention level of dose for relocation and decontaminating factor, respectively. In this paper IL is defined as the potential individual dose in open air. D G 1 represents the projected individual dose in the first year following an accident due to ground external exposure in the open air. D G T indicates the dose over the Tth year from the same exposure pathway. ILback is the dose level for resettlement. It has been defined as IL·Cback, where Cback is less than or equal to one. The time period that a relocation
Fig. 1. Illustration of the modeling of the protective actions considered.
J. Qu / Nuclear Engineering and Design 208 (2001) 235–244 Table 1 Principal data used in the calculation of cost as a result of relocationa Cost category
Transport (private, public) Accommodation Loss in income Loss in capital service Buildings Equipment Private property
Unit cost
50 DM/cap
Depreciation rate (1/a)
237
parameters used to calculate economic costs are given in Table 1 (Qu, 1991).
3. Source term and other assumptions
–
3000 DM/cap–yr 28 800 DM/cap–yr
78 500 DM/cap 0.03 17 100 DM/cap 0.11 24 000 DM/cap 0.15
a General assumption for all cost categories: interest rate: 0.07/a; discount rate: 0.05/a. Note: Current exchange rate from DM to US$ is about 2:1.
may take depends on the relocating speed given and the area affected. The relocating speed assumed in this paper is 100 km2 d − 1. Once the individual dose decreases to a level below ILback, resettlement of the relocated population will start. Because the implementation of ground decontamination needs some time for technical preparation, it has been assumed in this paper that decontamination will be only operable from the second year following an accident. The relevant
The source term assumed in the calculations is the source term F3b-DE of German risk study DRS-B (GRS, 1990). This source term can be described as follows. The containment is bypassed due to steam generator heating pipe leak. As a result of this, the primary side pressure relief opens. Up to the melting through of the reactor pressure vessel there still exists 12 m water supply in the defected steam generator. Under this source term the distance range of taking relocation will not exceed 150 km under all the weather conditions considered in this paper when IL is set at a level of 50 mSv. This is also the distance range in which we take relocation as a practicable protective measure. The important radionuclides and their release fractions as well as time dependence of this source term are given in Table 2. Mainly because German economic data have been applied in the calculation of economic costs, the nuclides inventories given in German risk study DRS-A (GRS, 1979) have been used in this paper. Other principal parameters of this source term are the following: physical release height: 10 m; thermal energy discharge rate: 0 kJ h − 1;
Table 2 Time-dependent activity release of radionuclides Nuclide group
Release fraction
Kr–Xe
1.7E−01
I
2.5E−02
Cs
2.5E−02
Te
1.5E−02
a
Nuclide
Kr-88 Xe-133 Xe-135 I-131 I-132 I-133 I-135 Cs-134 Cs-137 Te-129m Te-132
Activity release (1015 Bq) T= 9 h (l h)a
T= 10 h (l h)a
328.10 7523.20 2921.00 35.20 48.98 56.75 27.50 2.65 2.81 0.11 3.13
0.00 0.00 0.00 53.31 73.86 83.88 38.38 3.96 4.21 2.42 69.00
T stands for delay of release. The value in the parentheses is release duration.
Total release (1015 Bq)
328.10 7523.20 2921.00 88.51 122.85 140.63 65.89 6.61 7.02 2.53 72.13
J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
238
Fig. 2. The 99% percentiles of individual dose in function of distance from release point.
release duration: 1 h; cross-sectional area of reactor building: 40 m×40 m. In all the calculations done in this paper 288 weather sequences have been used. They have been selected using stratified sampling technique (Panitz et al., 1989) from the database of the atmospheric dispersion parameters collected from the meteorological tower at the Karlsrune Research Center, Germany. The population distribution data around the Biblis Nuclear Power Plant, Germany has been adopted in the calculation of collective dose. The shielding factor to external exposure from radioactive plume and deposited nuclides has been assumed to be 0.3 and 0.2, respectively. No shielding effect has been taken into account in the calculation of internal exposure due to inhalation of radioactive materials. The integration time period for dose calculation has been assumed to be 70 yr.
4. Calculation results
4.1. Indi6idual dose 6ersus IL Fig. 2 shows the 99% percentiles of residual individual dose (ID99) in function of distance at
various ILs. A percentile here has been defined as the probability that the quantity under consideration will not exceed a certain value. For example, the 99% percentiles presented in Fig. 2 indicate that in 99% of all cases the residual individual dose at different distances will not exceed its corresponding value presented on the ordinate. The potential individual doses without countermeasures as well as the sum of the external exposure from radioactive plume and the internal exposure due to inhalation of nuclides in the plume are also included. The value of Cback and DF has been assumed to be 0.5 and 3, respectively. In this paper relocation has been assumed to be implemented after the passage of radioactive plume. Therefore, it has no effect both on the external exposure from the passing plume and internal exposure from inhalation of radionuclides in the plume. Finally, the total potential dose from all exposure pathways may at most be reduced to the level of dose contributed from those two pathways. It is clearly shown that the averted dose (DD) increases as IL decreases. The averted dose is defined as the difference between the projected dose and the residual dose. Suppose that Se be the shortest distance range within which relocation is effective in reducing dose. Then it increases with
J. Qu / Nuclear Engineering and Design 208 (2001) 235–244
decreasing IL. It is also indicated that DD increases with decreasing distance given an IL. Because of this, introducing relocation can significantly reduce the potential dose in the near range where high individual dose usually occurs.
4.2. Collecti6e dose 6ersus IL In Fig. 3 the expectation of collective dose in function of IL is presented. In the calculation of collective dose a distance range of 150 km has been used. This has also been assumed to be the distance range in which relocation is considered. Meanwhile, the potential collective dose without protective actions is also illustrated in this figure. It is obviously shown that the reduction of collective dose will be very limited when relocation is taken at a level above about 500 mSv. The explanation of this is that the collective dose contributed from population groups with high individual doses is considerably low. The collective dose decreases substantially with decreasing IL when IL is below about 200 mSv. Fig. 4 presents the collective dose averted in function of distance from release location. The shape, e.g.
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peaks and valleys, of the curves mainly reflects the feature of the distribution of population in function of distance assumed in this paper.
4.3. Economic costs 6ersus IL The economic cost considered in this paper as a result of implementing countermeasures is dependent upon the number of people affected and the duration of the actions taken. The results of our study have shown that the number of people affected by relocation is approximately inversely proportional to IL. Obviously, the duration of the relocation depends on the potential individual dose at the time relocation starts and the dose level for resettlement. Fig. 5 presents the economic cost as a result of relocation in function of IL. It can be seen that the total cost for relocation and the loss in income increases significantly with decreasing IL for ILs below a level of about 200 mSv. This is determined by the fact that the number of people affected by relocation will increase substantially with decreasing IL when IL locates in that range. It has been found that the economic cost as a
Fig. 3. Expectation of collective dose in function of intervention level of dose for relocation.
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Fig. 4. Collective dose averted in function of distance from release point.
result of relocation is mainly composed of the loss in income and loss in property. (The loss in power plant generation of electricity was not included in this paper.)
4.4. Indi6idual dose 6ersus ILback As presented above, in this paper the dose level for resettlement of relocated population has been defined as the product of intervention level for relocation IL and the factor Cback. For individuals whose potential dose is far greater than the IL applied, radiation dose will be significantly reduced by means of relocation. However, the reduction in exposure will be considerably limited in case the potential individual dose is close to the IL used. It will be particularly this case when IL does not differ from ILback significantly. The results of calculations done have shown that the effect of ILback on the residual individual dose after relocation is very limited, especially when Cback 00.1. It has been found that the averted dose by relocation will be greater than the residual dose when the following relationship is satisfied:
Cback B
1 PD , 2 IL
(1)
where PD represents the potential individual dose in the first year following an accidental release due to external exposure from radionuclides deposited on the ground.
4.5. Collecti6e dose 6ersus ILback The results of the present study have shown that the collective dose varies with ILback very gently. The dependency of the collective dose on ILback decreases gradually with increasing IL. For example, when IL is set at 50 mSv, the collective dose can be reduced only by about 10% of its potential value as Cback decreases from 1 to 0.3. This can be explained as follows. Although the individual dose in high dose ranges can be reduced significantly by relocation, it does not vary substantially with Cback. On the other hand, in dose ranges close to IL used Cback does not contribute much to the reduction of collective dose although the reduction of individual dose depends on Cback to a greater extent.
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4.6. Economic costs 6ersus ILback The number of people affected by relocation is merely dependent on IL. It has nothing to do with ILback. Usually, in the early phase of an accidental release the external exposure rate resulting from the radionuclides deposited decreases quickly. In case that Cs-137 dominates the external exposure in the longer term, the exposure rate with time can be approximately described by an exponential function (Kevin et al., 1990). In this case, the duration of relocation (Td) can be formulated as follows: Td =
1 PD ln u DF·Cback·IL
,
(2)
where u is the combined effective attenuation constant of radioactive decay and weathering. The other parameters in the equation have the same meaning as defined above. For relocation with longer duration the economic cost is approximately proportional to its duration. Furthermore, both theoretical analysis
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and the results of calculations have shown that the relationship between the cost of implementing relocation (KOrel) and the factor Cback can be described as follows: KOrel 8 ln
1 . Cback
(3)
4.7. Radiation dose 6ersus DF Radiation dose averted by relocation is basically determined by the relative difference between the potential individual dose and the dose level for resettlement. The population relocated can return to where they were before the relocation earlier by means of decontamination. Although decontamination can reduce the possible duration of relocation, it has little effect on the radiation dose finally averted because of the strategy of implementing relocation and decontamination considered in this paper. This has also been demonstrated by the results of calculations performed in the present work.
Fig. 5. Cost for relocation versus intervention level of dose for relocation.
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Fig. 6. Economic cost as a result of implementing protective actions.
4.8. Economic cost 6ersus DF As discussed above, decontamination can reduce the duration of relocation and hence the economic cost as a result of relocation. On the other hand, however, decontamination itself brings some economical cost with it. From Eq. (2), the maximum reduction in the duration of relocation as a result of decontamination (DTmax) can be expressed as follows: 1 DTmax = ln DF. u
(4)
As mentioned above, loss in income is the main component of the economic cost that may emerge as a result of carrying out relocation. It is approximately proportional to the time period relocation may last. The economic cost resulting from the implementation of decontamination (KOde) depends upon the area affected by decontamination and the cost of decontaminating a unit of area, i.e., KOde = Fde·f(DF),
(5)
where Fde and f(DF) stands for the area affected by decontamination and the cost of decontaminating a unit of area, respectively. Clearly, f(DF) is a function of DF. In this study, f(DF) has been assumed to be 7.0, 18.6 and 42.0 DM m − 2 for DF = 3, 5 and 10, respectively (Qu, 1991). The economic cost as a result of taking relocation as well as decontamination in function of DF is presented in Fig. 6. It can be seen that the economic cost for relocation decreases with increasing DF while the cost for decontamination shows an approximately linear increase with increasing DF. The 99th percentiles of relocation cost and decontamination cost show a stronger dependence on DF than their mean values does. As shown in Fig. 7, the total economic cost of taking relocation and decontamination increases with time in form of a power function approximately. The indicator d or a behind the numbers in the parentheses on the time axis represents days or years after the introduction of relocation, respectively. From Fig. 7 it can be seen that in the early phase the cost as a result of relocation increases rapidly with time. The cost will finally
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approach to a defined value. This is essentially decided by the fact that the majority of the population relocated will be able to return to their homes after a certain time period following an accidental release.
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potential difficulties in the implementation of this protective action, we have not included this action in this paper.
5. Conclusions
4.9. Influence of source terms For the source term given in Table 2 the projected individual dose in the first year following an accident will mainly come from the external exposure from radioactive isotopes of iodine and cesium. This exposure will be dominated by the exposure from the isotopes of cesium (mainly 134 Cs and 137Cs) when the release fractions of important isotopes of iodine and 132Te are similar to that of cesium. However, the exposure from iodine will contribute a lot to the total dose occurred in the first year if the release fractions of iodine isotopes are significantly greater than that of cesium. Therefore, the area affected by relocation and hence the economic cost resulting from relocation will also increase considerably accordingly. Obviously, administration of stable iodine can usually be a useful measure in reducing the internal exposure due to inhalation. Considering
For a densely populated area with active industrial and commercial business as the reference site considered in this paper, the economic cost as a result of taking relocation depends significantly on the intervention level of dose for relocation. It increases substantially with decreasing intervention levels when the intervention level locates in a range below about 200 mSv. In general, the individual dose averted by relocation increases as the intervention level for introducing this measure decreases. Especially, implementing relocation can significantly reduce the individual dose projected in the near range where high individual dose usually occurs. So far as the collective dose is concerned, the reduction in collective dose will be very limited when relocation is taken at a level above about 500 mSv. The reason behind this is that the collective dose is dominantly contributed from area with a large
Fig. 7. Economic cost as a result of taking countermeasures in function of relocation duration.
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amount of people and relatively low individual doses. However, the collective dose decreases substantially with decreasing intervention level for relocation below about 200 mSv. On the other hand, both the individual dose and the collective dose show a week dependency on the dose level for resettlement. Because of this, it would not be a wise approach to using dose level for resettlement far below the intervention level for relocation for it would result in longer duration of relocation and hence higher economic cost. Decontamination does not significantly affect the radiation dose that may finally be averted when it is implemented as a measure to reduce the possible duration of relocation. As the decontaminating factor increases, the cost of taking relocation decreases while the cost resulting from decontamination increases. The total cost as a result of implementing the two protective measures will reach to a minimum value when the decontaminating factor locates in the range between about 2 and 3.
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