Relative doses instead of relative concentrations for the determination of the consequences of the radiological atmospheric releases

Journal of Environmental Radioactivity 196 (2019) 1–8

Contents lists available at ScienceDirect

Journal of Environmental Radioactivity journal homepage: www.elsevier.com/locate/jenvrad

Relative doses instead of relative concentrations for the determination of the consequences of the radiological atmospheric releases

T

Primož Mlakar∗, Marija Zlata Božnar, Boštjan Grašič MEIS d.o.o., Mali Vrh pri Šmarju, Slovenia

ARTICLE INFO

ABSTRACT

Keywords: Radioactive air pollution Population dose calculation Relative concentrations Relative doses X/Q Atmospheric dispersion factor

Radiological atmospheric releases require population dose calculation for proper determination of preventive measures. The old concept of relative concentrations requires long lasting constant emission which is not realistic. The proposed concept of the “relative doses” is the generalization and expansion of the known concept of relative concentrations. Relative doses allow an evaluation of the general non-stationary pollutants emission under the real weather conditions over complex terrain. Relative doses can be calculated even before the actual source term – quantified emission - is known. The relative impact is also very useful for considering the possible impact of an accident scenario on the surroundings for various meteorological situations. This is applied for environmental impact assessments which require long term statistical evaluation. The method has a practical possible application for realistic dose assessment of effectiveness of additional protection achieved by installation of Passive Containment Filtered Venting Systems (PCFVS). PCFVS is considered an obligatory safety upgrade after the Fukushima accident.

1. Introduction In the event of an accident at a nuclear power plant, the emission of pollutants into the atmosphere impacts the surrounding environment over short time-scales before the protracted contamination of water and soil leads to the exposure of the population over longer periods. Hence, when evaluating the consequences, we wish to determine the actual state as quickly as possible. A radionuclide cloud would disperse from a nuclear power plant into the surrounding atmosphere depending on the initial buoyancy properties, kinetic energy and depending on the current meteorological properties of the surrounding atmosphere. The route of the cloud and the radionuclides' concentration in the cloud above the surrounding territory are described by models describing the dispersion of pollution in the atmosphere; these are typically referred to as “dispersion models” (Benamrane et al., 2013). The development of dispersion models has been going on for several decades, where it began with simple Gaussian models (Gifford, 1959; U.S. Nuclear Regulatory Commision, 1977), also in the nuclear field (U.S. Nuclear Regulatory Commision, 1979, 1977). However, since these models are only applicable for steady state conditions under relatively strong winds over flat terrain, the development of the models continued in various ways that also include very complex numerical methods. These are Gaussian puff, Eulerian and Lagrangian particle models (LGPM), ∗

whereas nowadays, computational fluid dynamics (CFD) models are making their way into practice. With regard to all models, the confirmation that they are able to realistically reproduce events in nature is of key importance. This process is usually called validation. Validation is testing model results on data on various tracer experiments that were measured in nature (Elisei et al., 1992; Mlakar et al., 2015a; Stocki et al., 2008; Van dop et al., 1998). The usual application of such models is that meteorological data and data on the mass flow of pollutant at the point of emission, dependent on time (also called source strength, unlike the total emission volume that we call source term) are used as input data. It is precisely these data - mass flow - that represent the key information that we usually do not have in time in the event of a nuclear accident involving an emission into the atmosphere and requires emergency pollutants dispersion modelling (Connan et al., 2013). We do not have it because it has yet to be evaluated, what kind of accident occurred and then, based on the instantaneous measurements or other procedures including the comparison with previous PSA categories, determined, as precisely as possible, the value of the source term for each radionuclide. However, since it is sensible that the calculations of the dispersion model already take place in advance (for various types of accidents) or at least simultaneously with the determination of the source term, such approaches have been recommended in U.S. Nuclear Regulatory

Corresponding author. MEIS d.o.o., Mali Vrh pri Šmarju 78, SI-1293, Šmarje - Sap, Slovenia. E-mail address: [email protected] (P. Mlakar).

https://doi.org/10.1016/j.jenvrad.2018.10.005 Received 9 July 2018; Received in revised form 15 October 2018; Accepted 15 October 2018 Available online 23 October 2018 0265-931X/ © 2018 Elsevier Ltd. All rights reserved.

Journal of Environmental Radioactivity 196 (2019) 1–8

P. Mlakar et al.

Commision Regulatory Guides (RGs): RG 1.111 (U.S. Nuclear Regulatory Commision, 1977), and RG 1.145 (U.S. Nuclear Regulatory Commision, 1979). These Regulatory Guides introduced the concept of “relative concentration” that is defined as “X/Q”:

X /Q =

X Q

legislation does not deal with the specifics of nuclear power plants. An example of annual statistical evaluation of effective dose is given in paper (Zali et al., 2017). After Fukushima accident Passive Containment Filtered Venting Systems (PCFVS) are considered an obligatory safety upgrade for all European nuclear power plants. Emissions through PCFVS have time dependent shape which is known in advance and is technology dependent. It is this time dependency that prevents the use of traditional relative concentrations. On the other hand our novel concept of relative doses inherently allows realistic evaluation of PCFVS emissions impact on the population.

(1) 3

3

where “X/Q” [s/m ] is relative concentration, “X” [Bq/m ] is the effluent concentration and “Q” [Bq/s] is the constant source strength. The dose rate received by an inhabitant who is exposed to the cloud and the inhalation of such polluted atmosphere is proportional to the thus defined relative concentration:

H (x , y , z ) = C X / Q ( x , y , z ) Q

2. Materials and methods

(2)

where “H” [Sv/s] is the dose rate at point (x,y,z), “C” [(Sv/s)/(Bq/m3)] is the dose conversion factor that is defined for half of a spherical cloud (cloud shine) or for inhalation, “X/Q (x,y,z)” [s/m3] is the relative concentration at point (x,y,z), and “Q” [Bq/s] is the constant source strength. However, sometimes the term “dispersion coefficient” was also established for such a defined relative concentration (U.S. Nuclear Regulatory Commision, 2003). The essence of this definition is in the fact that it presumes a time-constant unit speed of mass flow of the emitted pollutant. On the basis of the presumption, the dispersion model itself can calculate the relative concentrations without the actual emission being known. It was thus allowed with the introduction of relative concentrations that, upon an accident event, the meteorological dispersion model can be used to simulate the processes in the atmosphere even before the source term is known. This usually takes place in such way that the input in the dispersion model is the unit constant emission rate for the most probable locations of the emission from the nuclear power plant (e.g. ground emission, emission from the main ventilation, emission through the discharge of steam etc.). In such an instance, the model shows us the spatial distribution of the pollution cloud in the time when the accident takes place (diagnostic application). However, we may have calculations that are also prepared few days in advance to actual time based on prognostic weather data (Mlakar et al., 2015b). Materially speaking, such defined relative concentrations' most important shortcoming is in the fact that this is not the most realistic imitation of the actual state. The emission upon an accident, especially in the event of an explosion or using most advanced Containment Filtered Vent Systems (CFVSs) (Song et al., 2013), is not a continuous one and is not constant in time. The expected uneven form represents a significant deviation from the presumption of the classic relative concentration which is why it is not suitable for the realistic calculation of consequences in the atmosphere for such emissions. If we apply the classic concept of relative concentrations, we cannot, in the event of a prior-unknown source term, even with the most efficient numerical dispersion model, obtain sufficiently realistic answers as to what will happen or what is actually taking place in the natural atmosphere environment. We remedy this shortcoming by still wanting to prepare calculations before the source term is known and in such a way that we consider the actual expected and not the constant form of the mass flow of the emission into the atmosphere. We implemented these requirements by introducing novel concept of relative doses in this article. Relative doses allow the upgrade of the relative calculations that were established until now for actual nuclear accidents or for statistical prior considerations of possible emissions from a nuclear power plant for the purposes of an evaluation of the impact on the environment as it is usually done in the Updated Safety Analysis Report (USAR) documents (U.S. Nuclear Regulatory Commision, 2017). Thus far, this was regulated in the US legislation in RG 1.145 and RG 1.111, issued by the NRC. However, elsewhere in the world, we apply these two RG's as an example when the formal national

2.1. Relative dose methodology If we wish to evaluate the consequences of a nuclear accident even before the source term is known or before the accident actually occurs, we propose the introduction of relative doses. A relative dose is a dose relativized to the source term, i.e. to the total mass of the emitted pollutants and to emission's temporal and physical form of the exhaust (emitted pollutant quantities vary in time). In relation to the above-stated definition, the emission is, in principle, of a limited duration, it has a time-based uneven emission rate of pollutants and in general, the time-wise uneven remaining three key emission properties that impact the dispersion of the cloud when released into the atmosphere. These three emission properties are the mass flow of the outlet aerial masses, their temperature and the speed of the emitted masses. These three emission properties are key for the plume rise. In relation to the stated, we comprehend aerial masses as air and water vapour mixed with hazardous substances in the containment that behave like buoyant gases in the atmosphere. Dense gases or large particles require special type of dispersion model and are usually not treated in this frame. The methodology that we propose presumes that the time-based form of the emission is known in advance, however, only relatively given the expected total emission. In the first part of this chapter, we shall define the formulae for the calculation of relative doses. We shall implement the relative dose for three components of the impact of radionuclides on the population. These three components are the following: the relative dose due to inhalation, relative dose due to the radiation from the cloud and the relative dose rate due to the deposition. The implementation includes the relative dose for all three components. The formulae are derived in such a way that their application is possible for a general real situation. Thus, the locations where the population lives, may be at any given real location over a complex terrain, however, we require that we can realistically calculate the dispersion of the cloud over this complex terrain with the applied atmospheric dispersion model. An example of a realistic evaluation is given by Rakesh et al. (2015). 2.2. Definitions - relative dose implementation We call the aggregate of radionuclides that are released into the atmosphere an emission (also source term). An emission is composed of various radionuclides, each of which we know its activity at the time of the release of the emission into the atmosphere. In a calculation, we usually consider all the radionuclides that may be created in the reactor and released into the atmosphere. The range of these radionuclides is of course dependent on the reactor's technology. We will evaluate the example on the basis of which the aggregate of the radionuclides is dispersed in the surroundings after they are released into the atmosphere and then impact the inhabitants, by introducing the relative dose. However, in order to prepare the final calculation of the dose, the relativized impact of each individual radionuclide that is expressed 2

Journal of Environmental Radioactivity 196 (2019) 1–8

P. Mlakar et al.

Fig. 2. Presentation of the general form of pollutant emission rate Q(t) with discrete values Q (ti ) .

Fig. 1. Presentation of the general form of the pollutant emission rate Q(t).

with a relative dose must then be multiplied with its activity and the dose conversion factors, so that we then acquire the dose that the selected radionuclide causes to the population. Below are the formulae for calculating of the entire chain through the relative dose to the final dose. The entire calculation through the relative dose may, however, be also applied for the evaluation of the harmful effects due to exposure to non-radioactive substances.

the emission and then calculate the dispersion of the pollution cloud over the modelled domain. We call the discrete form as Q(ti) :

Q (¯ti ) =

Q (t ) dt t = t0

(5)

ti = t 0 + N T

A=T

Q (ti ) ti = t 0

(6)

where “A” [Bq] is the source term, “Q (ti ) ” [Bq/s] is the average source strength between time ti and ti + T, “T” [s] is the time averaging period, “N” is the number of periods, “ti” [s] is the discrete time, “t0” [s] is the starting time of the emission and “t” [s] is time. An example of presentation is in Fig. 2. However, we calculate the discrete emission using the following formula:

N (ti ) = Q (ti )/ A

(7)

where “N(ti)” [1/s] is the normalized average source strength between time ti and ti + T. “Q (ti ) ” [Bq/s] is the average source strength between time ti and ti + T, “T” [s] is the time averaging period, “ti” [s] is the discrete time and “A” [Bq] is the source term. Then we must normalize the time-dependent emission, which we give to the dispersion model, with the surface area (A) under the emission rate for the entire period. The emission that was relativized this way is the input data for the dispersion model. It is the task of the dispersion model that, in relation to the computational model domain, the given meteorological numerical data, the relative emission rate and the other physical parameters relating to the emission (e.g. the temperature of the emitted gases, chimney height, vertical speed of the emitted gases after discharge from the chimney), it calculates the concentrations in the 3D area above the considered model domain. Let us presume that the form of the function for the emission rate Q (t) is the same for all considered radionuclides or gas pollutants. However, its maximum value for each pollutant varies which is why the emissions of individual pollutants are also different. Despite the fact that this is a simplification that we introduced, it sufficiently reflects the actual state for the nuclear power plants when the containment air accumulates various radionuclides before their release into the atmosphere. We presume that these radionuclides or pollutants are evenly

(3)

where “A” [Bq] is the source term, “Q(t)” [Bq/s] is the source strength at the time “t” [s] and “t0” [s] is the starting time of the emission. However, we calculate the normalized source strength with the following formula:

N (t ) = Q (t )/ A

Q (t ) dt T

where “Q (ti ) ” [Bq/s] is the average source strength between time ti and ti + T, “Q(t)” [Bq/s] is the source strength at time t, “T” [s] is the averaging period, “ti” [s] is the discrete time. However, we calculate the source term A using the following formula:

2.2.1. Emission description Let Q(t) be the source strength or emission rate that is expressed with the unit of Bq/s or g/s. Q(t) has a general, but a priori known, expected form. An example of a presentation is in Fig. 1. The emission is limited in time and lasts from the beginning of the emission t0 to t0 + M*T, where T is the time interval in the dispersion model for the calculation of the concentrations of the radionuclide cloud in the atmosphere (this is usually 10 min, half an hour or 1 h), M is the number of calculation intervals when the emission finishes, and N is the number of calculation intervals – periods – when we monitor the passage of the cloud through the domain above which we are modelling the dispersion of the pollution in the atmosphere. Whereby it must be taken into account that M is less than N. The meteorological data is also usually given in the intervals of the calculation interval. This is the usual way how the computer implementation of the model calculates the dispersion. The integral of the pollutant emission rate Q(t), as presented in Formula (3), represents the total emission of the pollutant “A” that is expressed in Bq or g:

A=

t = ti+ T t = ti

(4)

where “N(t)” [1/s] is the normalized source strength at the time “t”, “Q (t)” [Bq/s] is the source strength at the time “t” [s] and “A” [Bq] is the source term. Some models have the option of the input of a detailed time-dependent emission Q(t), while others only offer the input of average in an individual calculation interval. We present an example for models where we must, for the purpose of the calculation of the entire chain of dose of population, calculate discrete values of Q(t) in such a way that we give the value of Q(t) for each calculation interval when we consider 3

Journal of Environmental Radioactivity 196 (2019) 1–8

P. Mlakar et al.

mixed together. Providing a detailed procedure for quantification of source term is beyond the scope of this article. For catastrophic scenarios, involving a major explosion in the core, each radionuclide should be calculated separately.

concentration in the modelled cell, we apply to this calculation the radiation shine from the cloud that impacts the considered modelled cell. Since we must, in principle and in such an instance, calculate the impact in 3D space over the modelled domain on the selected modelled cell, this is a numerically very complex procedure (Bedwell et al., 2010), for which we can introduce a few simplifications so that it is more time-effective. The description of such a simplification significantly exceeds the frame of this article which is why the reader may search for an example of one possible way of simplification of cloud shine calculation in our article on cloud shine calculation (Mlakar et al., 2014a). However, the calculation process from the virtual cloud coefficient through the relative dose due to cloud shine to the final dose due to cloud shine is the same as in the case of the dose due to inhalation. The difference is only that we must apply a suitable dose conversion factor for the dose due to cloud shine instead of that due to inhalation. These two dose conversion factors have different values, which reflects the path of radionuclides influence on the body. We define the virtual cloud coefficient as the quotient of the actual calculated cloud shine at the selected point in space and the total pollutant emission:

2.2.2. Relative dose due to the inhalation of the radionuclide cloud The most direct impact of the radionuclides' cloud that is released in the atmosphere onto the population, takes place through inhalation when the cloud also spreads to the ground layer where we presume, people are situated. In order to evaluate the impact due to inhalation, we must first introduce the virtual relative concentration vX/Q. It depends on the location above the domain in question (the location is determined by the spatial coordinates x, y, z) and the time t in which we monitor the value of the virtual relative concentration. We define the virtual relative concentration as the quotient of the actual calculated concentration of the pollutant in the selected point in space and the total pollutant emission:

vX / Q (x , y , z , t ) =

X (x , y , z , t ) A

(8)

3

where “vX/Q(x,y,z,t)” [1/m ] is the virtual relative concentration at point (x,y,z) and at time “t”, “X(x,y,z,t)” [Bq/m3] is the effluent concentration at point (x,y,z) and at the time t, and “A” [Bq] is the source term of the effluent. Based on vX/Q - virtual relative concentration - we implement the relative dose due to inhalation vX for the entire passage of the pollutant cloud over the domain. We propose that the relative dose that records the entire passage of the cloud, is marked with the time when the emission begins (t0). The relative dose is an integral of the virtual relative concentration in time:

vX (x , y , z , t 0) =

vX / Q (x , y, z, t ) dt t = t0

vC / Q (x , y , z , t ) =

where “vC/Q(x,y,z,t)” [1/m ] is the virtual cloud coefficient at point (x,y,z) and at time “t” [s], “C(x,y,z,t)” [Bq/m3] is the effluent cloud shine at point (x,y,z) and at time “t” [s], and “A” [Bq] is the source term of the effluent. We implement from vC/Q - the virtual cloud coefficient - the relative dose due to cloud shine vC for the entire passage of the cloud of the pollutant over the domain. We propose that the relative dose that records the entire passage of the cloud is marked with the time when the emission begins (t0). The relative dose is an integral of the virtual cloud coefficient in time:

(9)

where “vX(x,y,z,t0)” [s/m ] is the relative dose due to inhalation at point (x,y,z), “t0” [s] is the starting time of the emission, “vX/Q(x,y,z,t)” [1/m3] is the virtual relative concentration at point (x,y,z) and at time“t” [s]. However, if we calculate with discrete values of the virtual relative concentration, the formula is as follows:

vC (x , y , z , t 0) =

vX / Q (x , y, z, ti )

(13)

3

where “vC(x,y,z,t0)” [s/m ] is the relative dose due to cloud shine at point (x,y,z), “t0” [s] is the starting time of the emission, “vC/Q(x,y,z,t)” [1/m3] is the virtual cloud coefficient at point (x,y,z) and at time “t” [s]. However, if we calculate using the discrete values of the virtual coefficient, the formula is as follows:

(10)

ti = t 0 + N T

vC (x , y , z , t 0) = T

3

where “vX(x,y,z,t0)” [s/m ] is the relative dose due to inhalation at point (x,y,z) and the starting time of emission “t0” [s], “vX / Q (x , y , z , ti ) ” [1/m3] is the average virtual relative concentration at point (x,y,z) and at the discrete time “ti” [s], “T” [s] is the time averaging period and “N” is the number of periods. On the basis of the relative dose due to inhalation, we can, after the actual emission - source term - is known, calculate the dose due to inhalation EX in such way that we multiply the relative dose vX with the total emission and with the suitable dose conversion factor:

EX (x , y , z , t 0) = Cx A vX (x , y, z, t 0 )

vC / Q (x , y, z, t ) dt t = t0

ti = t0+ N T ti = t0

(12)

3

3

vX (x , y , z , t 0) = T

C (x , y , z , t ) A

vC / Q (x , y, z, ti ) ti = t 0

(14)

3

where “vC(x,y,z,t0)” [s/m ] is the relative dose due to cloud shine at point (x,y,z) and the starting time of the emission “t0” [s], “vC / Q (x , y , z , ti ) ” [1/m3] is the average virtual cloud coefficient at point (x,y,z) and at a discrete time “ti” [s],“T” [s] is the time averaging period and “N” is the number of periods. Based on the relative dose due to cloud shine, we can, when the actual emission - source term is known, calculate the dose EC in such way that we multiply the relative dose vC by the total emission and by a suitable dose conversion factor:

(11)

where “EX(x,y,z,t0)” [Sv] is the dose due to inhalation at point (x,y,z) and at the starting time of emission “t0” [s], “Cx” [(Sv/s)/(Bq/m3)] is the dose conversion factor defined for inhalation that incorporates the breathing rate, “vX(x,y,z,t0)” [s/m3] is relative dose at point (x,y,z), “A”[Bq] is the source term.

EC (x , y , z , t 0) = Cc A vC (x , y , z , t 0 )

(15)

where “EC(x,y,z,t0)” [Sv] is the dose due to cloud shine at point (x,y,z) and at the starting time of emission “t0” [s], “Cc” [(Sv/s)/(Bq/m3)] is the dose conversion factor defined for cloud shine, “vC(x,y,z,t0)” [s/m3] is the relative dose due to cloud shine at point (x,y,z), “A” [Bq] is the source term, and “t” [s] is time.

2.2.3. Relative dose due to cloud shine In the same way as we implemented the series of formulae for the impact of radionuclides on the dose due to inhalation, we also implement the series of formulae for the impact due to cloud shine. The key difference is expected in the sense that instead of the

2.2.4. Relative deposition dose rate after the cloud's passage The dispersion models also allow for the possibility of calculating the deposition. We usually include three types of deposition in the total 4

Journal of Environmental Radioactivity 196 (2019) 1–8

P. Mlakar et al.

deposition - a dry and wet deposition and the deposition on the surfaces due to a cloud's passage (touch factor). Further divisions are also possible, especially in the case of a wet deposition. The details about the implementation of a deposition calculation are beyond the scope of this article and dependent on the implementation of the air pollution dispersion model. However, in the calculation of the dose due to the deposition after a cloud's passage, there is a significant difference with regard to the remaining two components (due to inhalation and due to cloud shine). The remaining two components are different from zero only during the passage of a radioactive cloud over a domain. The dose due to deposition after the passage of a cloud is proportional to the exposure time of an inhabitant to this ground-deposited activity which is independent of the time that elapsed for the passage of a cloud over a domain. This is why we will present in this subchapter the calculation of a dose rate and not of a dose as in the previous two subchapters. To this end, we must first, similar to the virtual relative concentration, define the virtual deposition rate coefficient from which we can then implement the relative dose rate. In the final calculation of the dose rate due to deposition, we must apply a suitable dose conversion factor for the impact on the dose rate due to the deposition. We define the virtual relative deposition rate as the quotient of the actual calculated deposition rate of the pollutant in the selected point in space and the total pollutant emission:

vD / Q (x , y, t ) =

D (x , y , t ) A

after the cloud has passed the domain, “t0” [s] is the starting time of emission, “Cd” [(Sv/s)/(Bq/m2)] is the dose conversion factor defined for deposition, “vD(x,y,t0)” [1/m2] is the relative deposition dose rate at point (x,y,z = 0), and “A” [Bq] is a source term. 2.3. Implementation of relative doses in a software package As an implementation example we have applied the Lagrangian particle model SPRAY for the dispersion model (Tinarelli et al., 2000) together with the mass-consistent model for a wind field MINERVE (Geai, 1987), and the meteorological pre-processor SURFPRO (Anfossi et al., 1998). However, the preparation of the input data, the results' data base, the software for the evaluation and presentation of the results and the software for the calculation of relative doses and doses are made by using Environmental Information System (EIS) (Božnar et al., 2017; Grašič et al., 2017) and DOZE (Breznik et al., 2003; Mlakar et al., 2014a). The emission is limited in time, whereby the computer simulation must last long enough for the pollutants to leave the model's domain. The simulation lasts from the beginning of the emission t0 to the maximum t0 + N*T, where T is the time-based calculation interval in the dispersion model for the calculation of the concentrations of the radionuclide cloud in the atmosphere. The relative emission rate that was calculated in accordance with formula (4) or (7) is the input data for the dispersion model. It is the task of the dispersion model that, in relation to the domain in question, the given meteorological numerical data, the relative emission rate and the other physical parameters relating to the emission (e.g. the temperature of the emitted gases, chimney height, vertical speed of the emitted gases upon the exhaust from the chimney), it calculates the concentrations in the 3D area above the considered model domain. Concentrations are changeable in time and place. The concentrations with such defined relativized emission are already virtual relative concentrations. After the stated, we must also calculate in the same manner the virtual cloud coefficients and the virtual relative deposition rate. We must store all the results - 2D fields for all three virtual coefficients - in the data base for each separately for all calculation intervals from the beginning of the emission to the number of half-an-hour intervals when we monitor the passage of a cloud over the entire domain and when we presume that the cloud will be carried out of the domain after this time. We calculate the relative dose due to inhalation vX using formula (10). Similarly, we also calculate the relative dose due to cloud shine vC, based on formula (14) and the relative deposition dose rate vD using formula (18). In the following chapters, we describe the implementation of the calculated example of a relative dose in more detail.

(16) 2

where “vD/Q(x,y,t)” [(1/m )/s] is the virtual relative deposition rate at point (x,y,z = 0) and at time “t” [s], “D(x,y,t)” [(Bq/m2)/s] is the effluent deposition rate at point (x,y,z = 0) and at time “t” [s], and “A” [Bq] is the source term of the effluent. From vD/Q - the virtual relative deposition rate - we implement the relative deposition dose rate vD after the passage of a pollutant cloud over a domain. We propose that the relative deposition dose rate that records the entire passage of the cloud, is marked with the time of the beginning of the emission (t0). The relative deposition dose rate is an integral of the virtual relative deposition rate in time:

vD (x , y, t0 ) =

vD / Q (x , y , t ) dt t = t0

(17)

2

where “vD(x,y,t)” [1/m ] is the relative deposition dose rate at point (x,y,z = 0) after the cloud has passed the domain, “t0” [s] is the starting time of the emission, “vD/Q(x,y,t)” [(1/m2)/s] is the virtual relative deposition rate at point (x,y,z = 0) and at time “t” [s] that is changeable during the cloud passage and constant after it if we do not take into account the radioactive decay. However, if we calculate using the discrete values of the virtual relative deposition rate, the formula is as follows: ti= t0 + N T

vD (x , y, t0 ) = T

vD / Q (x , y , ti ) ti= t0

3. Results

(18)

where “vD(x,y,t0)” [1/m2] is the relative deposition dose rate at point (x,y,z = 0) after the cloud has passed the domain, “t0” [s] is the starting time of the emission, vD / Q (x , y, ti ) [(1/s)/m2] is the average virtual relative deposition rate at point (x,y,z = 0) and at the discrete time “ti” [s], “T” [s] is the time averaging period and “N” is the number of periods. We can, from the relative deposition dose rate after the passage of a cloud, once the actual emission - source term is known, calculate the dose rate in such a way that we multiply the relative deposition dose rate vD with the total emission and with a suitable dose conversion factor for the deposition:

H (x , y , t 0 ) = Cd A vD (x , y , t 0)

In this chapter, we give an example of a relative dose calculation. We carried out the calculation based on old validation data from the example of Šoštanj 1991. The experiment is well-documented in the literature (Elisei et al., 1992; Mlakar et al., 2015a). However, in this chapter, we only state the key descriptions that are relevant for understanding the case based on which we demonstrated the relative dose calculation. Šoštanj 1991 is a dataset that describes the air pollution measurement campaign that was carried out in 1991 with the purpose of collecting data for the validation of dispersion models over very complex terrain on the domain measuring 15 km × 15 km in the vicinity of the Šoštanj thermal power plant in Slovenia. The campaign was carried out by the institutions Jožef Stefan Institute from Ljubljana, Slovenia, and the ENEL and CISE institutes from Milan, Italy. The authors of this

(19)

where “H(x,y,t0)” [Sv/s] is the deposition dose rate at point (x,y,z = 0) 5

Journal of Environmental Radioactivity 196 (2019) 1–8

P. Mlakar et al.

article, Mlakar and Božnar, participated in the implementation. The dataset is described in detail in several articles, however, we rearranged it in the form that is suitable for current software tools in the scope of the testing of dispersion models in the International Atomic Energy Agency (IAEA) programme MODARIA (International Atomic Energy Agency, 2017). The descriptions of the measurement campaign and the newly arranged dataset are available in article (Mlakar et al., 2014b). Out of the experimental data, we only applied the static data on the domain for this demonstration (terrain, land use), the measured meteorological data from ground level stations and the vertical wind profile from SODAR. At the location where the thermal power plant is situated, we set up a fictional chimney, and the consequential emissions of which we wished to monitor effects on population in the form of a relative dose. 3.1. Meteo case Šostanj 1991 and Spray LGPM As an example of the calculation of a relative dose due to cloud inhalation, we selected a meteorologically simple day, before noon and early afternoon on 30 March 1991 when the wind was blowing directly from the power plant towards the Veliki Vrh hill (with the environmental measuring station) that is one of the hills in the second set of hills south of the power plant chimneys. We applied models Minerve, SURFPRO and SPRAY for which we have proven in the previous validations that are capable of realistically reconstructing the dispersion of pollution in the atmosphere over such complex terrain (Grašič et al., 2011).

Fig. 4. The sequence of the discharged particles images in 3D perspective (view from above, contours and colours from cyan, then green and finally brown show the relief from basin bottom to high mountain, contours represent the heights above the ground, red dots represent Lagrangian particles shown in perspective in the air above the ground). The domain is 15 km × 15 km wide with centre in the town of Šoštanj, Slovenija (46.375N, 15.049E). Emission started at 10:00 on 30 March 1991. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

virtual relative concentrations that demonstrate the time evolution of dispersion of the emitted plume gases. Virtual relative concentration is the first step in calculation as described in formula (8). Under the conditions over the complex terrain in Šoštanj, the cloud of effluents, due to the considerable plume rise due to its buoyancy and the kinetic energy, only touched the ground in a few areas. We can monitor in the sequence of images how intense was the impact of the emission on the virtual relative concentrations in the first hours of the emission and how it was gradually lost after the finished emission as the cloud moved out of the observed modelling domain. As defined in the Methodology chapter, we calculated from the virtual relative concentrations for the emission that started at 10:00, the relative dose due to inhalation. The relative dose is marked at the beginning of the emission interval. In this relative dose due to inhalation, we summarise all the consequences of this formed 3-h emission that was caused by the passage of a cloud. The relatively strong wind carried most of the cloud after the completion of the emission out of the observed domain within 2 h. The time of calculation is 5 h. Let us presume that the source term for our case is 1.0e10 Bq iodine I-131. In the International Atomic Energy Agency report (International Atomic Energy Agency, 2001), the dose conversion factor in the inhalation of an adult 8400 m3/a (equals 2.66e-4 m3/s) of air is 7.1e-9 [(Sv/h)/(Bq/m3)] (equals 1.97e-12 [(Sv/s)/(Bq/m3)]). Based on formula (11), we calculate the relative dose due to inhalation for the maximum value vX that is 4.44e-06 s/m3 as shown on Fig. 6. The calculated inhalation dose is 8.76E-08 Sv. In the calculation, we did not consider the decay of I-131, as its halflife is significantly longer than the time of calculation which is 5 h. The demonstrated example graphically represents the manner of the relative dose calculation. The selected example of a calculation may be expanded to any initial hour of emission in a series of measured data on the meteorological events of the case in question. In this way, we can review and compare how the relative dose changes are only due to the different meteorological conditions. It is realistic to expect over a complex terrain that various meteorological conditions may strongly emphasize or reduce the consequences of the emission into the atmosphere. The calculations for a longer time period, usually for several years of considered consequences of possible various terms of emissions from a nuclear power

3.2. Emission of known properties We placed on the location of the thermal power plant from the dataset Šoštanj 1991, a virtual chimney that is 100 m high and measures 2 m in diameter, and the emissions of which serve us for the demonstration of the relative doses' calculation. The modelling system is set to 30-min averages. We have chosen for demonstration the relative normalized emission rate that has the values and the form as presented in Fig. 3: The temperature of the chimney emissions is set to a constant 200 °C for the entire period, while the vertical velocity of the plume gases in the chimney was set to a constant 10 m/s. We set the time of the beginning of the emission release at 10:00 on 30 March 1991. 3.3. Relative dose due to inhalation In Fig. 4, we first show the sequence of the 3D movement of the virtual mathematic particles that the Lagrangian particle model applies to demonstrate the dispersion. In Fig. 5, we demonstrate the 2D fields of average 30-min ground

Fig. 3. The normalized emission that we applied. 6

Journal of Environmental Radioactivity 196 (2019) 1–8

P. Mlakar et al.

Fig. 5. The sequence of images of the average 30-min virtual relative concentrations for the ground layer.

atmosphere. This means, for emissions that have a non-constant function of their emission rate, a defined beginning and end of emission duration, and in between a real defined form. A typical example is emission pattern from PCFVS – nowadays the most advanced filtering system for NPPs (Song et al., 2013). The emission temporal form at PCFVS depends on particular technical implementation details. However, even if we do not have a known emission temporal form like at PCFVS, we can benefit from using relative dose approach. If no better information is available, we can at least treat the emission temporal form as simple geometric shape. The relative concentrations that were applied until now presume the constant unit emission rate and do not allow for such consideration. Thus, the proposed relativization represents progress towards a realistic evaluation of the consequences of emissions into the atmosphere for the population dose. In the article, we did not especially deal with the dispersion model, as it represents an independent issue, which is not relevant for relativization. It is important that the applied dispersion model is efficient enough for the field of application and that the evaluation of the potential accidental emissions from the nuclear power plant prior to the application is successfully validated over a similarly complex terrain based on the tracer experiment. Only under such terms can we trust the model's calculations. Validation should be done using an appropriate methodology. We proposed one of the possible methodologies in our article (Grašič et al., 2011) where we successfully validated the set of models Spray and Minerve on the complex terrain experimental data set Šoštanj 1991.

Fig. 6. Relative dose due to inhalation vX for the emission that started at 10:00 on 30 March 1991. The maximum value vX is 4.44e-06 s/m3 in cell x = 46 and y = 29 of the domain that has 100 × 100 grid cells or a size of 15 km × 15 km.

plant are a standard tool for the statistical evaluation of a range of possible impacts on the surroundings as part of Updated Safety Analysis Report (International Atomic Energy Agency, 2004; U.S. Nuclear Regulatory Commision, 2017).

5. Conclusions In the article, we introduced a new method of virtual relative concentrations or coefficients and the relative doses. They both replace the relative concentrations applied up to now, as introduced by RG 1.111 and RG 1.145. The usual relative concentrations presume a time constant emission rate. This is an essential limitation that disables the realistic evaluation of the changeable emission rate as a consequence of

4. Discussion The relativization through the relative doses and the virtual relative coefficients as proposed in this article allow the consideration of the impact on the environment for non-constant emissions into the 7

Journal of Environmental Radioactivity 196 (2019) 1–8

P. Mlakar et al.

a real emission in the event of an accidental event in a nuclear power plant. The new proposed method allows a realistic consideration of the consequences of the time changeable emission rates. This represents a significant step forward to a more realistic consideration of the consequences in the form of a dose for the population due to an emission upon an accidental event with the release of radionuclides into the atmosphere. Regarding the calculation procedures, the reader should note the following details. Upon the presumption that various radionuclides in the emission are homogeneously distributed between each other (i.e. in a constant share given the total emission), all relative doses of individual radionuclides are the same and we can calculate them only once. If the proportions of particular radionuclides are not constant in time relative to the total emission, then the entire calculation procedure should be repeated for each radionuclide separately. In that case, in general, the set of proposed formulae is also valid in the event that we must presume, for each radionuclide, its own, unique, time dependent form of emission. This would be appropriate when we wish to consider, for each nuclide separately, its dispersion due to the greater accuracy of the calculation. Under other envisaged situations, due to various reactions in the reactor, firstly, noble gases are formed and are immediately released into the atmosphere, and later on, particulates are also released into the atmosphere. In such cases of uneven time dependent forms of emissions, we must calculate the relative dose for each radionuclide or a group of radionuclides separately. All these features of the proposed new method allow realistic evaluation of air pollution following emission through PCFVSs for NPPs. The proposed relativization concept allows prior calculations of realistic scenarios, which are important for training. However, for a larger scale considering longer time period meteorological data sets, we can calculate a realistic possible range of consequences in the surroundings due to an accidental emissions into the atmosphere. This involves the procedure of evaluating the possible impact of the facility on the environment where this is firstly considered to be the human population, but if we change the dose conversion factors (in formulas (11), (15) and (19)), the same formulae can be used to determine impacts on plants and animals as well. In conclusion, the method is suitable for the application in emergency preparedness plans.

models. Int. J. Environ. Pollut. 20, 278–285. https://doi.org/10.1504/IJEP.2003. 004291. Connan, O., Smith, K., Organo, C., Solier, L., Maro, D., Hébert, D., 2013. Comparison of RIMPUFF, HYSPLIT, ADMS atmospheric dispersion model outputs, using emergency response procedures, with 85Kr measurements made in the vicinity of nuclear reprocessing plant. J. Environ. Radioact. 124, 266–277. https://doi.org/10.1016/J. JENVRAD.2013.06.004. Elisei, G., Bistacchi, S., Bocchiola, G., Brusasca, G., Marcacci, P., Marzorati, A., Morselli, M.G., Tinarelli, G., Catenacci, G., Corio, V., Daino, G., Era, A., Finardi, S., Foggi, G., Negri, A., Piazza, G., Villa, R., Lesjak, M., Božnar, M.Z., Mlakar, P., Slavic, F., 1992. Experimental Campaign for the Environmental Impact Evaluation of Šoštanj Thermal Power Plant, Progress Report. Milano, Italy and Ljubljana, Slovenia. Geai, P., 1987. Methode d'Interpolation et de Reconstitution Tridimensionelle d’un Champ de Vent: le Code d'Analyse Objective MINERVE. Report EDF/DER, HE/3487.03. . Gifford, F., 1959. Statistical Properties of a Fluctuating Plume Dispersion Model. pp. 117–137. https://doi.org/10.1016/S0065-2687(08)60099-0. Grašič, B., Mlakar, P., Božnar, M.Z., 2011. Method for validation of Lagrangian particle air pollution dispersion model based on experimental field data set from complex terrain. In: Nejadkoorki, D.F. (Ed.), Advanced Air Pollution. INTECH Open Access Publisher, pp. 535–556. https://doi.org/10.5772/17286. Grašič, B., Mlakar, P., Božnar, M.Z., Popović, D., 2017. EIS – Opis Baze Podatkov in Nadzora Delovanja. (MEIS storitve za okolje d.o.o., Mali Vrh pri Šmarju). International Atomic Energy Agency, 2017. MODARIA: Modelling and Data for Radiological Impact Assessments. [WWW Document]. http://www-ns.iaea.org/ projects/modaria/default.asp?l=116, Accessed date: 7 November 2017. International Atomic Energy Agency, 2004. Format and Content of the Safety Analysis Report for Nuclear Power Plants. IAEA Safety Standards Series. International Atomic Energy Agency, Vienna. International Atomic Energy Agency, 2001. Generic Models for Use in Assessing the Impact of Discharges of Radioactive Substances to the Environment. Safety Reports Series No.19. Vienna. Mlakar, P., Božnar, M.Z., Breznik, B., 2014a. Operational air pollution prediction and doses calculation in case of nuclear emergency at Krško Nuclear Power Plant. Int. J. Environ. Pollut. 15, 184–192. https://doi.org/10.1504/IJEP.2014.065119. 54. Mlakar, P., Božnar, M.Z., Grašič, B., Brusasca, G., Tinarelli, G., Morselli, M.G., Finardi, S., 2015a. Air pollution dispersion models validation dataset from complex terrain in Šoštanj. Int. J. Environ. Pollut. 57. https://doi.org/10.1504/IJEP.2015.074507. Mlakar, P., Božnar, M.Z., Grašič, B., Brusasca, G., Tinarelli, G., Morselli, M.G., Finardi, S., 2014b. “Šoštanj” data set for validation of models over very complex terrain. In: HARMO 2014 - 16th International Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes, Proceedings. Mlakar, P., Grašič, B., Božnar, M.Z., Borut, B., 2015b. Online relative air dispersion concentrations one week forecast for Krško NPP prepared for routine and emergency use. In: Jenčič, I. (Ed.), 24th International Conference Nuclear Energy for New Europe - NENE 2015, Portorož, Slovenia, September 14-17. Nuclear Society of Slovenia, Ljubljana, pp. 601–602. Rakesh, P.T., Venkatesan, R., Hedde, T., Roubin, P., Baskaran, R., Venkatraman, B., 2015. Simulation of radioactive plume gamma dose over a complex terrain using Lagrangian particle dispersion model. J. Environ. Radioact. 145, 30–39. https://doi. org/10.1016/J.JENVRAD.2015.03.021. Song, Y.M., Jeong, H.S., Park, S.Y., Kim, D.H., Song, J.H., 2013. Overview of containment filtered vent under severe accident conditions at Wolsong NPP unit 1. Nucl. Eng. Technol. 45, 597–604. https://doi.org/10.5516/NET.03.2013.712. Stocki, T.J., Armand, P., Heinrich, P., Ungar, R.K., D'Amours, R., Korpach, E.P., Bellivier, A., Taffary, T., Malo, A., Bean, M., Hoffman, I., Jean, M., 2008. Measurement and modelling of radioxenon plumes in the Ottawa Valley. J. Environ. Radioact. 99, 1775–1788. https://doi.org/10.1016/J.JENVRAD.2008.07.009. Tinarelli, G., Anfossi, D., Trini Castelli, S., Bider, M., Ferrero, E., 2000. A new high performance version of the Lagrangian particle dispersion model Spray, some case studies. In: Gryning, S.-E., Batchvarova, E. (Eds.), Air Pollution Modeling and its Application XIII. Springer US, Boston, MA, pp. 499–507. https://doi.org/10.1007/ 978-1-4615-4153-0_51. U.S. Nuclear Regulatory Commision, 2017. U.S. Nuclear Regulatory Commission Regulations: Title 10, Code of Federal Regulations, Part 50—domestic Licensing of Production and Utilization Facilities, vol. 50 34 Contents of applications; technical information. [WWW Document]. https://www.nrc.gov/reading-rm/doc-collections/ cfr/part050/full-text.html. U.S. Nuclear Regulatory Commision, 2003. Regulatory Guide RG 1.194, Atmospheric Relative Concentrations for Control Room Radiological Habitability Assessments at Nuclear Power Plants. [WWW Document]. https://www.nrc.gov/docs/ML0315/ ML031530505.pdf, Accessed date: 7 November 2017. U.S. Nuclear Regulatory Commision, 1979. Regulatory Guide RG 1.145, Atmospheric Dispersion Models for Potential Accident Consequence Assessment at Nuclear Power Plants. [WWW Document]. https://www.nrc.gov/docs/ML0037/ML003740205. pdf, Accessed date: 7 November 2017. U.S. Nuclear Regulatory Commision, 1977. Regulatory Guide RG 1.111, Methods for Estimating Atmospheric Transport and Dispersion of Gaseous Effluents in Routine Releases from Light-water-cooled Reactors. [WWW Document]. https://www.nrc. gov/docs/ML0037/ML003740354.pdf, Accessed date: 7 November 2017. Van dop, H., Addis, R., Fraser, G., Girardi, F., Graziani, G., Inoue, Y., Kelly, N., Klug, W., Kulmala, A., Nodop, K., Pretel, J., 1998. ETEX: a European tracer experiment; observations, dispersion modelling and emergency response. Atmos. Environ. 32, 4089–4094. https://doi.org/10.1016/S1352-2310(98)00248-9. Zali, A., Shamsaei Zafarghandi, M., Feghhi, S.A., Taherian, A.M., 2017. Public member dose assessment of Bushehr Nuclear Power Plant under normal operation by modeling the fallout from stack using the HYSPLIT atmospheric dispersion model. J. Environ. Radioact. 171, 1–8. https://doi.org/10.1016/J.JENVRAD.2017.01.025.

Acknowledgement The authors acknowledge projects (“Method for the forecasting of local radiological pollution of atmosphere using Gaussian process models” ID L2-8174, “Assesment of natural and antropogenic processes in micrometeorology of Postojna cave system by numerical models and modern methods of data aquisition and transfer” ID L2-6762, and “Karst research for sustainable use of Škocjan Caves as World heritage” ID L7-8268) were financially supported by the Slovenian Research Agency. References Anfossi, D., Desiato, F., Tinarelli, G., Brusasca, G., Ferrero, E., Sacchetti, D., 1998. TRANSALP 1989 experimental campaign—II. Simulation of a tracer experiment with Lagrangian particle models. Atmos. Environ. 32, 1157–1166. https://doi.org/10. 1016/S1352-2310(97)00191-X. Bedwell, P., Wellings, J., Haywood, S.M., Hort, M.C., 2010. Cloud gamma modelling in the UK Met Office's NAME III model. In: Proc 13th International Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes (Paris, France), pp. 441–444. Benamrane, Y., Wybo, J.-L., Armand, P., 2013. Chernobyl and Fukushima nuclear accidents: what has changed in the use of atmospheric dispersion modeling? J. Environ. Radioact. 126, 239–252. https://doi.org/10.1016/J.JENVRAD.2013.07.009. Božnar, M.Z., Mlakar, P., Grašič, B., Popović, D., Kokal, D., 2017. Program Za Pregledovanje Podatkov MUNGO. Mali Vrh Pri Šmarju. Breznik, B., Boznar, M.Z., Mlakar, P., Tinarelli, G., 2003. Dose projection using dispersion

8