Water-related Risk Assessment of Nuclear Power Plants Based on Simulation

As of the end of June 2022, there were 441 nuclear power reactors in operation worldwide, spanning 33 countries, with a combined installed nuclear power capacity of 394GW. The International Atomic Energy Agency (IAEA) categorizes the world’s nuclear power plant sites into coastal, riverfront and lakeside locations. The safe and stable operation of nuclear power stations is of paramount importance and has garnered significant attention from scholars worldwide [1-3], particularly those situated along coastlines. In the event of a coastal nuclear power plant posing a threat, it could have a substantial impact on marine ecology, as was evidenced by the discharge of nuclear waste water into the ocean following the 2011 Fukushima nuclear power plant incident, which posed a serious threat to marine ecological safety [4,5]. The primary objective of nuclear safety is to establish and maintain effective defenses against radiation hazards in order to protect plant personnel, the general public and the environment. Currently, research on the operational risks of coastal nuclear power stations predominantly focuses on internal operational technologies, including geological disaster risks, nuclear waste disposal risks, nuclear leakage risks and so forth [6-8]. There is a notable gap in the research concerning the potential risks that maritime traffic poses to the safe operation of coastal nuclear power stations.

Through expert consultation and literature review, it has been determined that the main sources of water risk for nuclear power plants stem from ships navigating within the engineering waters [9,10]. Issues such as out-of-control ships, anchoring and oil spills present threats to the safety of nuclear power plants. Specifically, oil spills from ships can impact the safe operation of nuclear power plants. The extensive spread of an oil spill may enter the water intake of the nuclear power plant, leading to decreased water quality of the cooling water, which in turn affects the cooling capacity and could result in nuclear power plant shutdowns and other accidents. Most of China’s nuclear power plants have established relevant oil spill protection mechanisms to ensure the safety of the cooling water supply [11,12]. In order to accurately identify the water-related risks for coastal nuclear power stations, including the risks associated with ship adrift and oil spills, specific measures are taken. Regarding the risk of out-ofcontrol ships, the Beijing Institute of Water Science (BIWS) utilizes the V. Dragon 5000 large-scale navigation simulator in conjunction with on-site observations of ship types at nuclear power plants. Using mathematical simulations of ship movements, a mathematical model of ship movements and electronic nautical charts of the waters near the engineering docks are created for representative ship types (test ship types). Through simulated ship maneuvering trials considering the most adverse hydrodynamic conditions in various regions, including normal and typhoon weather, data on the time and speed of ships drifting to within 1 nautical mile of the nuclear power plant are obtained. As for the risk of ship oil spills, DELFT software is employed to simulate and emulate the flow field in the waters near the nuclear power plant to provide an environmental dynamic field for pollutant simulation. The OILMAP model is then used to simulate a series of processes related to oil spills, including drift, weathering, dispersion, dissolution and shoreline adsorption, in order to predict the trajectory of oil film drift and the fate of leaked crude oil and to assess the extent of its harm.

Ship drifting simulation

On the basis of fully considering various factors affecting ship navigation safety, combined with the hydrologic and meteorological conditions of the waters near the project, the ship control simulator is used to simulate the ship runaway drifting in the route, and the influence of the ship runaway drifting on the safety of the nuclear power plant is obtained. The representative ship type is divided into oil tanker and bulk carrier. The purpose of the simulation test is to carry out the ship navigation safety simulation test in the waters near nuclear power plant and study the movement trajectory and safety impact of the navigation representative ship sailing, encountering and overtaking in the waters near nuclear power plant, so as to evaluate the degree of influence of external factors on nuclear power plant. It provides decision basis and reference data for effective protection of maritime traffic risk and formulation of safety zone near nuclear power plant. The simulation uses the navigation simulator of Beijing Institute of Water Science, which consists of a 180° 5-channel projection of the main ship, a 120° 3-channel TV replica ship and a set of two-three-dimensional integration of the port area stereo monitoring system equipment, model V. Dragon 5000. The simulation equipment used for the test is shown in Figure 1 of the Supplementary materials.

Figure 1:Location and number of the test area.

Ship maneuvering dynamic simulation platform is a twodimensional simulation system based on electronic chart. Selecting the latest chart to digitize, the electronic chart of the waters near the project wharf is made. On this basis, according to the engineering design drawings and other materials, the hydraulic structure of the engineering platform, water plane layout and other data are added to the electronic chart. Specifically, through the following four steps to carry out experiments
A. According to the real ship data, create a database model and through the debugging data, test the simulation data and real ship data error, so as to get a more accurate ship model;
B. Collect and research the meteorological and hydrological data of the waters near the project, including the wind, currents, tides and other natural environment data and then enter the accurate data into the simulation system or using virtual reality simulation technology
C. According to the main types of ships navigating in the project waters, the degree of influence of the environment (wind, current and tide), the characteristics of the navigating waters and the characteristics of the ship’s maneuvering, study and determine the types and number of simulation test programs;
D. Analyse the degree of influence of wind, current and other external factors, and derive the safety spacing and width of waters required for the safe navigation of the ship; analyse the ship’s navigational trajectory, and derive the Optimization of engineering platform site selection and recommendations for ship navigation in engineering waters.

Considering that an oil spill may occur after a ship drifts out of control in the waters near the nuclear power plant and drifts to the waters near the outlet of the nuclear power plant under adverse wind conditions, which will cause serious risks to the nuclear power plant, the ship maneuvering simulation test considers that the ship type will lose control under the most unfavourable wind conditions in ordinary weather and typhoon weather in various regions. Obtain the floating time and floating speed of the ship to the 1nmile near the nuclear power plant. Specific test conditions are shown in Table 1 in Supplementary materials.

Table 1:Summary of runaway drift test results.

In order to facilitate the identification of risks in different water areas, this study divides the 4.5nmile water area centered on nuclear power plant into four fan-shaped areas, each circle being a semicircular area with a central radius of 1nmile, 2nmile, 3nmile and 4.5nmile, and then divides the area into three parts at a 60° Angle. The waters are divided into 11 zones. Among them the nuclear power plant as the center of the 1nmile range of ship navigation is considered to be a high threat to the safety of nuclear power plants and generally non-nuclear power plant working ships or spent fuel transport ships are generally not allowed to enter, pretending to be a prohibited area, and no test research is carried out in this range. According to the relative position of the coastal nuclear power plant and the coastline, we divided the study into 8 regions with the nuclear power plant as the center and the minimum interval of 1 nautical mile, as shown in Figure 1.

Ship oil spill simulation

In order to effectively evaluate the impact on the water intake of the nuclear power plant caused by the possible oil spill accidents of ships sailing and anchoring ships in the waters near the nuclear power plant, this section mainly adopts the numerical simulation of the possible oil spill accidents of ships, evaluates the time of oil spill to the water intake, the amount of pollution and other information, so as to assess the possible risks caused by oil spill. After pollutants enter the water body, their drift and diffusion movement are affected by current and sea surface wind, especially ocean current, which plays an important role. In this study, we use DELFT software to simulate the flow field in study area, so as to provide environmental dynamic field for the simulation of pollutants.

Tidal current model: Tidal current is the basic flow in offshore shallow waters and the numerical calculation of tidal current is the basis to simulate the drift and fate of oil spill. The simulation uses a two-dimensional tidal current model to model the tidal current field in the nearby waters. The two-dimensional tidal current model is used to describe the average depth motion of the barotropic ocean and the equations are composed of the continuity equation and the momentum equation:

Where: 𝜁-water level; 𝑑-Water depth; 𝐺𝜉𝜉, 𝐺𝜂𝜂-rectangular coordinate system (𝑥 𝑦) and orthogonal curvilinear coordinate system (𝜉, 𝜂) conversion coefficient, and ; The mean velocity component of water depth in the direction of 𝑈, 𝑉 -- 𝜉 and 𝜂; 𝑄-outlet of per unit area, evaporation and precipitation’s contribution to the traffic, including -Source and sink per unit volume.

Where: 𝐺_𝜉𝜉, 𝐺_𝜂𝜂 -conversion coefficient between rectangular coordinate system (𝑥, 𝑦) and orthogonal curvilinear coordinate system (𝜉, 𝜂). The mean velocity component of water depth in the direction of 𝑈, 𝑉 -- 𝜉 and 𝜂; 𝑓 -Coriolis force coefficient; Turbulent momentum fluxes in the directions of 𝐹_𝜉, 𝐹_𝜂 -- 𝜉, 𝜂; The water pressure gradient in the direction of 𝑃_𝜉, 𝑃_𝜂 -- 𝜉 and 𝜂; The source or sink of momentum in the direction of 𝑀_𝜉, 𝑀_𝜂 -- Δ, (𝑡−1=𝑡− δ𝑡); 𝑡−1 - Water depth at reference level; 𝐶1 - Water depth below the reference level; 𝐶1 -vertical eddy coefficient. Closed boundary condition: the normal velocity of vertical shoreline is 0. Open boundary condition: 8 main component tides M2, S2, K1, O1, N2, P1, K2, Q1 are used to control by harmonic constant. Numerical method: semi-implicit finite difference numerical algorithm.

Simulation and prediction of oil spill accident: OILMAP model was used to simulate and predict the consequences of oil spill accidents. The model simulates a series of processes such as oil spill drift, weathering, diffusion, dissolution and shoreline adsorption to predict the trajectory of oil film drift and the destination of oil spill and to assess its harm degree. The simulation program is shown in Figure 2 of the Supplementary materials.

Figure 2a:Incidence diagram of diesel oil in general weather.

Figure 2b:Incidence diagram of crude oil in general weather.

Figure 2c:Incidence diagram of bunker in general weather.

Drift model: Assuming that the oil spill can be divided into many independent oil spills, each oil spill is regarded as a Lagrange particle. The position component of the oil spill particle at time t is represented by X_t.

Where: Δt - time step (s); X_t-1 - 𝑡−1 Oil spill spot (m); U_oil - Oil particle drift velocity (m/s). Oil spill particle drift velocity U_oil(m/s) is defined as follows:

Where: U_t -velocity component generated by water flow (m/s); U_w -Velocity component of wind generation (m/s); U_disp -The velocity component (m/s) produced by the dispersion process. The flow field is calculated by the environmental fluid dynamics model and output to the oil spill model. The velocity component U_w generated by the wind is determined by the following formula:

The wind drift factor C1 is a constant, which varies from 1-4.5% and is determined by actual measurements. 3-3.5% is suitable for open ocean. For closed or semi-enclosed seas, C₁ has a smaller value. U_windspeed indicates the windspeed.

Dispersion model: U_dd (m/s) and V_dd (m/s) represent the north and east components of the diffusion velocity, which are defined as follows:

Where D_x is the horizontal diffusion coefficient in the eastwest direction (m²/s);
D_y-- North-South horizontal diffusion coefficient (m²/s); 𝛥𝑡 -Time step (s); 𝑟 -Random coefficient (-1 to 1). Horizontal diffusion coefficients D_x and D_y are usually equal.

Extended model: The spread area of surface oil spill is calculated by the spread model. The spread area of oil spill directly affects the proportion of oil spill evaporation, dissolution, dispersion and photooxidation. Expansion is caused by the interaction of waves, gravity, inertial forces, viscosity and surface tension. It is assumed that more than 90% of the oil pellets are thick oil films. The change velocity of thick oil film surface area A_tk ( m²/s) is defined as follows:

Where A_tk -oil film surface area (m²); 𝑘₁ -Expansion rate constant (1/s); 𝑉_𝑚 -Oil film volume (m³); 𝑡 - Time (s). Kolluru adds the correction of the effective radius, and its calculation of the change velocity of the independent oil spill particle surface area A_tk ( m²/s) is as follows:

Where: A_tk-- surface area of independent oil spill particle (m²); 𝑘₁ -Expansion rate constant (1/s); 𝑉_𝑚 -Individual spill particle volume (m³); R_s -- Independent oil spill radius (m); R_e -Effective radius of surface oil film (m); 𝑡 - Time (s). The effective radius of the surface oil film is as follows:

Where: A_tk -- surface area of independent oil spill particle (m2); 𝑁 - The number of oil particles in the surface oil film.

Evaporation model: Evaporation is the process of mass transfer from liquid to gas of the lighter components of petroleum hydrocarbons in water spill to the atmosphere. It is the main part of the oil spill quality transmission process, evaporation can make 20-40% of the spilled oil from the water surface into the atmosphere, especially light crude oil or refined oil products such as gasoline, diesel, etc., evaporation loss can reach more than half of the total amount of spilled oil. Evaporation is related to oil species. The evaporation rate is determined by the oil spill surface area, thickness, steam pressure and mass transfer coefficient. These, in turn, are determined by oil, wind speed and temperature. When oil evaporates, comprehensive factors change, and the density and viscosity of oil also change, thus affecting evaporation. The most volatile hydrocarbons (low carbon number) evaporate the fastest, within a day and sometimes even within an hour. When the oil continues to weather, evaporation will be significantly weakened if part of the water/oil emulsion is formed. The evaporation model is calculated as follows:

Where: F_e -volume component of oil spill evaporation; T -oil spill temperature; A_s -oil film area; V₀ -initial oil spill volume; K_e -Mass transfer coefficient is calculated as follows:

A, B - experience coefficient; T₀ -initial boiling point; T_G -distillation curve gradient; For crude oil:

Emulsion model: Emulsification is formed due to the presence of surfactants, like aromatic hydrocarbon mixtures. Crude oil contains dissolved aromatic hydrocarbons that form stable mixtures. Due to weathering, when the aromatic hydrocarbons are exhausted, the asphalt begins to precipitate. Bitumen reduces the surface tension of oil and water, thus initiating the emulsification process. Water enters the oil phase by breaking or destroying the oil-water interface. Oil spill mixing speed wc F can be calculated as follows:

Where: U_w -Wind speed (m/s); C₁ -- empirical constant, 2×10- 6 for emulsified oils and 0 for other oils; c₂ -Constant, controlled maximum water content, 0.7 for heavy oil and crude oil, 0.25 for home fuel oil; 𝐹_𝑤𝑐 -the maximum water factor in the oil (oil characteristic input value); 𝑡 - Time (s). Viscosity of emulsified oil 𝜇 (cP):

Where: μ₀-Initial oil viscosity (cP); 𝐹_𝑤𝑐 -maximum water factor in oil; C₀ -Emulsification constant (0.65). Effect of evaporation on viscosity 𝜇 (cP):

Where: μ₀-initial oil viscosity (cP); C₄ -- constant, light oil is 1, heavy oil is 10; F_v -oil film evaporation coefficient. The exponential increase formula has been used by many oil spill simulators for many years. In this paper, the above model is used to calculate the oil spill emulsification process.

Shoreline sedimentation model: For the purpose of calculating indices of adsorption capacity and removal rates for different types of shorelines, we categorized the shorelines into 11 classes. Included: Open rocky coast, open rocky platform coast, four types of beaches (flat fine beach, medium-coarse sand covered beach, sand-gravel mixed beach, sand-pebble mixed beach), open intertidal zone, sheltered rocky coast, sheltered intertidal zone, sheltered marshland. The fate of oil spills that reach the shoreline depends on the characteristics of oil spills, the type of shoreline and the environmental kinetic energy.

For different types of shorelines (m), the corresponding maximum adsorption capacity A_m,max and adsorption leakage rate V_m are defined. The dynamic ability of leakage adsorbed by shorelines is determined by the formula:

Where: A_m is the adsorption capacity of leakage of m type shoreline.

Density change: Oil spill density is determined by the following formula:

Where: ρ_e--temperature T density during emulsification; ρ_oil --reference temperature 𝑇₀ Density of preferred pure oil; ρ_w -water density; c_DE and c_DT is empirical coefficient. The value for c_DE= 0.18 and c_DT = 8×10-4.

Viscous change: Viscosity changes with temperature, evaporation and emulsification processes. The effect of temperature on viscosity can be determined by below formal:

μ -Viscosity of oil at temperature 𝑇; 𝜇₀ -Viscosity of oil at reference temperature 𝑇₀; 𝑐_𝑇 --Empirical constant; The recommended value is 5000k; The change in viscosity during emulsification is determined by equation:

𝐹_𝑤𝑣 -Water content of the emulsion; 𝑐_𝑉 -Dimensionless empirical constant (recommended value is 2.5); 𝑐_𝑀 -Append constant to 0.65. The change of viscosity during evaporation is determined by the following equation:

𝐹_𝑒𝑚 -Mass number of evaporated oil spill; 𝑐_𝐸 -Select dimensionless empirical constants between 1 and 10 depending on the oil. For light oil spill at 15 ℃, the initial viscous motion coefficient exceeds 38cSt, 𝑐_𝐸 is 10; for oil spill with low viscous motion coefficient, 𝑐_𝐸 is determined by the following formula:

Design of ship pollution simulation test scheme: In order to quantitatively assess the waters where oil spill may occur, the project divided the main waterways and anchorage waters around the project into eight areas, and carried out simulation tests with the center points of each area representing the possible locations of oil spill accidents. Considering Marine fuel oil and Marine diesel specifically, the main physical and chemical parameters of the leaked oil are shown in the Table 2 & 3 in Supplementary materials. Based on the above related descriptions, the ship oil spill test scheme under seasonal average state and typhoon state of this project is finally determined and shown in the Table 2 & 3 in Supplementary materials.

Table 2:Summary of oil spill hazards in ordinary weather.

Table 3:Summary of oil spill hazards in typhoon weather.

Experimental results of uncontrolled drifting of a ship

The results of the experiment are shown in Table 1: It can be seen from the ship drift simulation test that in ordinary weather, due to a certain deviation between the normal wind direction and the position of the nuclear power plant, Half of the ships tested did not drift Within the 1nmile range of the power station (operating conditions 1, 4, 6, 8); In addition, due to the low wind speed and velocity in ordinary weather, the ship’s floating speed is low (average speed is about 0.5kn), and the time is long (average time is about 3h), and the threat to the nuclear power plant is relatively small. Under the influence of typhoon weather, due to the obvious increase of wind power, the time of out-of-control drifting of ships in each test area to the 1nmile of the nuclear power plant is significantly reduced, ranging from 11min (working condition 10) to 33min (working condition 15). At the same time, under the influence of typhoon, the floating speed of ship increases obviously, and under the continuous effect of typhoon, the floating speed of ship continues to accelerate. According to the test results, when the ship enters the 1nmile range of the nuclear power plant, the ship speed can be increased to a maximum of 4.5kn (working conditions 13, 14, 15) and the risk of oil spill is more likely to occur after collision or grounding, which is a high threat to the nuclear power plant.

Oil spill simulation experiment results

According to the above set ship oil spill simulation test scheme, a total of 36 groups of ship oil spill simulation tests were carried out in this study, and the test results are shown in Table 2 & 3:

According to the results of oil spill drift and diffusion, under the influence of adverse wind direction in each region, oil spill will affect the water intake of nuclear power plant. The closer the distance, the faster the arrival time, the fastest about 3 hours (plan A-1, A-2, A-6), the slowest about 12 hours (plan A-13, A-15), and then under the continuous influence of adverse wind direction, the faster the arrival time. Concentrated along the shoreline of the nuclear power plant. The thickness of the oil film at the time of arrival is different due to the difference in the amount of oil spilt. The diesel oil film is thin, the lowest is 1.1mm (program A-13, A-16), while the persistent oil film such as crude oil and heavy fuel oil is thick, the highest is 5.6mm (program A-6) and the impact is greater. According to the results of oil spill drift and diffusion, under the influence of typhoon, the oil spill from ships in various regions reaches the shoreline of nuclear power plant at a faster speed and the closer the distance, the faster the arrival time, the fastest about 45 minutes (plan B-1, B-2, B-3), the slowest about 2 hours and 30 minutes (plan B-18), and then under the continuous influence of adverse wind direction, the oil will gather on the shoreline of nuclear power plant and have a continuous impact. The thickness of the oil film at the time of arrival is different due to the difference in the amount of oil spill and each of them is different. The thin diesel oil film and the high wind speed of the typhoon will further promote volatilizing, and the thickness is only 0.4mm at the thinnest (Plan B-16).

Persistent oils, such as crude oil and heavy fuel oil, are not volatile and have a fast arrival time and a thicker oil film, up to 8.7mm thick (Scenarios B-2 and B-4), which has a greater impact. The simulation results of diesel oil, crude oil and fuel leakage are shown Figure 2-3. As can be seen from the simulation renderings in Figure 2a, due to the strong volatility of diesel itself, and the local temperature is relatively high, so that after 10 hours, diesel volatilization reaches more than 40%, after 30 hours, volatilization approaches 50%, and after 70 hours, it approaches 55%. It can be seen from the simulation effect in Figure 2b that the volatility of crude oil is not strong, which belongs to the persistent oil, when the crude oil first leaked, nearly 98% of the crude oil will float on the water, 10 hours later, the total amount of crude oil volatilized 10%, 72 hours, the evaporation amount is only 20% of the total, about 80% of the crude oil is still floating on the water. It can be seen from the simulation effect in Figure 2c that the fuel oil is also a persistent oil, when the first leak, about 99% of the fuel oil will float on the water, 28 hours later, the fuel oil volatilized 10% of the total, remove the evaporation of the fuel oil, and finally about 85% of the fuel oil is still floating on the water.

Figure 3a:Incidence diagram of diesel oil in general weather.

Figure 3b:Incidence diagram of crude oil in general weather.

Figure 3c:Incidence diagram of bunker in general weather.

As can be seen from the simulation renderings in Figure 3a, due to the strong volatility of diesel itself and the high sea surface wind speed under the typhoon condition, the volatilization of oil products was further promoted. After about 1 hour, the diesel volatilized 37% of the total amount. At the same time, due to the influence of wind speed, the diesel oil all diffused into the water body at a very fast speed and the oil spill on the sea surface was reduced.

It can be seen from the simulation effect in Figure 3b that crude oil is a persistent oil with low volatility. However, under the strong influence of the typhoon, 10% of the total oil volatilized after 3 hours and 20% of the total oil volatilized after 37 hours. At the same time, when the crude oil first leaked, nearly 36% of the crude oil would float on the water surface, while the oil on the water surface would continue to decrease. At the same time, the strong wind made the crude oil enter the subsurface surface of the water body. About 72 hours later, there was no oil floating on the water surface and a large amount of remaining crude oil entered the water body. It can be seen from the simulation effect in Figure 3c, bunker is also a persistent oil, not volatile, after 6 hours, 10% of the total volatilization, to 70 hours, volatilization reached 20%. At the same time, due to the small proportion and large viscosity, most of the fuel floats on the water, about 96% of the bunker will float on the water within 1 hour, to 50 hours, 80% of the floating on the sea, 72 hours there are still 78% of the bunker floating on the water.

This study, based on an in-depth investigation of the coastal nuclear power plants and the surrounding marine environment, achieved comprehensive identification of the water-related risks for coastal nuclear power plants. Two models, namely the ship drifting and oil spillage model, were established to address the risks of ship oil spills and uncontrolled drifting. The research divided the waters surrounding the nuclear power plants into 9 risk zones based on the distribution of coastlines and port functional areas near the nuclear power plants. For cargo ships and ships carrying hazardous materials, the study conducted simulation experiments on ship uncontrolled drifting and oil spillage under normal weather conditions and typhoon weather conditions. The research delved into the level of threat posed by various risk events in each area to the nuclear power plants. Based on the results of the simulation experiments and previous research, the study identified the navigational risks in the waters surrounding the nuclear power plants. When the navigational risks for ships in the waters around the nuclear power plants are excessively high, accidents such as oil spills and uncontrolled drifting will pose significant safety threats to the nuclear power plants. Therefore, based on the simulation results, the study proposed graded control measures and safety management recommendations for the waters surrounding the nuclear power plants under normal weather conditions and typhoon weather conditions. This research fills a gap in the study of maritime transportation risks for coastal nuclear power plants and provides applicable methods for related research to draw upon.

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