Nonlinear Advection–Diffusion–Reaction Phenomena Involved in the Evolution and Pumping of Oil in Open Sea: Modeling, Numerical Simulation and Validation Considering the Prestige and Oleg Naydenov Oil Spill Cases

Abstract

The main goal of this article is to improve upon a previous model used to simulate the evolution of oil spots in the open sea and the effect of a skimmer ship pumping oil out from the spots. The concentration of the pollutant is subject to the effects of wind and sea currents, diffusion, and the pumping action of a skimmer (i.e., cleaning) ship that follows a pre-assigned trajectory. This implies that the mathematical model is of the advectiondiffusion-reaction type. A drawback of our previous model was that diffusion was propagating with infinite velocity; in this article, we use an improved modeling relying on a nonlinear diffusion term, implying that diffusion propagates with finite velocity. To reduce numerical diffusion when approximating the advection part of the model, we consider second order discretization schemes with nonlinear flux limiters. We consider also absorbing boundary conditions to insure accurate results near the boundary. To reduce CPU time we use an operator-splitting scheme for the time discretization. Finally, we also introduce the modeling of coastlines and dynamic sources of pollutant. The novel approach we advocate in this article is validated by comparing our numerical results with real life measurements from the Oleg Naydenov and the Prestige oil spills, which took place in Spain in 2015 and 2002, respectively.

Designing optimal trajectories for a skimmer ship to clean, recover and prevent the oil spilled on the sea from reaching the coast

“…Furthermore, to limit the artificial diffusion effect, typically produced by this kind of numerical model [11], we use second-order accurate time discretization schemes with nonlinear limiters to treat the transport. The full scheme of the considered numerical model can be found in Reference [16].…”

“…Another case is the ship 'Oleg Naydenov' that sunk near the Canary Islands coast, Spain, on 14 April , 2015 [16]. The tanks of this ship were filled with around 1400 tons of oil.…”

“…In order to be able to improve the efficiency of this pumping process, we first simulate the movement of the oil spots in both space and time using our Eulerian mathematical model proposed in [2,16]. We note that in the literature, the prevailing models to forecast the fate oil spills on the sea are based on Lagrangian approaches [29,30].…”

“…In particular, during the experiments proposed here, we consider the characteristics of the so called 'Controlled Floating Skimmer' pump, build by the Novetec company (see http://www.novetec.es), that may incorporate a crushing device in order to be able to pump emulsified oil (in this case, the pumping power is reduced). We have used the 2002 Prestige oil spill [16] as a test case, to show the efficiency of our approach. Although in the case of the Prestige spill, the use of Skimmer ships was not suited because of the high viscosity of the oil spilled, we are only using here, data from this hazard (i.e., the geographical region, the path and the amount of oil spilled, the wind and sea currents) to create a benchmark case.…”

“…In Section 2.2, we present the formulations of different objective functions to optimise the trajectory of the skimmer ship. In Section 3.1, we describe numerical experiments based on the 2016 Oleg Naydenov and the 2002 Prestige oil spills [16], citing the sources of data, to validate the forecast of the movement of the oil obtained with our model and to compare them with satellite images and discuss the results. Then, in Section 3.2, using the results obtained by the model, we solve several optimization problems to find optimal trajectories for the pumping process and analyse the behaviour of the solution regarding some key parameters (as the pumping power of the skimmer).…”