RASCAL code was developed by U.S. NRC for the purpose of independent assessment of dose projections during the response to radiological emergencies. RASCAL could provide the rapid assessment of an incident or accident and help a decision-making process of implementing protective actions [6]. The source term to dose (STDose) module in RASCAL was used to evaluate projected radiation doses from the plume of the released radioactive substances to the public downwind based on input information of plant conditions. This STDose module first generated time-dependent source terms which then provided the input to an atmospheric dispersion and transport model. In this study, an accident scenario of LTSBO was simulated. In order to calculate the dose to the population, the STDose module included the information on event type, event location, source term, release path and meteorological data. Gaussian plume and Gaussian puff models have been employed for the atmospheric transport, diffusion and deposition of radioactive materials in the vicinity of release point.

The conventional straight Gaussian equation used in RASCAL as follows [7]

And, a simplified version of the straight-line Gaussian model was expressed as;

where,

X = average concentration,

Q' = release rate,

F_y, F_z = lateral and vertical exponential terms,

x= downwind distance at which X , and are evaluated,

u = wind speed,

t = time

RASCAL could not consider the effect of secondary building such as auxiliary building, and hence it did not delay radioactive material’s movement between the fuel and containment or between containment and the atmosphere, which was probably the main contribution to the overestimates [7]. RASCAL also simulated the reduction mechanism as a single filter at the point of release to the atmosphere rather than a time-varying depletion mechanism in containment [8]. This consequence assessments were based on simple models and had inherent uncertainties for their estimates.

The HYSPLIT model using Lagrangian dispersion formula is a complete system for computing simple air parcel trajectories, as well as complex transport, dispersion, chemical transformation and deposition simulations. HYSPLIT can estimate forward and backward trajectory of air mass by assuming either puff or particle dispersion based on meteorological data. HYSPLIT model is often driven by meteorological data from the Global Data Assimilation System (GDAS) which has a horizontal resolution of 1° which corresponds to about 100 km×100 km and 23 vertical layers. Considering a particle, the particle follows the wind and its trajectory is just the integration of the particle position vector in space and time (t). The final position can be computed from the average velocity (V) at the initial position (P) and first‐guess position (P′). The computation of new position at a time step (t+∆t) due to the mean advection by wind determines the trajectory that a particle or puff will follow [9].

Equations above are the basis for the calculation of trajectories in HYSPLIT. Only the advection component is considered when running trajectories. The turbulent dispersion component is only needed to describe the atmospheric transport and mixing processes for three-dimensional movement of particles and puffs [10]. Dispersion equations are formulated in terms of the turbulent velocity components. In the three-dimensional model of particles, the dispersion process is represented by adding a turbulent component to the mean velocity obtained from the meteorological data, namely,

where,

U′ and W′ correspond to the turbulent velocity components, X_mean and Z_mean are the mean components of particle positions, X_final and Z_final are the final positions in the horizontal and vertical, respectively.

In order to understand the modeling of atmospheric dispersion of radionuclide releases in the event of a severe NPP accident, benchmarking of FDNPP accident was performed. This FDNPP accident involved very complicated accident sequences and large atmospheric radioactive releases. The accident was due to the Japan earthquake and tsunami of March 2011 that led to LTSBO and damaged the nuclear reactor’s safety features. FDNPP experienced core melt, hydrogen explosions (unit 1 and unit 3) and the releases of significant radioactive materials from 12^th to 15^th March 2011. Reactor cores of unit 1 and unit 3 were uncovered for more than 12 hours. Table 1, Table 2 and Table 3 showed the time sequences of FDNPP unit 1, unit 2 and unit 3, respectively, immediately after the accident. Reactors of FDNPP were boiling water reactors (BWRs) designed with Mark I containment. The source term merge tool in RASCAL was used to calculate source term by combining consequences of multi-reactor events for two or more reactors at a single site. The simulation considered a period of 11^th to 15^th March 2011 and the releases were observed for 96 hours after the core melt. Drywell and direct releases were considered as the release pathway. Leak rates were adjusted according to the accident sequence in the report of Institute of Nuclear Power Operations (INPO) [11] and they were used in RASCAL. RASCAL’s default leak rate for BWR was 0.5% volume per day. This leak rate was changed from 0.5% volume per day to 1% volume per hour at the beginning phase of core damage. It was changed to 25% volume per hour for 1 hour for the containment venting and to 50% volume per hour for 1 hour following the hydrogen explosions of unit 1 and unit 3. After the containment venting and hydrogen explosions, the leak rate was returned to 1% volume per hour [11].

This study analyzed radiological consequences that would occur if both unit 3 and unit 4 at Shin Kori NPP underwent a core melt. Unit 3 and unit 4 of Shin Kori NPP are APR1400 type reactors which are two-loop PWRs supplying a rated thermal output of 4,000 MWt or electrical output of 1,400 MWe, respectively. An accident scenario of LTSBO imbedded in RASCAL was applied to derive source terms as shown in Table 4 and Table 5. This scenario considered unmitigated scenario which would occur if operators failed to carry out key mitigation measures to prevent the accident from progressing. Ulsan’s wind data from Korea Meteorological Administration (KMA) for the year of 2018 was analyzed using wind rose as shown in Fig. 1. It was observed that the frequent wind direction of the east occurred in the month of August and would cause the most harmful effect on the atmospheric dispersion and ground deposition of radionuclides into the inland of Korea after the event of an accident. Because most NPPs in Korea were located at coasts, sea-land breeze effect was relatively high. Therefore, it was expected that wind direction and wind speed had a large effect on the atmospheric dispersion of radioactive materials in the case of a severe accident.

Total amount of source terms released from FDNPP to the atmosphere was estimated to be 1.3×10¹⁸ Bq using RASCAL code. Noble gases consisted of significant parts in the early releases from FDNPP. However, noble gases did not contribute to ground depositions and their releases had minor influences on the radiological consequences to the general public. ¹³¹I and ¹³⁷Cs were found to be the most important radionuclides because they had a high activity of 100~400 PBq for ¹³¹I and 7~20 PBq for ¹³⁷Cs [12]. These two radionuclides adversely affected human health through the contamination of air, water, soil and food [13]. Table 6 and Table 7 showed source terms for radionuclides important to the exposure doses and accumulated doses, respectively. ¹³³Xe had the highest source term because of its large inventory of 61% at the point of reactor shutdown [12]. Additionally, Fig. 2 and Fig. 3 illustrated total releases of the main radionuclides important to the exposure doses with time and foot print of the accumulated TEDEs within 8 km and 40 km, respectively. According to the simulation results above, it was found that the population within 30 km would receive radiation doses greater than 10 mSv in the first 4 days and would require immediate protective actions for sheltering-in-place. In this study, only source terms for ¹³¹I and ¹³⁷Cs were compared with other previous results as shown in Table 8 and Fig. 4 [14~19]. Further, comparisons of release rates between this study and previous estimates using inverse modeling were carried out in order to find the correlation as shown in Fig. 5 [20]. The highest peaks of the release rates were observed due to the explosions on 12^th and 14^th March of unit 1 and unit 3, respectively. The differences were attributed to the assumed values of leakage rates, mathematical models, computer codes and uncertainties in the measured values. Along with the leakage rates used in this study, the high concentration of ¹³⁷Cs and ¹³¹I might be attributed to RASCAL because it could not consider an effect of secondary building, and thus there was no delay in the movement of radioactive materials between the reactor fuel and containment or between containment and the atmosphere. The source terms published by IAEA in 2015 were derived using inverse modelling and accident progression [12]. Inverse modelling involved a comparison of measurements in the environment with estimates derived from simulations. The release rates of source terms obtained from RASCAL were then applied to HYSPLIT code. The top six radionuclides of ¹³⁷Cs, ¹³⁴Cs, ¹³³Xe, ¹³¹I, ¹³²Te and ¹³²I were analyzed because they were important to the public doses in the first week of a nuclear accident [21,22]. The air parcel forward trajectories using HYSPLIT code showed that air parcels originating from FDNPP after the accident moved into Pacific Ocean on 12 March and continued to move mostly to the northeastward as shown in Fig. 6 and Fig. 7. Most releases were dispersed over Pacific Ocean whereas some of the releases were dispersed over Japan’s main land causing areas of significant deposit. Airborne concentrations ranged from 3.2×10⁶ to 1.4×10¹⁶ Bq･m^-3 whereas maximum and minimum depositions of 1.7×10⁸ Bq･m^-2 and 6.3×10^-15 Bq･m^-2, respectively, in 96 hours were estimated in this study.

Source terms of Shin Kori NPP unit 3 and unit 4 were calculated through the simulation of 4 days using RASCAL as shown in Table 9. Total amount of radioactive materials released was estimated to be 4.1×10¹⁶ Bq which was less than source terms of FDNPP, 1.3×10¹⁸ Bq as previously mentioned. ¹³³Xe contributed the highest fraction of the source term because this radionuclide was attributed to the large inventory within the nuclear reactor. Additionally, ¹³¹I was the radionuclide of concern due to the source of internal exposure of thyroid gland and its amount was estimated to be 9.3×10¹⁴ Bq. The merging technique of source terms provided a means to calculate radiation doses of gaseous releases from multiple units at a single site as shown in Table 10. It was found that estimated TEDEs within PAZ (5 km) ranged from 11 mSv at 4.83 km to 50 mSv at 1.61 km from Shin Kori NPPs. And, the release rates of the main radionuclides important to the radiation doses and TEDEs within 8 km and 40 km were depicted in Fig. 8 and Fig. 9, respectively. No deterministic effects would be expected since the maximum TEDE fell below 100 mSv. And, deterministic thyroid effects would not be expected to occur because the highest thyroid CDE received by a person in 50 years was below 100 mSv as shown in Table 10. Based on Korean standards for emergency response, sheltering-in-place would be required in the early phase of accident because TEDEs were estimated to be 11~50 mSv within PAZ of 5 km around Shin Kori unit 3 and unit 4. Korean standards recommended sheltering-in-place for the projected radiation dose of 10 mSv in 2 days and evacuation for 50 mSv in 1 week.

The air parcels showed that most radionuclides were transported northwards due to southern winds and some of the air masses moved westwards towards the main land of Korea as shown in Fig. 10. Radioactive materials released to the atmosphere were largely dispersed over the main land of Korea due to the frequency of eastern winds. Noble gases did not get deposited and therefore the airborne concentrations were expected to remain high and further transported into other areas outside of Korea depending on their half-lives. The airborne concentrations at ground level were estimated to be between 1.4×10^-5 and 1.2×10² Bq･m^-3 while the ground depositions ranged from 9.7×10^-9 to 7.7×10⁴ Bq･m^-2 as shown in Fig. 11 and Fig. 12, respectively. The ground depositions were mainly contributed by ¹³⁷Cs and ¹³⁴Cs and the precipitation on 10^th and 11^th August 2018 according to the weather data from KMA.