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# A numerical study of oil spill spreading in the Gulf of Thailand

*Advances in Difference Equations***volume 2019**, Article number: 214 (2019)

The Correction to this article has been published in Advances in Difference Equations 2019 2019:366

## Abstract

An oil spill is the release of liquid petroleum into the marine ecosystem leading to huge damages in the natural resources. Prediction of oil spill spreading can help in handling accidental oil spills. This study is to present numerical simulation to predict the movement of oil slicks in the Gulf of Thailand, based on the wind speed prediction obtained by an ocean wave model. The numerical results show that oil slicks can move toward different coastal areas.

## Introduction

In the past few decades, there have been nine oil spills in the Gulf of Thailand according to the Thai Marine Knowledge Hub (MKH). The effect of oil spill in the sea surface is represented by several factors including advection, biodegradation, dispersion, dissolution, evaporation, emulsification, sedimentation, and spreading [1]. The Gulf of Thailand is located on the east coast of Thailand and is very important economically for fishery, traveling, and ship transport [2]. It is also a crucially important tourist attraction and economic maritime. The forecast of wave height is very important to people living in the coastal areas. It affects the human activities in seas. The winds and waves are the two important factors for driving forces which generate several oceanic phenomena in the coastal area and open ocean. Waves are very essential for activities such as exploitation of natural resources, ship-routing, design of harbors, breakwaters and jetties, loading and unloading of ship’s cargo, and estimation of sediment transport [3]. There are some research which used altimeter wind speed to provide information on the distribution of energy within the wave spectrum [4]. The wave data has been used to assimilate altimeter in a third generation wave model [5]. In 2000, Vethamony *et al.* [3] used winds from the model of the European Centre for Medium-Range Weather Forecast (ECMWF) to hindcast waves over the Indian Ocean and to compare with Geosat wave parameters. There were striking differences among the three sets of results, basically due to limitation of the model in shallow water and inaccuracy in the visually observed wave data. In 2004, Bhatt *et al.* [6] used winds from multi-frequency scanning microwave radiometer (MSMR) in the WAM model and compared the results with buoys and altimeter observations in the Indian Ocean. The result showed that ingestion of MSMR winds in the forecast model improves surface wind analysis and wave prediction. In 2005, Kanbua *et al.* [7] investigated the significant wave height in the Gulf of Thailand during Typhoon Linda in 1997 by using WAM and the general regression neural network model (GRNN). As a result, the GRNN model showed the better forecasting results compared with those obtained from the WAM model with RMSE < 0.15 m. In 2006, Sebastiao and Soares [8] presented the uncertainties in the predictions of oil spill trajectories using a classic oil spill model. The wind, wave, and current data were used in this model.

The objective of this paper is to predict oil spill movement in the Gulf of Thailand based on the ocean wave model. The ocean wave model, WAM, is chosen in this study because it is widely used to predict the transport of the two-dimensional wave spectrum [9]. The prediction data from WAM are selected on a fine weather day and on a day with the storm Pabuk, one of the severe cyclones in the Gulf of Thailand.

## Mathematical model

The first generation wave models, developed in the 1960s and early 1970s [10], applied a simple model of spectrum for wind waves using the wave frequency in the equilibrium range based on wave breaking [11]. The second generation models were developed in 1970s based on some experiments [10, 12, 13] and the direct measurements of the wind input to the waves. In 1981, Snyder *et al.* [14] fundamentally changed the view of the spectral energy balance on the first generation model. This was the main reason for developing the second generation wave models. In this study, we use the ocean wave model which is a third generation wave model that solves the wave transport equation explicitly without any presumptions on the shape of the wave spectrum [15]. It represents physics of the wave evolution in accordance with full set of degrees of freedom of a two-dimensional wave spectrum. The model runs for any given regional or global grid system with a prescribed topographic data set. The grid resolution can be arbitrary in space and time. The propagation of waves can be done on a latitudinal–longitudinal or Cartesian grid [16]. In the present study, we use the ocean wave model to obtain wave prediction in the Gulf of Thailand, and we focus on the wave generation by wind and wave-wave interactions.

### Ocean wave model

In ocean wave modeling, wave prediction can be described by the wave energy balance equation [17] as follows:

where *E* is the wave energy density, *θ* is the wave propagation direction, \(c_{g}\) is the group velocity, \(S_{\mathrm{in}}\) is the process of wave generation by wind, \(S_{\mathrm{nl}}\) is the processes of nonlinear-transfer, and \(S_{\mathrm{wc}}\) is the processes of white capping dissipation. The last three terms are source terms. The input source term \(S_{\mathrm{in}}\), adopted from Snyder *et al.* [14], is given by

where \(\beta= \max \{0,0.25 \frac{\rho_{a}}{\rho_{w}} (28\frac{u_{*}}{c}\cos\theta-1 ) \} \omega\), *F* represents the ocean wave spectrum, \(u_{*}\) denotes the friction velocity, *c* is the phase speed of the waves, \(\omega= 2\pi f\), \(\rho _{a}\) and \(\rho_{w}\) are the density of air and water, respectively. The dissipation source function \(S_{\mathrm{wc}}\), proposed by Komen *et al.* [17], is defined as

where \(\hat{\alpha} = E\hat{\omega}^{4}g^{-2}\), and *ω̂* is an inverse of the mean frequency, \(\hat{\alpha}_{\mathrm{PM}} = 3.016\times 10^{-3}\) is the theoretical value of *ᾱ* for a Pierson–Moskowitz spectrum [15]. The nonlinear source function \(S_{\mathrm{nl}}\) is in the form [10, 15]

where \(n_{j} = F(\mathbf{k}_{j})/\omega_{j}\) is the action spectrum and the coefficient \(\sigma(\mathbf{k_{1}}+\mathbf{k_{2}}-\mathbf {k_{3}}-\mathbf{k_{4}})\) describes the coupling strength of resonantly interacting wavenumber quadruplet \(\mathbf{k_{1}},\mathbf{k_{2}},\mathbf {k_{3}},\mathbf{k_{4}}\). The nonlinear source function \(S_{\mathrm{nl}}\) was presented by Hasselmann *et al.* [10]. The ocean wave model is formulated in circular latitude–longitude coordinates. A numerical technique, based on a finite difference method, is used for wave computation in an arbitrarily specified global or regional grid areas. The wave energy density can be used to derive the significant wave height \(H_{s}\) as follows [17]:

### Oil spill model

The oil spill can be modeled as the diffusion of oil in water, and the concentration of oil over time can be determined based on the diffusivity of oil in water. In this paper, the model of oil spill includes spreading and the movement model of oil slick processes. When an oil spill occurs in the ocean, it initially spreads in the water surface, depending on its relative density and composition. Wind, water current, and wave forces are affected to drift the oil slick over the large areas. Wind and wave data used in the model are generated by the ocean wave model in Equation (1).

#### Movement of oil slick

In this section, the mathematical model for the oil slick movement into the area of the Gulf of Thailand is presented. The shape of oil slick is assumed to be circular. The seabed area of the Gulf of Thailand is approximately 304,000 km^{2} ranging from latitude 5°N to 15°N and longitude 95°E to 105°E. The northern part of the Gulf of Thailand is at the estuary of Chao Phraya River [18]. The Gulf of Thailand is a shallow sea which has 58 m in mean depth and the maximum depth is only 85 m [2]. We assume that the oil droplets can be neglected. The position of the oil slick can be determined by

where *U* and *V* are the predicted wind velocity components in *x* and *y* directions, respectively, which can be obtained by an ocean wave model. The coordinate \((X,Y)\) is the center of the circular oil slick and \((X_{0},Y_{0})\) is the position of oil spill at the initial time.

## Numerical results and discussions

In this section, we present the numerical simulation to predict spreading of the oil slick in the Gulf of Thailand. In this study, their oil slicks, denoted by OS1, OS2, and OS3 are assumed to be originating at three drilling rigs, namely, Benchamas, Pathong, and Bongkot South, respectively. The locations of the three drilling rigs are at the following latitudes and longitudes: 10.42N 101.30E, 9.68N 101.40E, and 7.37N 102.60E, as shown in Fig. 1(a). The movement of oil slicks is based on Equation (6) which requires wind prediction, including wind speeds, and wind directions as input data. These data can be obtained from WAM, an ocean wave model. In our simulation, we present two study cases: a fine weather day on 6 December 2018 and a day with the tropical storm Pabuk on 4 January 2019. On the fine weather day, three snapshots of the three oil slicks are illustrated in Fig. 1. Table 1 shows the information of each snapshot in Fig. 1. The information includes the time duration between two snapshots, the positions of each oil slick, the distances that the oil slick can travel between two snapshots, the wind speed, and the significant wave height. Table 2 shows the significant wave height and the wind speed in the path that traveling each oil slick means along the total traveling distance, and the total traveling time of each oil slick. It can be seen that the oil slick OS3 moves relatively faster toward a coastal area compared to the oil slicks OS1 and OS2. This is because the averaged wind speed is higher. On the day with the cyclone Pabuk, similar snapshots are presented in Fig. 2. Tables 3 and 4 show similar information as in those for the fine weather day. A similar result is obtained as in the case of the fine weather day.

Comparing the averaged wind speeds and the averaged significant wave heights in Tables 2 and 4, it shows that the wind speed on the day with the storm Pabuk is roughly three times larger than that on the fine day. This leads to the larger value of the averaged significant wave height in the same order. Therefore, the wind is a major factor that affects the wave energy density which is represented by the significant wave height. It is also seen from Figs. 1 and 2 that the coastal areas with the three oil slicks moving toward them on the fine weather day are larger than those on the day with the cyclone Pabuk. This is because the wind direction varies in a great range. Therefore, a good management of oil spill would be greatly needed.

## Conclusions

In this paper, we present a numerical simulation to predict oil spill spreading in the Gulf of Thailand. In the simulation, we use the wind prediction, obtained from an ocean wave model, as the input to simulate the oil slick movement starting at three different drilling rigs. The results show that for a fine weather day the oil slicks land on larger areas compared to those on a day with the cyclone Pabuk.

## Change history

### 02 September 2019

After publication of this article [1], it was brought to our attention that the article type should be “Research” rather than “Review”.

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## Acknowledgements

We would like to thank the Marine Meteorological Center, Thai Meteorological Department for suggestion on WAM. We also would like to thank Nikita Savchenko for suggestion on the oil spread model.

### Funding

The first author would like to thank Panyapiwat Institute of Management for funding scholarship. The second author would like to thank the Centre of Excellence in Mathematics, Commission on Higher Education, Thailand, for financial support.

## Author information

### Affiliations

### Contributions

KS simulated, analyzed simulation results, and wrote the research paper. KC designed the research work, analyzed and interpreted simulation results, and wrote the research paper. WK analyzed, interpreted simulation results, and revised the research paper. All authors read and approved the final manuscript.

### Corresponding author

Correspondence to Kittisak Chayantrakom.

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The authors declare that they have no competing interests.

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### Keywords

- Linear geometric interpolation
- Ocean wave model
- Oil spill
- Spreading