This paper presents a simulation method for oil spills in a multi-island area. The simulation considers three parts, which consist of
With the rapid development of modern industry, human demand for energy has grown. The increasing energy demands have resulted in the increased exploitation of fossil energy, such as crude oil and gas [
Spreading is the horizontal expansion of an oil slick due to gravity, inertia, viscosity, and surface tension forces, which plays an important role in the fate process of surface spilled oil. The transport and fate of spilled oil in water are processes affected by dynamic factors, nondynamic factors, and variable oil properties [
Early researchers adopted various numerical methods to simulate the movement of an oil slick based on the advection-diffusion equation. In the mid-1990s, an oil-particles model was developed by Johansen, Elliot, and Reed [
In recent years, there have been breakthroughs in terms of understanding the complex geometry for oil spill model research. Gjosteen [
In this study, an oil spill simulation method in a multi-island area is presented, and the processing modes for oil slick longshore transport and its penetration-resistant boundaries are developed. In addition, a local search method that can specify the search radius is proposed and adopted. What is more, the Euler-Lagrange method is adopted to track the spill location and the position of particles on the edge of oil slicks, which can easily calculate the oil slick area. Based on the Monte Carlo method, a mathematical model for marine oil spills is established to simulate the movement of oil spills in the Luanjiakou District of the Port of Yantai (Figure
Map of the Luanjiakou District near the Port of Yantai and survey stations.
The Euler-Lagrange systems are divided into two parts, that is, Euler and Lagrange approaches. The Euler approach describes the distributions of the variables in flow field at any time, whose computational mesh is fixed in space, while the Lagrange approach traces each particle from a certain time and describes its trajectory, whose computational mesh is fixed on the centroid of the research object and can be used to simulate the trajectory of an oil slick [
In the coastal area, the horizontal movement scale of the tidal current is much larger than the vertical movement scale and the hydraulic parameters are unconspicuous in the vertical direction, so the flow field can be expressed by the average flow quantities along the direction of the water depth [
The equations for conservation of momentum are given by
Waves are generally induced by the wind on the sea surface. According to the temporal and spatial variation, the waves can be divided into regular and irregular waves. Regular waves have constant amplitudes and wavelengths, whose waveforms do not vary with time and space. It is possible to form such waves only when the problem is two-dimensional, the water depth is constant, and the disturbance source generating wave periodically varies with time. Irregular wave patterns are transient, whose elements vary with time and space. The waves generated when the wind blows over the sea surface are a common type of irregular wave [
Fay’s [ Gravity-inertia spreading phase: Gravity-viscous spreading phase: Surface tension viscous spreading phase:
where
The drift of the oil slick is a vector sum of surface current and wind, of which the velocity vector is shown in Figure
Velocity vector of oil slick drift.
The spreading thickness
The spill flux is very similar to the mass transfer flux in molecular diffusion, so the spreading thickness
Due to the influence of various dynamic factors, such as wind, wave, and current, the diffusion of spilled oil on the sea surface has certain randomness at any time, which can be properly described by the Monte Carlo method [
The Monte Carlo method is adopted to calculate the oil movement in the present study. First, the spill location and the position of particles on the edge of oil slicks are tracked and recorded by using the Euler-Lagrange method. Next, the diffusion random number is added to the module. As a result, the action of the wave-guide and wind-induced currents on dispersion and fragmentation of oil slicks is taken into account to describe the trajectory and irregular shape of these same spills.
Assuming the sampling step
Specifically, supposing that position coordinates of an oil particle are
The evaporation rate is influenced by the temperature, waves, wind speed, and oil slick areas, among other factors. Hence, the evaporation amount of surface oil slick can be calculated by the following distillation formula [
When drifting on the sea surface under the influence of wind and waves, oil particles disperse to the aqueous phase and water particles also disperse to the oil phase continuously. Subsequently, an oily emulsion is generated. The emulsification equation is given by [
In this study, a simulation method for oil spills in a multi-island area is presented to simultaneously observe and study the edge and centroid motion of an oil slick (see Figure
Description of the computing mode of the oil slick (the area surrounded by the solid line represents the oil slick, black points represent discrete nodes along the edge of the oil slick, line between discrete nodes represents oil surface, and the area surrounded by the dashed line represents the combination of particles and oil surface).
Marine oil spill models usually cover large areas using many grids. Furthermore, in most calculations one does not only need to determine the scope of the search unit, but also need to ascertain whether or not the search node is in this unit. In addition, the centroid and edge of an oil slick are not necessarily near the previous location because the transport of the oil slick with water movement may be very large over a short period. However, using the global search method (i.e., searching the entire study area) would lead to the huge calculation. Therefore, the local search method is proposed in this paper, which specifies the search radius, thereby reducing the amount of computation (see Figure
Schematic diagram of the local search method (red circular area for the search range, pink point for the circle center, yellow point for the search node, yellow arrow for the search radius, blue solid line for the contour line of an oil slick in the previous moment, and blue dashed line for the contour line of an oil slick in the present moment).
During oil spills around multi-island areas, coastal structures such as breakwaters, quays, jetties, wharfs, and docks are likely obstacles to the spreading and transport of oil slicks [
Comparison of different movement conditions of oil particles (black point) when arriving at the solid boundary (solid line) ((a) represents the modes of the penetration-resistant boundary as well as the longshore transport and adsorption of the oil slick and (b) represents the unlikely case of oil particles penetrating the solid boundary).
Comparison of the major axes scales of the oil slick.
Spill volume (m3) | 102 | 103 | 104 | 105 |
---|---|---|---|---|
Simulated values of this paper (km) | 15.33 | 28.14 | 45.1 | 64.83 |
Simulated values of [ |
12.67 | 25.91 | 43.54 | 65.49 |
Comparison of the minor axes scales of the oil slick.
Spill volume (m3) | 102 | 103 | 104 | 105 |
---|---|---|---|---|
Simulated values of this paper (km) | 5.99 | 11.69 | 20.69 | 34.15 |
Simulated values of [ |
5.18 | 11.74 | 21.10 | 34.04 |
The major (a) and minor (b) axes of the oil slick versus time.
Comparison of the simulated and experimental results.
Item | Initial size (cm) | Final size (cm) | Movement distance (m) | Movement time (s) |
---|---|---|---|---|
Simulated results | 15 | 21 | 1.17 | 30 |
Experimental results | 15 | 22 | 1.2 | 30 |
Comparison of the flume experiment (a, c) and the simulated result (b) of the spreading and drift of the oil slick.
The Luanjiakou District is located in the western portion of Penglai-Yantai City, Shandong Peninsula. The district faces the Miaodao Islands, whose eastern coastline extends in the direction of Penglai City and the Yellow Sea and the western coastline extends in the direction of the Laizhou Gulf (see Figure
The model domain and its bathymetry are shown in Figure
(a) Bathymetry and (b) unstructured grids for the model domain.
To account for the lack of observational data, the astronomical tide, we induced the tidal level condition at the three open boundaries. Four main constituents in this domain are considered, that is, K1, M2, O1, and S2, whose harmonic constants can be derived from the global ocean tide model from the United States Department of the Navy [
According to historical data [
The validation results of the tidal level are shown in Figure
Comparison of the tidal level between the modeled (solid line) and the observed (dots) results at three stations (H1, H2, and H3).
There are many diurnal tide survey stations (see Figure
Comparison of flow velocity between the modeled (solid line) and the observed (dots) results at three stations (U1, U4, and U7).
Comparison of flow direction between the modeled (solid line) and the observed (dots) results at three stations (U1, U4, and U7).
In particular, three criteria are adopted to assess the model performance for tidal level, flow velocity, and flow direction simulation, including the mean absolute error (MAE), the root mean square error (RMSE), and bias (BIAS) [
Statistical errors at tidal survey stations for model verification.
Station | Tidal level | Station | Flow velocity | Flow direction | ||||||
---|---|---|---|---|---|---|---|---|---|---|
MAE (cm) | RSME (cm) | BIAS (cm) | MAE (m/s) | RSME (m/s) | BIAS (m/s) | MAE (deg) | RSME (deg) | BIAS (deg) | ||
H1 | 9.18 | 11.04 |
|
U1 | 0.09 | 0.11 | 0.06 | 12.83 | 17.63 | 1.63 |
H2 | 8.29 | 10.32 |
|
U4 | 0.06 | 0.08 |
|
10.55 | 14.98 |
|
H3 | 10.02 | 12.10 |
|
U7 | 0.07 | 0.09 |
|
11.72 | 15.18 | 1.06 |
The distributions of the flow field at ebb and flood periods are shown in Figure
Distributions of the flow field at the times of ebb (a) and flood (b).
In summary, the hydrodynamic field can serve as the basis for studying marine oil spills in our study area.
In the concentration diffusion verification of an oil slick, the results of a dyestuff tracing experiment carried out by South China Sea Institute of Oceanology, Academia Sinica, from 2:30 to 5:30 on January 29, 2002, were compared with the modeled results, as shown in Figure
Comparison between the experimental result (a) and the modeled result (b) of the concentration diffusion of the oil slick.
The port has 10,000-tonne tanker berths and the channel is an important shipping route for oil tankers and ships. Hence, the simulation assumes that spill locations are evenly distributed in the western, middle, and eastern portions of the port covering the entire channel, which are all the high-risk oil spill areas.
According to the relevant specifications [
Properties of the oil.
Name | Density (kg/m3) | Water content of emulsion (%) | API |
---|---|---|---|
Condensate oil | 830.5 | 74 | 38.874 |
Low sulfur fuel oil | 972 | 80 | 14.08 |
In this region, the prevalent wind directions are SSW and S and the frequency is 15.14%. The static wind frequency is 0.47%. The strong wind directions are N, NW, and NNE, and the instantaneous maximum wind speed is 28 m/s [
Wind conditions of the model.
Wind direction | No wind | Southwest wind (SW) | South wind (S) | Northwest wind (NW) | Northeast wind (NE) |
---|---|---|---|---|---|
Wind speed (m/s) | 0 | 4.9 | 2.0 | 3.4 | 2.7 |
Note | Maximum wind direction | Wind Direction 1 | Wind Direction 2 | Wind Direction 3 |
Wind rose diagram for Luanjiakou District in 2002–2006.
The trajectories of instantaneous oil spills from the western portion of the channel under five wind conditions are shown in Figure
Trajectories of instantaneous oil spills (red line) from the western portion of the channel (black star symbol for the western spill location) under five wind conditions ((a) represents oil spill trajectory in the case of no wind, (b) represents oil spill trajectory under the influence of southwest winds, (c) represents oil spill trajectory under the influence of south winds, (d) represents oil spill trajectory under the influence of northwest winds, and (e) represents oil spill trajectory under the influence of northeast winds).
Figures
Transport processes of instantaneous oil spills (red area) from the western portion of the channel (black star symbol for the western spill location) in the case of no wind.
Transport processes of instantaneous oil spills (red area) from the eastern portion of the channel (red star symbol for the eastern spill location) under the influence of south winds.
Figures
Transport processes of continuous oil spills (red area) from the western portion of the channel (black star symbol for the western spill location) in the case of no wind.
Transport processes of continuous oil spills (red area) from the eastern portion of the channel (red star symbol for the eastern spill location) under the influence of south winds.
From Section
Figures
Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spill location, blue line for the middle spill location, and red line for the eastern spill location) in the case of no wind.
Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spill location, blue line for the middle spill location, and red line for the eastern spill location) under the influence of southwest winds.
Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spill location, blue line for the middle spill location, and red line for the eastern spill location) under the influence of south winds.
Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spill location, blue line for the middle spill location, and red line for the eastern spill location) under the influence of northwest winds.
Area of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spill location, blue line for the middle spill location, and red line for the eastern spill location) under the influence of northeast winds.
From Figures
Figures
Slick thickness of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spill location, blue line for the middle spill location, and red line for the eastern spill location) in the case of no wind.
Slick thickness of instantaneous (a) and continuous (b) oil spills versus time in different spill locations (black line for the western spill location, blue line for the middle spill location, and red line for the eastern spill location) under the influence of northeast winds.
In the present study, the oil fate mainly includes the oil on the sea surface, evaporated, emulsified, and adsorbed near the shoreline after coming ashore. Figure
Fate processes of the instantaneous oil spill that occurred in the west of the channel in the case without wind (a) and in the east of the channel under the action of northwest wind (b).
Figure
Fate processes of the continuous oil spill that occurred in the west of the channel in the case without wind (a) and in the east of the channel under the action of northwest wind (b).
The scenario simulations of marine oil spills in this study were preliminary using a two-dimensional oil spill model, which is actually a large-scale simulation in large areas. Further work remains to be done to improve the model performance, such as the multiscale simulation. For instance, the vertical diffusion of spilled oil in the water column can be carried out by the advanced SPH (Smoothed Particle Hydrodynamics) method, that is, the mesh-free particle method, which describes the transport of an oil slick with a series of particles and is more in coincidence with the idea of “oil-particles” model. In addition, the acquisition and usage of remote sensing information are essential to simulate and predict the marine oil spills in the near future due to its wide area coverage and the all-weather and all-day capabilities.
In this paper, a simulation method for the spreading and drift of an oil slick in a multi-island area and the mode of the penetration-resistant solid boundary are presented. To improve the computation efficiency, a local search method that can specify the search radius is adopted. The Euler-Lagrange method is adopted to track the spill location and the position of particles on the edge of oil slicks in order to calculate the slick area easily. Based on the Monte Carlo method, a mathematical model for marine oil spills was established for the Luanjiakou District, near the Port of Yantai. A series of verifications of the tidal current field and the movement of an oil slick show that the model can reflect the actual oil slick movement.
The model has been applied to simulate the movement of oil slicks, including the trajectory, transport, area, thickness, and fate processes. It was concluded that the scope of spill trajectories was the largest under the influence of southwest winds, and it was the smallest under the influence of northwest winds; the transport of oil slicks was mainly affected by flood/ebb currents and oil slicks could reciprocate with flood/ebb currents; the spreading area of instantaneously spilled oil reached the maximum in the eastern spill location, under southwest winds, after spilling for 48 h. The minimum oil area appeared in the western and middle spill locations, which continuously spilled oil under the influence of northwest and northeast winds, respectively; the wind had a significant influence on drift and thickness of oil slicks, especially when the flow velocity was relatively small. The fate processes of oil volume on the sea surface gradually increase during the initial 10 h and subsequently the variation tendency is basically consistent with the instantaneous oil spill. The fate processes of evaporated, emulsified, and adsorbed oil volume of two types of oil spills are basically the same.
Overall, the proposed model provides a reasonable method for the study of marine oil spills. Moreover, the simulation results will be helpful for controlling and handling of accidental oil spills efficiently.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was financially supported by the Opening Foundation of Key Laboratory of Marine Spill Oil Identification and Damage Assessment Technology, State Oceanic Administration (SOA). The authors greatly appreciate the assistance from Dr. Yangyang Li for subject research.