Keywords

1 Introduction

Emergency planning zone refers to the area around the nuclear power plant which has emergency plans and emergency preparedness so as to take effective protective actions to protect the public in case of a nuclear accident. The aim of establishing emergency planning zone is to divide the zone that requires protection measures in advance and make emergency preparedness in this zone so as to take intervention actions in the event of an accident at the nuclear power plant, protect the public and reduce the harm to the public and the environment [1]. Reasonable division of emergency planning zone is an important technical basis for making emergency plans.

HPR1000 is the third generation nuclear reactor researched and developed by CNPE (China Nuclear Power Engineering Company) independently, which has active and passive safety features. The research on the division of emergency planning zone for HPR1000 nuclear power plant site is helpful to the subsequent optimization work for HPR1000. Based on the current main calculation models of atmospheric dispersion factor and the current main weather sampling methods, this paper puts forward the optimization method of emergency planning zones for HPR1000 nuclear power plant site.

2 Calculation and Division of Emergency Planning Zones at Home and Abroad

2.1 Calculation of Emergency Planning Zones Abroad

D. W. Hummel et al. [2] calculate atmospheric dispersion factors, dose consequences and the reasonable size of emergency planning zone of small modular reactors including high temperature gas-cooled reactor, molten salt reactor, lead cooled fast reactor and small pressurized water reactor using ADDAM and compare the calculation results with the calculation results of emergency planning zones for CANDU 6 under the USBO accident. The calculation results show that the dose consequences of small modular reactors are much smaller than that of CANDU 6. A relatively smaller emergency planning zone can be chosen for small modular reactors. Mazzammal Hussain et al. [3] calculate dose consequences of 10 MW nuclear research reactor using InterRAS developed by IAEA. The calculation considers accidents of 61 m high reactor source release and ground release and selects constant weather conditions. The calculation results are consistent with the dose consequences of PARR-1 calculated by Hotspot and meet the standard for emergency planning zone of IAEA and PAK/914.

2.2 Calculation of Emergency Planning Zones at Home

Luo Haiying et al. [4] calculate dose consequences of emergency planning zone of Taishan Nuclear Power Plant which adopts the third generation EPR using MACCS2. The calculation considers three design basis accidents including large loss of coolant accident, steam generator tube rupture and fuel operation accident and selects the hourly weather data. The calculation results show that the radius of the emergency planning zone of Taishan Nuclear Power Plant is less than 0.5 km, which is consistent with the design goal of EPR. Considering social conditions and the public psychology near Taishan Nuclear Power Plant, the inner radius of the emergency planning zone of Taishan Nuclear Power Plant is recommended to be 4 km and the outer radius is recommended to be 7 km. Huang Ting et al. [5] select some coastal nuclear power plant site which adopts AP1000, calculate the atmospheric dispersion factor using PAVAN and calculate the dose consequences using MACCS. The calculation considers large loss of coolant accident and core melt release accident and selects the hourly weather data. The calculation results show that the inner radius of the emergency planning zone of the AP1000 nuclear power plant site is recommended to be 3 km and the outer radius is recommended to be 7 km. Yu Fei et al. [6] select some underground nuclear power plant site, consider large loss of coolant accident and calculate the atmospheric dispersion factor using Hotspot. The calculation results are compared with the intervention level in GB18871-2002. The results show that the dose level at any distance outside the underground nuclear power plant is far less than the standard value.

2.3 Size of Emergency Planning Zones of Operating Nuclear Facilities at Home

Size of plume emergency planning zone is generally determined within a radius of 10 km with the reactor as the center according to the thermal power of the reactor, the inner zone of the plume emergency planning zone is generally determined within a radius of 5 km with the reactor as the center. Size of ingestion emergency planning zone should be determined according to the radiation consequences of the accident and can be determined according to the actual radiation monitoring results during emergency response. Sizes of emergency planning zones of current nuclear power plants in China are shown in Table 1 [1, 7].

Table 1. Sizes of Emergency Planning Zones for operating Nuclear Power Plants in China
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The data in Table 1 can be used as a reference for the subsequent calculation and optimization of the emergency planning zone of HPR1000 nuclear power plant site. The general method of determining the emergency planning zone and the optimization method of HPR1000 nuclear power plant site are introduced below.

3 General Method for Determining Emergency Planning Zone [8]

The process of determining emergency planning zone of nuclear power plant is shown in Fig. 1:

  1. (1)

    Determine the accident type and source type, weather data, weather sampling methods and atmospheric dispersion factors.

  2. (2)

    Calculate the expected dose that the accident may cause to the public through the passing plume and the dose that can be prevented after taking specific protective actions and estimate the contamination level of contaminated food and drinking water.

  3. (3)

    Compare the calculated dose level and contamination level with the general optimization intervention level or action level in GB18871-2002 [9] and determine the size of the emergency planning zone. Ensure that the public dose and contamination level of contaminated food and drinking water caused by the accident are lower than the corresponding general optimization intervention level and action level.

When calculating the dose consequences caused by the accident through passing plume, it is necessary to determine the appropriate atmospheric dispersion factor according to the actual working conditions and evaluation purposes. Based on the determination of atmospheric dispersion factor, the optimization method of emergency planning zone for HPR1000 nuclear power plant site is put forward below.

Fig. 1.
figure 1

Process of determining emergency planning zone

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4 Introduction and Comparison of Different Calculation Models of Atmospheric Dispersion Factors

In the evaluation of consequence of nuclear power plant accidents, the calculation mode of atmospheric dispersion factor depends on the evaluation purpose. In this section, the current main calculation models of atmospheric dispersion factor are introduced and analyzed. The optimization idea of emergency planning zone of HPR1000 nuclear power plant site under the light wind and the calm wind condition is put forward.

4.1 RG1.145 Model

RG1.145 model is based on Gaussian plume model, that is, the radioactive material is normally distributed about the plume axis in the atmosphere, it is assumed that the plume between the release point and points at all distances where the X/Q value needs to be calculated is flat.

RG1.145 model realizes the transformation of atmospheric dispersion estimation from RG1.4 determinism to probability theory and introduces the important idea that dispersion conditions are related to orientation. At the same time, it considers building wake effect and plume wind vibration effect. It can make calculations under the ground source release and elevated release conditions. The model takes the joint frequency data of wind direction, wind speed and atmospheric stability of nuclear power plant site as input and calculates the atmospheric dispersion factor X/Q values of radioactive materials at the boundary of exclusion area boundary (EAB) and the outer boundary of the low population zone (LPZ) in different time periods and different locations under the design base accident conditions.

4.2 NUREG/CR-6331 Model

NUREG/CR-6331 model adopts linear Gaussian plume dispersion model, assuming that the release rate of contaminants is uniform and constant in the whole period, which is convenient for users to evaluate the accident consequences without fully understanding the accident release sequence.

ARCON96 based on NUREG/CR-6631 model can make calculations in the case of ground release, mixed release and elevated release and consider the influence of building wake effect on atmospheric dispersion factor in the case of ground release. The calculation result of mixed release is a simple superposition of that of ground release and elevated release and their respective proportions are determined by the ratio of the vertical outflow velocity of pollutants to the wind speed at the release height. The calculation result of elevated release will consider the downwash effect of the building and the influence of the height difference of the control room.

ARCON96 uses hourly weather data to calculate atmospheric dispersion factors and uses hourly results to calculate atmospheric dispersion factors in different periods from 2 h to 30 days to obtain cumulative percentage distribution, from which the value of 95% probability level is selected as the atmospheric dispersion factor value in each period.

4.3 NUREG/CR-4691 Model [10, 11]

NUREG/CR-4691 model adopts one-dimensional Gaussian linear plume model to simulate atmospheric transport, dispersion and deposition of radioactive materials, considers physical and chemical phenomena including building wake effect, plume rise, dry/wet deposition, radioactive decay and resuspension and finally obtains the atmospheric dispersion factor X/Q values of different probability levels on the downwind axis of plume at different distances from the center of the nuclear power plant site (such as mean, 50th, 90th, 95th, 99.5th, etc.).

Gaussian linear plume model regards the release of radionuclide as a continuous point source and assumes that the contaminant concentration is normally distributed in the vertical and horizontal directions when weather conditions (such as wind direction, wind speed, stability, etc.) do not change with time and distances, as shown in Formula (1):

$$ C(x,y,z) = \frac{Q}{{2\pi \overline{u}\sigma_{y} \sigma_{z} }} \cdot \exp \left[ { - \frac{{y^{2} }}{{2\sigma_{y}^{2} }}} \right] \cdot \exp \left[ {\frac{{ - \left( {z - h} \right)_{{}}^{2} }}{{2\sigma_{z}^{2} }}} \right] $$
(1)

where:

C(x, y, z): the time integrated air concentration (Bq \(\cdot\) s/m3);

Q: the quantity of radionuclides released (Bq);

\(\overline{u}\): average wind speed (m/s);

h: release height (m);

\(\sigma_{y}\), \(\sigma_{z}\): horizontal and vertical dispersion parameters (m).

4.4 Lagrange Gaussian Puff Model [12, 13]

Lagrange Gaussian puff model is used widely in CALPUFF, which is based on unsteady Lagrange Gaussian puff dispersion model and simulates the dispersion, transformation and removal of puff on the moving path by tracking the movement of discrete puff released from the emission source until the puff leaves the simulation area. In addition, changes in time and space of weather conditions are considered in the process of puff dispersion. An important role of unsteady dispersion is that puff can change its moving path with the change of wind direction. In the process of movement, the puff responds to the surface characteristics changing with space, such as surface roughness, soil moisture content, etc.

The CALPUFF Modeling System includes three main modules: CALMET, CALPUFF and CALPOST. CALMET is a meteorological model, which develops wind and temperature fields on a three-dimensional gridded modeling domain and simultaneously develops two-dimensional fields including mixing height, surface characteristics and dispersion properties. CALPUFF is a transport and dispersion model which advects puffs of material emitted from sources and simulates dispersion and transformation processes along the way. CALPUFF uses fields changing with time and space generated by CALMET. The primary output files from CALPUFF include concentration fields or deposition fluxs. CALPOST is used to process postprocess modules of output files, produces time series files, count the maximum value of concentration and the exceeding rate of some certain threshold concentration, etc.

CALPUFF has two kinds of puffs: the Gaussian puff with isotropic distribution and the puff stretched along the wind direction. CALPUFF can choose either puff or the mixed simulation method to make full use of the advantages of the two puffs.

The unsteady process of the puff model is based on the theory that the contaminant concentration at a certain point in space is the superposition result of dispersion contributed by the continuously released puffs. Formulas describing the concentration contribution of a certain puff at a certain receptor point are shown in Formula (2) and Formula (3):

$$ C = \frac{Q}{{2\pi \sigma_{x} \sigma_{y} }}g\exp \left[ { - d_{a}^{2} /\left( {2\sigma_{x}^{2} } \right)} \right]\exp \left[ { - d_{c}^{2} /\left( {2\sigma_{y}^{2} } \right)} \right] $$
(2)
$$ g = \frac{2}{{\left( {2\pi } \right)_{{}}^{1/2} \sigma_{z} }}\sum\limits_{n = - \infty }^{\infty } {\exp \left[ { - \left( {H_{e} + 2nh} \right)_{{}}^{2} /\left( {2\sigma_{z}^{2} } \right)} \right]} $$
(3)

where:

C: ground concentration (g/m3);

Q: the quantity of contaminant (g);

\(\sigma_{x}\), \(\sigma_{y}\), \(\sigma_{z}\): dispersion parameters (m) in longitudinal horizontal, transverse horizontal and vertical directions;

da, dc: the distance (m) between the longitudinal puff center and the transverse puff center and the receptor;

g: the vertical term (m) in the Gaussian equation;

He: the effective height (m) from the center of the puff to the ground;

h: mixing height (m);

The sum term in g represents multiple reflections between the top of the mixed layer and the ground. When \(\sigma_{z}\) > 1.6 h, the mixed layer is nearly uniform in the vertical direction.

In the medium distance scale transmission, the piecewise change of the puff volume in the sampling step is small and the integral puff can meet the calculation requirements. When dealing with local scale problems, the integrated puff may not meet the requirement because some puffs may grow very fast.

Stretched puffs can be used to deal with local scale air contamination because stretched puffs can reflect the influence of contamination source on the near field. Stretched puffs can be regarded as a group of overlapping puffs with small separation distances. The concentration contribution of a stretched puff is shown in Formula (4) and Formula (5):

$$ C\left( t \right) = \frac{Fq}{{\sqrt {2\pi } u^{\prime}\sigma_{y} }}g\exp \left[ {\frac{{ - d_{c}^{2} }}{{2\sigma_{y}^{2} }}\frac{{u^{2} }}{{u^{{\prime}{2}} }}} \right] $$
(4)
$$ F = \frac{1}{2}\left\{ {erf\left[ {\frac{{d_{a2}^{{}} }}{{\sqrt 2 \sigma_{y2} }}} \right] - erf\left[ {\frac{{ - d_{a1} }}{{\sqrt 2 \sigma_{y1} }}} \right]} \right\} $$
(5)

where:

u: vector average wind speed (m/s);

\(u^{\prime}\): scalar wind speed (\(u^{\prime}\) = \(\left( {u_{{}}^{2} + \sigma_{\nu }^{2} } \right)_{{}}^{1/2}\), \(\sigma_{\nu }^{{}}\) is the standard deviation of the wind speed);

q: source emission rate (g/s);

F: causal effect function;

g: the vertical term of the Gaussian equation;

dc, da: the distance to the receptor from the position perpendicular to the axis of the stretched puff and the position along the direction of the stretched puff, footmarks 1 and 2 represent the old release point and the new release point, the footmarks without numbers represent the values defined on the receptor.

4.5 Comparisons of Atmospheric Dispersion Factor Models

RG1.145 and NUREG/CR-4691 are both based on Gaussian plume models while CALPUFF is based on Gaussian puff models, the comparison between them are shown in Table 2. When calculating atmospheric dispersion factors, Gaussian puff model will consider the dispersion process while Gaussian plume model assumes that the plume forms instantly at every point in the space without considering the dispersion process. Under the low wind speed conditions, the Gaussian plume model is still suitable while the calculation results of Gaussian plume model tend to be infinite when the wind speed approaches zero. Gaussian plume model will dynamically consider the spatial change of meteorological field and topographic effect while Gaussian plume model ignores them. Gaussian puff model will consider the accumulation of calculation results at every time point while the calculation results of Gaussian plume model at each time point are independent of each other.

Therefore, compared with the Gaussian plume model, CALPUFF based on Gaussian puff model is more suitable for the calculation of atmospheric dispersion factor under the light wind and the calm wind condition. When calculating the emergency planning zone of HPR1000 nuclear power plant site under the light wind and the calm wind condition, it is more appropriate to choose CALPUFF based on Gaussian puff model.

Table 2. Comparisons between Gaussian plume model and Gaussian puff model
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5 Weather Sampling

When calculating the atmospheric dispersion factor, it is necessary to consider the weather conditions according to the actual working conditions and determine the atmospheric stability, the wind speed, the wind direction and the rainfall intensity when an accident occurs. According to the discussion in the previous section, it is appropriate to choose CALPUFF to calculate the atmospheric dispersion factor under the light wind and the calm wind condition. In order to consider the weather conditions throughout the year, CALPUFF uses the annual weather data to calculate hourly which can ensure the accuracy, but it takes a long time to calculate.

We can consider appropriate weather sampling methods which select representative weather data from the annual weather data to reduce the number of hours to be calculated. This part of weather data should represent the annual weather data: the error between the atomspheric dispersion factor value calculated by using this part of weather data and that calculated by using the annual weather data must be within a reasonable range. Therefore, by choosing the appropriate weather sampling methods, we can reduce the calculation time to optimize the calculation of atmospheric dispersion factor and the emergency planning zone of HPR1000.

5.1 Introduction to Different Weather Sampling Methods [14]

Weather sampling methods include the following three types: systematic sampling, simple random sampling and stratified random sampling [15]. Systematic sampling: determine the sampling starting point, the sampling interval and the sampling number, choose samples from the population in turn. Simple random sampling: the characteristics of the sampling population are completely ignored and the weather data are randomly selected with equal probability as the representative of the annual weather data. Stratified random sampling: divide the whole weather data into several subpopulations named layers, samples are chosen from each layer.

Compared with systematic sampling and simple random sampling, stratified sampling can fully consider various weather conditions, including those with low frequency but possibly causing serious accident consequences. For example, according to the actual working conditions and specific weather conditions, we can separate layers for those weather conditions that have a low frequency but may cause serious accident consequences so as to ensure that the weather conditions will be sampled during sampling. While simple random sampling and systematic sampling cannot do this. Therefore, maybe it is feasible to select stratified random sampling to optimize the calculation of the emergency planning zone of HPR1000 nuclear power plant site. Take the following typical stratified random sampling method of weather data as an example to briefly explain the stratified random sampling method.

5.2 Stratified Random Sampling of Weather Data

The current typical stratified sampling process of weather data is shown in Fig. 2.

  1. (1)

    Determine the standard of stratifying weather data and the characteristics of weather data of each layer. A typical weather classification standard is shown in Table 3. The weather stratification standard includes 32 weather bins according to the influence of weather conditions on the accident consequences.

  2. (2)

    According to the characteristics of weather data at each moment, divide the annual weather data into the corresponding weather bins. For example, the weather data of the first hour of the year, the atmospheric stability is A, the wind speed is 3 m/s, no rainfall, then the weather data at that moment should be put into weather bin 1.

  3. (3)

    Sample weather data from each weather bin. The weather data chosen are used as weather input for calculating the atmospheric dispersion factor. If four weather data are sampled from each weather bin, 128 weather data are finally sampled. For the sake of simplification, simple random sampling can be adopted to sample weather data from weather bins.

The final calculated atmospheric dispersion factor value is the sum of the atmospheric dispersion factor values calculated under different weather conditions multiplied by the corresponding weights. For the weather data sampled from the ith weather bin, its weight is shown in Formula (6):

$$ \frac{1}{{K_{i} }} \cdot \frac{{N_{i} }}{{\sum\limits_{i = 1}^{32} {N_{i} } }} $$
(6)

where:

Ki: the number of weather data sampled from the Nith weather bin, which is 4 in this example;

\(N_{i}\): The total number of weather data contained in the ith weather bin.

Fig. 2.
figure 2

The flow chart of stratified weather sampling

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Table 3. A typical weather classification standard
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In addition, Hu et al. [15,16,17] improve the typical weather stratification standard and put forward the weather stratification standards applicable to China coastal nuclear power plant sites. For the optimization of the emergency planning zone of HPR100 nuclear power plant site, when adopting stratified random sampling to sample weather data as the weather input of CALPUFF, two problems need to be considered, which are to be solved in the follow-up research:

  1. (1)

    Weather conditions of different nuclear power plant sites are different, so it’s necessary to determine appropriate weather stratification standards according to the actual weather conditions of nuclear power plant sites.

  2. (2)

    The weather input of CALPUFF is not the weather data at a certain moment, but a weather sequence containing the weather data changing with time and space. It is impossible to directly use the weather stratification standard to stratify the weather sequences, feature extraction of weather sequences may be needed to meet the weather stratification standard.

6 Conclusion

  1. (1)

    This paper puts forward the optimization method of HPR1000 emergency planning zone calculation. Based on different calculation models of atmospheric dispersion factors, it is suggested that CALPUFF based on Gaussian puff model is appropriate under the light wind and the calm wind conditions. Based on different weather sampling methods, it is proposed to select stratified random sampling to sample weather data from the annual weather data as the weather input for calculating atmospheric dispersion factor, which can reduce the calculation time and ensure the calculation accuracy.

  2. (2)

    There are two problems needed to be solved in the follow-up research: how to determine appropriate weather stratification standards to reflect the actual weather conditions of the nuclear power plant site and how to extract the features of CALPUFF weather sequences to meet the weather stratification standards.