# Modeling of the Fate and Behaviors of an Oil Spill in the Azemmour River Estuary in Morocco

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{3}/s. Along the Atlantic Moroccan coast, the tide is semi-diurnal, and at the estuary of the Oum Er-Rbia River, its amplitude alternates between approximately 1.5 m and 4 m, as reported by the Casablanca Port maritime services [27].

## 3. Model Theoretical Formulation

_{d}is a source or sink of fluid, g is the gravitational acceleration, η is the free surface elevation, (S

_{x}, S

_{y}) are the source or sink terms in the dynamic equations representing the wind, S

_{T}is the source or sink of tracer, (ν

_{t}, ν

_{T}) are momentum (eddy viscosity) and tracer diffusion coefficients, and T

_{p}is the passive (non-buoyant) tracer. Herein the unknowns are d, u, v, and T

_{p}.

_{k}= C

_{f}

^{(}

^{−1/2)}and C

_{ε}= 3.6(C

_{2ε}C

_{µ}

^{(}

^{1/2)})/C

_{f}

^{(}

^{−1/2)}, C

_{f}is the bed friction coefficient, u

_{∗}is the shear velocity, ν

_{t}= C

_{µ}(k

^{2}/ε), C

_{µ}= 0.09, C

_{1ε}= 1.44, C

_{2ε}= 1.92, σ

_{k}= 1.0, σ

_{ε}= 1.3. The use of the k-Epsilon model often requires a finer mesh than the constant viscosity model and, in this way, increases computation time. The model equations are solved by a fractional step method, with the convection of turbulent variables being processed at the same time as the hydrodynamic variables, and the other terms relating to the diffusion and production/dissipation of turbulent values being processed in a single step.

_{o}is the oil-slick velocity vector, V

_{c}is the current velocity vector at the free surface, V

_{w}is the wind velocity vector, and β is a wind drift factor. The current velocity can be estimated using the classical log-law assumption based on the depth-averaged velocity. By applying the second law of dynamics to the advected oil particle in steady condition, and after some assumptions and simplifications, considering the relative particle velocity with respect to the current and wind velocities, a value of almost 3.6% was defined for β.

_{c}is the neutral turbulent Schmidt number and ξ(t) is a vector with independent, standardized random components.

_{w}− ρ

_{o})/ρ

_{w}, ρ

_{w}is the water density, ρ

_{o}is the oil density, and ν

_{o}is the oil kinematic viscosity.

_{i}is the mass of component i, K

_{ev}is the evaporation mass transfer coefficient, A

_{i}is the area of component i, ΔH

_{i}is the molar enthalpy of component i, R is the universal gas constant, T

_{Bi}is the boiling point of component i, T is the ambient temperature, m

_{j}is the mass of an element j, and M

_{j}its molar mass.

## 4. Model Boundaries and Forcing Data

#### 4.1. Bathymetry

#### 4.2. Meteorological Parameters

## 5. Results

#### 5.1. Hydrodynamic Model Results

^{3}/s at the mouth of the Oum Er-Rbia River. Since the computational domain size is not large enough, the simulations were performed under barotropic conditions, with constant water temperature and salinity. At the offshore open boundaries, a tidal height of almost 2.8 m (see Table 1) was imposed, and a solid condition is used for the shorelines. Due to the unavailability of spatial wind data in the study area, a wind velocity of constant direction and magnitude of almost 4 m/s was considered. The numerical simulation was performed over a period of three days, which was considered sufficient to provide useful insights into the behavior of the oil spill in such a computational domain, as shown in Figure 3.

#### 5.2. Oil Spill Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Iouzzi, N.; Mouakkir, L.; Ben Meftah, M.; Chagdali, M.; Loudyi, D. SWAN Modeling of Dredging Effect on the Oued Sebou Estuary. Water
**2022**, 14, 2633. [Google Scholar] [CrossRef] - Zhu, G.; Xie, Z.; Xu, H.; Wang, N.; Zhang, L.; Mao, N.; Cheng, J. Oil Spill Environmental Risk Assessment and Mapping in Coastal China Using Automatic Identification System (AIS) Data. Sustainability
**2022**, 14, 5837. [Google Scholar] [CrossRef] - Balogun, A.L.; Yekeen, S.T.; Pradhan, B.; Wan Yusof, K.B. Oil Spill Trajectory Modelling and Environmental Vulnerability Mapping Using GNOME Model and GIS. Environ. Pollut.
**2021**, 268, 115812. [Google Scholar] [CrossRef] [PubMed] - Sun, S.; Lu, Y.; Liu, Y.; Wang, M.; Hu, C. Tracking an Oil Tanker Collision and Spilled Oils in the East China Sea Using MultiSensory Day and Night Satellite Imagery. Geophys. Res. Lett.
**2018**, 45, 3212–3220. [Google Scholar] [CrossRef] - Guo, W. Development of a Statistical Oil Spill Model for Risk Assessment. Environ. Pollut.
**2017**, 230, 945–953. [Google Scholar] [CrossRef] - Chen, J.; Zhang, W.; Wan, Z.; Li, S.; Huang, T.; Fei, Y. Oil Spills from Global Tankers: Status Review and Future Governance. J. Clean. Prod.
**2019**, 227, 20–32. [Google Scholar] [CrossRef] - TOPF. Oil Tanker Spill Statistics 2021; ITOPF Ltd.: London, UK, 2022. [Google Scholar]
- Osuji, L.C.; Onojake, C.M. Trace Heavy Metals Associated with Crude Oil: A Case Study of Ebocha-8-Oil-Spill-Polluted Site in Niger Delta, Nigeria. J. Chem. Biodivers.
**2004**, 1, 1569–1577. [Google Scholar] [CrossRef] - Ojimba, T.G.P.; Akintola, J.; Anyanwu1, S.O.; Manilla, H.A. An Economic Analysis of Crude Oil Pollution Effects on Crop Farms in Rivers State, Nigeria. J. Dev. Agric. Econ.
**2014**, 6, 290–298. [Google Scholar] [CrossRef] - Yang, S.; Xing, K.; Yang, Y. Offshore Oil Pollution and Prevention Measures. E3S Web Conf.
**2021**, 271, 02010. [Google Scholar] [CrossRef] - Jabbar, S.M. Effect of Oil Pollution on Growing and Diversity of Aquatic Plants. Plant Arch.
**2018**, 18, 2649–2655. [Google Scholar] - Allers, E.; Abed, R.M.M.; Wehrmann, L.M.; Wang, T.; Larsson, A.I.; Purser, A.; De Beer, D. Resistance of Lophelia Pertusa to Coverage by Sediment and Petroleum Drill Cuttings. Mar. Pollut. Bull.
**2013**, 74, 132–140. [Google Scholar] [CrossRef] [PubMed] - Carpenter, A. Oil Pollution in the North Sea: The Impact of Governance Measures on Ooil Pollution Over Several Decades. Hydrobiologia
**2019**, 845, 109–127. [Google Scholar] [CrossRef] - Yang, S.Z.; Jin, H.J.; Wei, Z.; He, R.X.; Ji, Y.J.; Li, X.M.; Yu, S.P. Bioremediation of Oil Spills in Cold Environments: A Review. Pedosphere
**2009**, 19, 371–381. [Google Scholar] [CrossRef] - Quoc, P.L.; Solovieva, A.Y.; Uspenskaya, M.V.; Olekhnovich, R.O.; Sitnikova, V.E.; Strelnikova Inna, E.; Kunakova, A.M. High-Porosity Polymer Composite for Removing Oil Spills in Cold Regions. ACS Omega
**2021**, 6, 20512–20521. [Google Scholar] [CrossRef] - Nyankson, E.; Rodene, D.; Gupta, R.B. Advancements in Crude Oil Spill Remediation Research After the Deepwater Horizon Oil Spill. Water Air Soil Pollut.
**2016**, 227, 29. [Google Scholar] [CrossRef] - Brakstad, O.G.; Lewis, A.; Beegle-Krause, C.J. A Critical Review of Marine Snow in the Context of Ooil Spills and Oil Spill Dispersant Treatment with Focus on the Deepwater Horizon oil spill. Mar. Pollut. Bull.
**2018**, 135, 346–356. [Google Scholar] [CrossRef] - Kvočka, D.; Žagar, D.; Banovec, P. A Review of River Oil Spill Modeling. Water
**2021**, 13, 1620. [Google Scholar] [CrossRef] - Niu, H.; Li, S.; Li, P.; King, T.; Lee, K. Stochastic Modeling of the Fate and Behaviors of an Oil Spill in the Salish Sea. Int. J. Offshore Polar Eng.
**2017**, 27, 337–345. [Google Scholar] [CrossRef] - Lopes, B.V.; Pavlovic, A.; Trombetta, T.B.; Oleinik, P.H.; Monteiro, C.B.; Guimaraes, R.C.; Silva, D.V.; Marques, W.C. Numerical Study of Oil Spill in the Patos Lagoon Under Flood and Ebb Conditions. J. Mar. Sci. Eng.
**2019**, 7, 4. [Google Scholar] [CrossRef] - Lavine, W.; Jamal, M.H.; Abd Wahab, A.K.; Kasiman, E.H. Effect of Sea Level Rise on Oil Spill Model Drift Using TELEMAC-2D. J. Water Clim. Chang.
**2020**, 11, 1021–1031. [Google Scholar] [CrossRef] - Eke, D.C.; Anifowose, B.; Van De Wiel, M.J.; Lawler, D.; Knaapen, M.A.F. Numerical Modelling of Oil Spill Transport in Tide-Dominated Estuaries: A Case Study of Humber Estuary, UK. J. Mar. Sci. Eng.
**2021**, 9, 1034. [Google Scholar] [CrossRef] - Monteiro, C.B.; Oleinik, P.H.; Leal, T.F.; Kirinus, E.D.P.; Junior, E.E.T.; Marques, W.C.; Lopes, B.D.C.F.L. Susceptibility to Oil Spill Spreading Using Case Studies and Simulated Scenarios. Environ. Pollut.
**2020**, 267, 115451. [Google Scholar] [CrossRef] [PubMed] - Brière, C.; Abadie, S.; Bretel, P.; Lang, P. Assessment of TELEMAC System Performances, a Hydrodynamic Case Study of Anglet, France. Coast. Eng.
**2007**, 54, 345–356. [Google Scholar] [CrossRef] - Villaret, C.; Hervouet, J.; Kopmann, R.; Merkel, U.; Davies, A.G. Morphodynamic Modeling using the TELEMAC Finite-Element System. Comput. Geosci.
**2013**, 53, 105–113. [Google Scholar] [CrossRef] - Zhang, Y.; Chen, S.; Hong, Z.; Han, Y.; Li, B.; Yang, S.; Wang, J. Feasibility of Oil Slick Detection Using BeiDou-R Coastal Simulation. Hindawi Math. Probl. Eng.
**2017**, 2017, 8098029. [Google Scholar] [CrossRef] - El Jakani, M.; Ettazarini, S.; Rhinane, H.; Raji, M.; Radid, M.; Talbi, M. Impact of Anthropogenic Facilities on the Morphodynamic Evolution of an Estuarine System: The Case of Oum Er-Rbia Estuary (Azemmour, Morocco). J. Mar. Sci. Eng.
**2019**, 7, 248. [Google Scholar] [CrossRef] - Lang, P.; Desombre, J.; Ata, R.; Goeury, C.; Hervouet, J.M. Telemac Modelling System, 2D Hydrodynamics, TELEMAC-2D Software, Release 7.0; User Manual. 2014. Available online: http://www.opentelemac.org/downloads/MANUALS/TELEMAC-2D/telemac-2d_user_manual_en_v7p0.pdf (accessed on 3 May 2023).
- Goeury, C.; Jean-Michel Hervouet, J.H.; Baudin-Bizien, I.; Thouvenel, F. A Lagrangian/Eulerian oil spill model for continental waters. J. Hydraul. Res.
**2014**, 52, 36–48. [Google Scholar] [CrossRef] - Brown, J.M.; Davies, A.G. Flood/ebb Tidal Asymmetry in a Shallow Sandy Estuary and the Impact on Net Sand Transport. Geomorphology
**2010**, 114, 431–439. [Google Scholar] [CrossRef] - Rahman, A.; Venugopal, V. Parametric Analysis of Three Dimensional Flow Models Applied to Tidal Energy Sites in Scotland. Estuar. Coast. Shelf Sci.
**2017**, 189, 17–32. [Google Scholar] [CrossRef] - Al Hakim, B.; Wibowo, M.; Kongko, W.; Irfani, M.; Hendriyono, W.; Gumbira, G. Hydrodynamics Modeling of Giant Seawall in Semarang Bay. Procedia Earth Planet. Sci.
**2015**, 14, 200–207. [Google Scholar] [CrossRef]

**Figure 3.**Meshing of the computational domain: unstructured triangular grid mesh (as shown by the enlarged view) of approximately 50 m resolution. The colors from blue to red indicate the increasing trend of the bathymetry.

**Figure 4.**Annual average wind direction rose in the Azemmour estuary. The vertical axis represents the frequency (percentage) from which winds originate (http://fr.wisuki.com, accessed on 3 May 2023).

**Figure 9.**Oil spreading under wind effect. The star symbol indicates the location of the oil release.

Tide | Low Tide | High Tide | Tidal Range |
---|---|---|---|

Exceptional high water | 0.20 | 3.90 | 3.70 |

Medium–high water | 0.70 | 3.50 | 2.80 |

Medium still waters | 1.50 | 2.80 | 1.30 |

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**MDPI and ACS Style**

Iouzzi, N.; Ben Meftah, M.; Haffane, M.; Mouakkir, L.; Chagdali, M.; Mossa, M.
Modeling of the Fate and Behaviors of an Oil Spill in the Azemmour River Estuary in Morocco. *Water* **2023**, *15*, 1776.
https://doi.org/10.3390/w15091776

**AMA Style**

Iouzzi N, Ben Meftah M, Haffane M, Mouakkir L, Chagdali M, Mossa M.
Modeling of the Fate and Behaviors of an Oil Spill in the Azemmour River Estuary in Morocco. *Water*. 2023; 15(9):1776.
https://doi.org/10.3390/w15091776

**Chicago/Turabian Style**

Iouzzi, Nisrine, Mouldi Ben Meftah, Mehdi Haffane, Laila Mouakkir, Mohamed Chagdali, and Michele Mossa.
2023. "Modeling of the Fate and Behaviors of an Oil Spill in the Azemmour River Estuary in Morocco" *Water* 15, no. 9: 1776.
https://doi.org/10.3390/w15091776