**1. Introduction**

The degradation of aquatic ecosystem is generally agreed to be undesirable. Historically, most evaluations of the ecological effects of petroleum contamination have related impacts to effects on the supply of products and services of importance to human cultures. According to Xu and Pang [1], most of the environmental and pollution control laws were legislated to protect ecological objectives and public health. Here, a substance is considered to be a pollutant if it is perceived to have adverse effects on wildlife or human well-being. In recent years, a number

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of substances appear to pose such threats. Among them is crude oil spillage, which first came to public attention with the *Torrey Canyon* disaster in 1967.

The risk of crude oil spillage to the sea presents a major threat to the marine ecology compared with other sources of pollution in the oceans. Before now, it was earlier reported that oil spillage impacts negatively on wildlife and their environments in various ways, which include the alteration of the ecological conditions, and can result into alterations of the environmental physical and chemical composition, destruction of nutritional capita of the marine biomass, changes in the biological equilibrium of the habitat, and as a threat to human health [2]. The same can also be said about Nigeria, where oil spillage is a major environmental problem and its coastal zone is rated as one of the most polluted spots on the planet in the year 2006 [3]. For instance, from 1976 to 2007, over 1,896,960 barrels of oil were sunk into the Nigerian coastal waters resulting in a serious pollution of drinkable water and destruction of resort centers, properties, and lives along the coastal zone. This was seen to be a major contributor to the regional crisis in the Nigeria Niger-Delta region.

As a case in point, after a spill in the ocean, oil in water body, regardless of whether it originated as surface or subsurface spill, forms a thin film called oil slick as it spreads in water. The oil slick movement is governed by the advection and blustery diffusion as a result of water current and wind action. The slick always spreads over the water surface due to gravitational, inertia, gluey, and interfacial strain force equilibrium. The oil composition also changes from the early time of the spill. Thus, the water-soluble components of the oil dissolve in the water column, whereas the immiscible components emulsified and disperse in the water column as small droplets and light (low molecular weight) fractions evaporate (for example, see [4]).

In essence, the frequency of accidental oil spills in aquatic environments has presented a growing global concern and awareness of the risks of oil spills and the damage they do to the environment. However, it is widely known that oil exploration is a necessity in our industrial society and a major sustainer of our lifestyle, as most of the energy used in Canada and the United States, for instance, is for transportation that runs on oil and petroleum products. Thus, in as much as the industry uses oil and petroleum derivatives for the manufacturing of vital products, such as plastics, fertilizers, and chemical feedstock, the drifts in energy usage are not likely to decrease much in the near future. In what follows, it is a global belief that the production and consumption of oil and petroleum products might continue to increase worldwide while the threat of oil pollution is also likely to increase accordingly.

Consequently, a fundamental problem in environmental research in recent time has been identified in the literature to how to properly assess and control the spatial structure of pollution fields at various scales, and several studies showed that mathematical models were the only available tools for rapid computations and determinations of spilled oil fate and for the simulation of the various clean-up operations.
