Mathematical Modeling and Forecasting the Spread of an Oil Spill

using Python

NIKOLAOS KASTROUNIS1, GEORGE MANIAS2, MICHAEL FILIPPAKIS2,

DIMOSTHENIS KYRIAZIS2

commonly used for marine oil spills, where the hydrocarbons are discharged into the ocean or coastal waters,

but they can also occur inland. Oil spills occur because of discharges of hydrocarbons from platforms, rigs,

wells, tankers and from refined petroleum products along with their by-products, also from heavier fuels. Thus,

oil spill simulation is used to predict transport and weathering processes. State-of-the-art tools such as

OILMAP, TRANSAS, OILFLOW2D, OSCAR and ANSYS, work by simulating the processes mentioned

prior. In contrary to these tools, the aim of this paper is to provide a comparison of the weathering models used

and propose a mathematical model using python to predict the spreading phenomenon of an oil spill.

Key-Words: Fate/Weathering Processes, Oil Spill, Simulation/Modeling

Received: June 19, 2021. Revised: June 26, 2022. Accepted: July 19, 2022. Published: September 22, 2022.

language, but it also enables a future use of CUDA

GPU (graphics processing unit) which will greatly

increase processing speed.

Oil spills are a matter of serious concern due to

their damaging nature. Due to the constantly

changing conditions in the sea/ocean, the physical

processes acting on a spill change. There are a

number of ways to counter the negative impact of an

oil spill in the sea, such as: skimmers, booms and

gravity. The effects of gravitational forces tend to

fade an hour after the start of the spill, (increase of

viscosity, and decrease in thickness); it is then that

diffusion starts to be the dominant mechanism in the

oil spill movement [1], [2].

bacteria, acid-producing bacteria and general aerobic

bacteria consumption play the role of natural

ecosystem oil removals. But due to the amount of oil

present their mass will replace other biomasses in the

food chain [1], [8]. Clean-up and recovery can prove

to be a difficult task. However, the process depends

on some factors: such as type of oil, temperature and

or shoreline topography. Oil spill recovery is often an

form of a literature review and the models that have

been utilized. While in Section 3 the oil weathering

process is being introduced and analyzed.

Afterwards, Section 4 presents the experimental

results and the visualization approach that was

followed to demonstrate the oil spilling through the

utilization of machine learning and time series

analysis techniques. Moreover, Section 5 discusses

the experimental results. Finally, Section 6 concludes

the paper and outlines some directions for future

engineering software is used to model oil spill by

simulating the oil processes. Quoting Spaulding ML.

“Current fields are generally considered to be the

vectoral sum of wind, tidal density, and pressure

gradient induced currents. Of these various

components, the wind-induced drift is often the most

important factor determining surface oil slick

trajectories over time scales greater than 1 day. The

extremely simple empirical approach, which assumes

surface drift current is approximately 3-4% of the

results if the study area does not include conditions in

which coastal or bathymetric effects are dominant; in

these cases wind-driven currents become much more

complex (e.g. Spaulding et al.)” [1], [11].

complexity of the oil interaction with the marine

environment. In this review they are categorized in

Operational Response Models and Deep-Sea

Blowout/Buoyant [14].

Operational Response Models can compute all of

the essential transport, fate/weathering processes. The

aim of the operational response models is to provide

support in case of an oil spill by predicting the

of-the-art model that replicates the fate, transport and

oil weathering processes [14], [15].

OpenDrift and OpenOil. OpenOil is a python

open-source transport and fate module (drift) build on

OpenDrift.

Blowout and spill occurrence or BLOSOM, is a

java model and is used to model the fate and transport

of surface and subsurface oil spills. BLOSOM is also

dissolution, sedimentation, evaporation, dispersion,

spreading, sedimentation and beaching [14].

TAMOC is an open-source oil spill model capable

of processing dissolution, particle tracking, transport

and plume dynamics of an oil slick [14].

OILMAPDEEP is capable of estimating the fate

processes and transport of sub-surface spills [14].

Comprehensive Deepwater oil and gas model or

CDOG is a three-dimensional oil spill model used for

deep-water spills. Using hydro and thermos dynamics

it can simulate disintegration, gas dissolution and

mechanisms produce aside from advection caused by

wind, currents, drift and displacements, time-

susceptible variations. Gravity is the first force that

acts on a slick after an incident occurs, making the

slick spread over an area, with individual particles

spreading. With the volume of oil being reduced due

to the evaporation of lighter oil, the reminder is either

absorbed or emulsified. Those changes are considered

as oil spill property changes. By breaking down the

main spill into various others instead of a whole one,

the middle and thin parts (sheen) around the edges.

Quoting Zodiatis, Oil spill forecasting (prediction)

“The sheen is very thin, generally of the order of 10

microns, whereas the thick slick may, in the case of a

large spill, be initially several centimeters thick. Flow

of oil from the thicker core feeds the thinner parts.

Evaporation and dispersion both occur much more

rapidly from the thin sheen than from the thick areas

and these processes are modelled differently for two

components of the s lick” [2].

Where, the rate of time of oil concentration change,

(3)

(4)

slick with a fraction α of the speed at an angle β.

(5)

Where Wx and Wy are wind Velocity comp. α and

β are the percentage of wind added to current velocity

and the deviation angle respectively.

The local sea currents consist of smaller

Lagrangian parcels, at which the impact of the wave-

(11)

Where the model parameters are C1 and C3, the

thickness of the thick part of the surface slick is Ttk

and dt is the timestep.

Proposed by Lehr et al. was a stretched ellipse

along the path of the wind model, to resolve the

attended non-symmetrical expanding of slicks [19]:

(12)

Where the length of the major and minor axis is R

and Q respectively. 20]

While Lehr et al. composed an altered Fay

(13)

Quoting Lehr et al.: “where A is the area of the oil

slick (m2); _ρ=ρw_ρo; V is the total volume of the

spilled oil in barrels; Uwind is the wind speed in

knots; and t is the time in minutes” [21].

Τhe issue of simulating and visualizing the spread of

machine learning and time series data exploratory

analysis approaches, such as time-based indexing and

multi-step forecasting, were utilized to depict the

expansion of an oil spill through the time and based

on the various iterations that were conducted. The

latter can also be utilized to forecast the time-and-

space-varying velocity of an oil spill. In this context,

the visualization was based on laboratory

experiments of an oil slick spread and was

implemented tasks with the Python programming

graphical representation of the results obtained from

the python model using the data from the laboratory

experiment, the graph shows the increase of the rate

of spread for one (1), five (5) and ten (10) droplets of

oil, 0.0228gr each against the time. As it is clear from

the illustration there is an exponential increase on the

rate of spread of the oil slick in relation to time with

the increase of the volume of oil being disposed.

From this figure it is easily understood that in the

simulations of the 5-Drop and 10-Drop there is a

great expansion in the final area that the oil spill

covers as in comparison with the 1-Drop simulation.

Fig. 2: Comparison between the rates of spreading

between the three different simulations

time are represented by the different color cycles as

depicted in the time scale on the right bottom of the

figure. In this respect, Fig. 2 provides a visual

representation of the spreading weathering effect that

occurs during an oil spill from the moment the

droplet reaches the water surface until the spreading

stops.

choose the appropriate oil spill model.

The spill augur is done using a mathematical model

of the weathering. Weathering involves evaporation

dispersion emulsification, oil properties, chemical

properties, environmental conditions etc. Most

models typically do not take into account dissolution

and degradation. But these two factors are vital in

order to approximate the effect of the spill on the

biodegradation. Taking into account the above

statements there is a clear need for the oil spill

modelling to make a distinction based on their

physical, chemical and toxicological characteristics

and trail their movement individually so that a higher

accuracy is achieved. Thus, it is crucial in order to

forecast the effect on the environment, to consider the

fate in the water column.

Deregulated Electricity Market Issues in South

vol. 206, pp. 390-399, 2015.

troops,” in Journal of occupational and