# Modeling of Accidental Oil Spills at Different Phases of LNG Terminal Construction

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Models

#### 2.1. Numerical Domain and Selected Scenarios

_{2}, S

_{2}, K

_{1}, and O

_{1}.

^{3}, a viscosity of 95.50 mm

^{2}/s at 15 °C, and a vapor pressure of 0.184 bar. Note that this gradual spill condition improves the relatively unrealistic oil spill scenarios with an instantaneous total spill condition applied in Lee et al. [3]. To evaluate the model predictability, the predicted tidal elevation and current speeds were compared to the observed data by the Korea Hydrographic and Oceanographic Agency. The validation was executed in the vicinity of the construction site at two points (T1 and T2) for the tidal elevation and three points (PC1, PC2, and PC3) for the current speed, as shown in Figure 2e.

#### 2.2. Hydrodynamic Model

_{x}and m

_{y}are the horizontal scale factors; H is the sum of the mean water depth (h) and free surface elevation (ζ) H = h + ζ; U and V are the horizontal velocity components in the curvilinear, orthogonal coordinates x and y, respectively; and W is the vertical velocity in the σ-stretched dimensionless vertical coordinate z [22].

_{e}is the Coriolis parameter; g is the gravitational acceleration; P is the pressure; A

_{v}is the vertical eddy viscosity, determined based on the second moment turbulence closure model [24,25]; Q

_{u}and Q

_{v}are the source and sink terms, respectively. Further details of the above formulations and numerical techniques employed in the EFDC model are provided in Hamrick [22].

#### 2.3. Oil Spill Model

**U**is the sea current mean field with components (U, V, W),

**K**is the diffusivity tensor which parameterizes the turbulent effects, and r

_{j}(C) are the M transformation rates that modify the tracer concentration by means of physical and chemical transformation processes.

_{1}is the oil concentration solution solely due to the weathering process, while the final time rate of change of C is given by the advection-diffusion acting on C

_{1}. Considering the oil volume, density $\rho $, and unit area A, the surface oil concentration (C

_{S}) and the dispersed oil concentration (C

_{D}), with units of kg m

^{−2}, can be defined as

_{D}are the surface and dispersed oil volumes. When the surface oil arrives close to the coasts, defined by a reference segment L

_{C}, the oil can be absorbed and the concentration of oil at the coasts, C

_{C}, is defined as

_{C}is the absorbed oil volume. In order to use the [26] transformation algorithms, the surface volume, V

_{S}, is subdivided into a thin part, V

^{TN}, and a thick part, V

^{TK}, as

^{TN}and A

^{TK}are the areas occupied by the thick and thin surface slick volume, and T

^{TN}and T

^{TK}are the thicknesses of the thick and thin surface slicks.

_{S}(Equation (7)), C

_{D}(Equation (7)), and C

_{C}(Equation (9)), the surface volume is broken into N constituent particles that are characterized by a particle volume index, v(n

_{k},t), particle status index, σ(n

_{k},t), and particle position vector

**x**

_{k}(n

_{k},t) defined as

_{k}is the particle identification number. Following uncoupled Langevin equations, the time evolution of the particle position vector

**x**

_{k}(n

_{k},t) is given as

**A**(

**x**

_{k},t) represents the deterministic part (i.e.,

**U**in Equation (4)), while the tensor

**B**(

**x**

_{k},t) and

**ξ**(t) characterizing random motion and a random motion factor represent the stochastic part of the flow field. Furthermore, the particle volume index, v(n

_{k},t), is subdivided into evaporative, v

_{E}(n

_{k},t), and non-evaporative, v

_{NE}(n

_{k},t), particle volume attributes as follows:

_{k},t), is updated using empirical formulas that relate to the time rate of change of oil slick volume state variables. The particle status index, σ(n

_{k},t), identifies the four particle classes (i.e., particles on the surface, subsurface or dispersed particles, sedimented particles, particles on the coasts). Further details of the expansion of Equation (10) and the description of the time rate of oil slick volume state variables are explained in De Dominicis et al. [17]. The above processes are summarized in a flowchart as shown in Figure 4.

## 3. Results and Discussion

#### 3.1. Model Verification

#### 3.1.1. Tidal Elevation and Current

_{2}, S

_{2}, K

_{1}, and O

_{1}. For all the gauge stations, the amplitude approximation error, E

_{app}, i.e., $\left({A}_{obs}-{A}_{comp}\right)/{A}_{comp}\times 100$, where A

_{obs}and A

_{comp}are the observed and computed amplitudes, averaged over the four tidal constituents, was below 10%, which indicates that, in general, the computed amplitudes and phases of the tidal currents did not deviate intensely from the observed data except for PC2.

#### 3.1.2. Residual Current

#### 3.2. Tidal Currents Variation Considering Permeable Revetments

#### 3.2.1. Water Circulation through Permeable Revetments

_{C}denotes a closed area surrounded by sea dikes, h

_{0}is the tidal elevation outside A, Q is the circulation flow rate per unit length of dike, and L is the total length of dike (Figure 9). In LHS of Equation (15, the time rate of change in h

_{0}is used because the permeability coefficient varies depending on the elevations both inside and outside of the revetments. Data for the time rate of change in h

_{0}were provided by Korean Ministry of Oceans and Fisheries.

#### 3.2.2. Tidal Current Velocity Fields

#### 3.3. Oil Spill Dispersion

#### 3.3.1. Scenario 1

^{2}and LSFO density is 910 kg/m

^{3}, may be estimated as 0.55 mm, largely comparable to typical values of oil slick thickness. Approximately 10 h after the initiation of the spill, the oil slick entered the expected reclamation area (Figure 14e). In 12 h, the oil slick is advected to the inner reclamation area and dispersed (Figure 14f). At the same time, oil slick with relatively lower oil concentration tends to be advected north following the alongshore current observed in Figure 11a. Note that the permeable revetment only allows a limited oil slick near the north edge of the western revetment (Figure 14f).

#### 3.3.2. Scenario 2

_{C}(Equation (9)) in MEDSLIK-II. Samaras et al. [30] explicitly showed that the oiled shoreline modeled with the modified version better matched satellite observation. With these modifications applied, the current model has the potential to enhance the predictability of oil behavior near the coastline in the future works. The accurate prediction of the expected length of the oiled shoreline is important to evaluate the clean-up costs correctly. For example, Etkin [32] reported that about 6000 USD/tonne are needed to clean-up an oiled shoreline of 2–5 km, while about 11,000 USD/tonne are needed for the recovery of an oiled shoreline of 8–15 km.

#### 3.3.3. Scenario 3

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Bathymetry contours in meters in the (

**a**) expanded and (

**c**) detailed domain. The extent of a multilayered orthogonal curvilinear grid system in the (

**b**) expanded and (

**d**) detailed domain. (

**e**) Enlarged view of target area. T1-T2 indicate the locations of the tidal elevation stations, and PC1-PC3 indicate the locations of the tidal current stations.

**Figure 3.**Ship collision scenarios based on a proposed construction plan of the Songdo LNG terminal in (

**a**) phase 1, (

**b**) phase 2, and (

**c**) phase 3. The three most likely scenarios have been chosen by considering distinguished construction stages with corresponding terminal architectures, vessel numbers, locations, types, sizes, and navigation routes. For each scenario, a collision symbol (a star in red) is included to highlight the location at which the oil spill is initiated.

**Figure 5.**Computed tidal elevations using the EFDC model compared with the corresponding observed data at (

**a**) T1 and (

**b**) T2.

**Figure 6.**Comparison of the temporal variations of the observed horizontal (U) and vertical (V) current velocity components at (

**a**,

**b**) PC2 and (

**c**,

**d**) PC3.

**Figure 7.**Comparison of the trajectories and the resultant magnitudes and directions of the average velocities of the residual currents between the (

**a**) observed and the (

**b**–

**d**) computed data at PC2.

**Figure 8.**Comparison of the trajectories and the resultant magnitudes and directions of the average velocities of the residual currents between the (

**a**) observed and the (

**b**–

**d**) computed data at PC3.

**Figure 9.**Schematic of the groundwater flow through permeable sea-dyke in (

**a**) plan view and (

**b**) side view.

**Figure 10.**Locations of the station inside and outside the revetment for comparison of the modeled results. Circles indicate the locations of the passage deployments for an additional seawater exchange consideration.

**Figure 11.**Current velocity fields in case 1 during the pre-construction phase without revetments installed. Current fields are shown in the enlarged views during (

**a**) flood and (

**b**) ebb and in the detailed domain near the LNG terminal construction site during (

**c**) flood and (

**d**) ebb.

**Figure 12.**Current velocity fields in case 2 with only revetments were constructed without the seawater passages installed. Current fields are shown in the enlarged views during (

**a**) flood and (

**b**) ebb and in the detailed domain near the LNG terminal construction site during (

**c**) flood and (

**d**) ebb.

**Figure 13.**Current velocity fields in case 3, with both revetments and passages constructed. Current fields are shown in the enlarged views during (

**a**) flood and (

**b**) ebb and in the detailed domain near the LNG terminal construction site during (

**c**) flood and (

**d**) ebb.

**Figure 14.**Temporal variation of the simulated oil concentration [tonne·km

^{−2}] in (

**a**) 2, (

**b**) 4, (

**c**) 6, (

**d**) 8, (

**e**) 10, and (

**f**) 12 h after initiation in Scenario 1. Background vectors visualize tidal current fields.

**Figure 15.**Temporal variation of the simulated oil concentration [tonne·km

^{−2}] in (

**a**) 2, (

**b**) 4, (

**c**) 6, (

**d**) 8, (

**e**) 10, and (

**f**) 12 h after initiation in Scenario 2. Background vectors visualize tidal current fields.

**Figure 16.**Temporal variation of the simulated oil concentration [tonne·km

^{−2}] in (

**a**) 2, (

**b**) 4, (

**c**) 6, (

**d**) 8, (

**e**) 10, and (

**f**) 12 h after initiation in Scenario 3. Background vectors visualize tidal current fields.

**Table 1.**Selected volumes of the fuel tanker for each scenario used in the current study. The spilled oil volume is assumed to be approximately 70% of the tanker capacity in the fuel tanker.

Scenario | Vessel Horsepower (HP) | Tanker Capacity (L) | Oil Spillage Volume (L) | Initial Spill Location |
---|---|---|---|---|

1 | 3200 | 42,000 | 29,400 | Western revetment |

2 | 2600 | 33,000 | 23,100 | Eastern revetment |

3 | 1000 | 15,000 | 10,500 | Eastern revetment |

**Table 2.**Computed tidal elevations using the environmental fluid dynamics code (EFDC) model compared with the corresponding observed data at (a) T1 and (b) T2.

Tidal Elevation | Amplitude (cm) | Phase (°) | Approximation Relative Error (%) | |||
---|---|---|---|---|---|---|

Gauge Station | Constituents | Observed | Computed | Observed | Computed | |

T1 | M_{2} | 286.2 | 279.3 | 141.4 | 138.5 | 2.0 |

S_{2} | 112.7 | 110.6 | 201.6 | 197.7 | ||

K_{1} | 39.4 | 39.1 | 306.8 | 305.8 | ||

O_{1} | 25.2 | 25.4 | 265.7 | 266.6 | ||

T2 | M_{2} | 278.5 | 127.5 | 274.0 | 134.0 | 2.5 |

S_{2} | 112.6 | 184.3 | 108.6 | 192.0 | ||

K_{1} | 38.8 | 301.7 | 39.2 | 302.8 | ||

O_{1} | 28.5 | 262.1 | 25.2 | 263.5 |

**Table 3.**Computed eastward tidal velocity components using the EFDC model compared with the corresponding observed data at PC1, PC2, and PC3.

Horizontal Velocity (U) | Amplitude, A (cm/s) | Phase, θ (°) | Approximation Relative Error, E_{app} (%) | |||
---|---|---|---|---|---|---|

Gauge Station | Constituents | Observed | Computed | Observed | Computed | |

PC1 | M_{2} | 59.2 | 57.9 | 45.8 | 46.6 | −0.3 |

S_{2} | 20.3 | 23.5 | 105.7 | 106.2 | ||

K_{1} | 6.6 | 5.0 | 238.1 | 217.1 | ||

O_{1} | 3.1 | 3.1 | 188.5 | 183.9 | ||

PC2 | M_{2} | 34.1 | 33.6 | 38.9 | 50.0 | −8.3 |

S_{2} | 9.9 | 17.5 | 281.4 | 307.7 | ||

K_{1} | 4.1 | 3.2 | 217.8 | 217.8 | ||

O_{1} | 3.8 | 1.9 | 232.6 | 182.0 | ||

PC3 | M_{2} | 28.8 | 29.8 | 95.2 | 94.5 | −6.3 |

S_{2} | 12.9 | 16.8 | 172.3 | 180.1 | ||

K_{1} | 4.2 | 3.8 | 296.0 | 300.9 | ||

O_{1} | 3.5 | 2.1 | 274.2 | 274.9 |

**Table 4.**Computed northward tidal velocity components using the EFDC model compared with the corresponding observed data at PC1, PC2, and PC3.

Vertical Velocity (V) | Amplitude, A (cm/s) | Phase, θ (°) | Approximation Relative Error, E_{app} (%) | |||
---|---|---|---|---|---|---|

Gauge Station | Constituents | Observed | Computed | Observed | Computed | |

PC1 | M_{2} | 26.3 | 24.5 | 57.8 | 42.8 | 3.1 |

S_{2} | 8.3 | 9.7 | 110.1 | 103.3 | ||

K_{1} | 2.9 | 2.2 | 251.2 | 217.1 | ||

O_{1} | 1.7 | 1.6 | 204.0 | 170.7 | ||

PC2 | M_{2} | 34.3 | 33.2 | 45.5 | 50.2 | 9.7 |

S_{2} | 15.7 | 13.1 | 30.9 | 39.5 | ||

K_{1} | 4.5 | 2.4 | 219.7 | 217.8 | ||

O_{1} | 1.0 | 1.4 | 15.8 | 15.0 | ||

PC3 | M_{2} | 7.3 | 7.0 | 111.6 | 121.4 | 3.6 |

S_{2} | 3.5 | 4.0 | 193.1 | 188.7 | ||

K_{1} | 1.7 | 1.5 | 296.0 | 300.0 | ||

O_{1} | 1.3 | 0.8 | 30.9 | 33.2 |

**Table 5.**Comparison of the computed tidal elevation at high tide with and without the installation of the three passages at T3 and T4.

Condition | Tidal Elevation at High Tide (m) | Δh_{0} (m) | |
---|---|---|---|

T3 | T4 | ||

Without passage | 9.19 | 7.73 | 1.46 |

With passage | 9.19 | 8.37 | 0.82 |

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**MDPI and ACS Style**

Na, B.; Son, S.; Choi, J.-C.
Modeling of Accidental Oil Spills at Different Phases of LNG Terminal Construction. *J. Mar. Sci. Eng.* **2021**, *9*, 392.
https://doi.org/10.3390/jmse9040392

**AMA Style**

Na B, Son S, Choi J-C.
Modeling of Accidental Oil Spills at Different Phases of LNG Terminal Construction. *Journal of Marine Science and Engineering*. 2021; 9(4):392.
https://doi.org/10.3390/jmse9040392

**Chicago/Turabian Style**

Na, Byoungjoon, Sangyoung Son, and Jae-Cheon Choi.
2021. "Modeling of Accidental Oil Spills at Different Phases of LNG Terminal Construction" *Journal of Marine Science and Engineering* 9, no. 4: 392.
https://doi.org/10.3390/jmse9040392