19
1 OILSPILLMODELINTHELITERATURE
1.1 Typesofoilspillmodels
Oil weathering models predict the changes in oil
characteristics–evaporate,emulsifyanddisperseinto
thewatercolumn.Thechangesmayoccurovertime
underthe influence of environmental conditionslike
water temperature, wind speed, wave heights, sea
state, salinit
y, sediment concentration. The
appropriateenvironmentalconditionsandoiltypeare
selectedfromthemodel’sdatabase.
Trajectoryordeterministicmodelsallowtopredict
not only weathering profiles but also potential
migration of an oil slick over time, slick volume, oil
properties like viscosity or flash point and other
detailssuchaspotentia
lbeachingsitesorthelengths
ofcoastlineimpacted.
Stochasticmodels(probabilitymodels)arebuilton
thebasisofhistoricalwindrecords.Thefrequencyof
wind speed and direction is allowed to estimate the
probability of where an oil spill might travel in
definedtimeperiods.Theresultsindicat
ewatersand
shorelines which are most at risk during various
seasons.
Hind‐cast models (backtrack models) are allowed
toestimatethespillorigin.Thesemodelsruncontrary
tothetrajectorymodels.
Three dimensional models (3D) estimate oil spill
trajectories, weathering profiles, oil component
concentrations and make simulations of dispersion
into the water column. These models required
complex current data and a sophi
sticated oil
characterization. These are the only models which
considertheoilmigrationatdepth.
Details of these models are described in the
TechnicalPaper(ITAC).
Oil Spill Models: A State of the Art of the Grid Map as
a Function of Wind, Current and Oil Parameters
J
.Mazurek&L.Smolarek
GdyniaMaritimeUniversity,Gdynia,Poland
ABSTRACT: An integrated model, which contains flow and tra nsport‐fate modules, will be presented for
simulatingtransportandfateofoilspillsatseas.Theflowmoduleusesdifferentkindsofmeshesthatprovide
great flexibility for modeling the flow in complex geometries of currents and barriers. The refined grid
resolutioninregionsofint
erestisimportant.Horizontaldiffusionissimulatedusingrandomwalktechniques
inaMonteCarloframework,whereastheverticaldiffusionprocesscanbesolvedonthebasisoftheLangeven
equation.Themodelcontainsthemostsignificantprocesseswhichaffectthemotionofoilpart
icles.Forabetter
fittothecurvatureof the coastlinethereareusedunstructurednonoverlappingrectangularortrianglegrid
cells. Special attention must be paid to choose the horizontal and vertical resolution in simulating the oil
trajectoryinthecoastalarea.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 7
Number 1
March 2013
DOI:10.12716/1001.07.01.02
20
1.2 Inputdataofoilspillmodel
Thequalityofthedatausedhasahugeinfluenceon
the effectiveness of the model results. The data
requirebymostoilspillmodelsrelatehydrodynamic
data,winddataandoiltype.
The most important parameter is hydrodynamic
data. Gathering a database
of currents is costly and
time consuming but currents have the greatest
influenceonoilmigration.Technological advance,the
development of models and simulation allow to
forecast currents but it is not useful in extreme
environments such as storms or high runoff.
Advective currents in oil spill simulations may be
derived from current atlases or other static
approximations. Wind data are much easier to
acquire.Weatherforecastingservicesprovidegeneral
informationonwinddirectionandmagnitude.Theoil
types are available from database of modeling
systems.Oildatabasecontainsessentialoilproperties.
1.3 Oilweatheringmodel
The Figure 1 presents the
general layout of
weathering model. Under the influence of hydro‐
meteorological condition and oil type there are
occured physical and chemical processes, which are
directorindirectlinked.Reedinthepaper(Reedetal.
1999) investigates an overview of different
approaches applied in numerical models of the
behaviorof
oilspillinthemarineenvironment.Early
oil spill models were typically two‐dimensional
models, present study use three‐dimensional
processes. The oil moves in the marine environment
notonlyhorizontallybutalsovertically,onandinthe
sea.Oilistransportedhorizontallyunderforceofthe
wind, current, wave and
vertically in the water
column as droplets of various sizes. In light winds
without brea king waves, 3.5% of the wind speed in
the direction of the wind gives a good simulation of
oil slick drift in offshore areas. As wind speed
increases,oilwillbedispersedintothewatercolumn,
andcurrentshearsbecomemoreimportant.
Figure1.Generallayoutofoilweathering(Reedetal.1999)
All physical and chemical processes related oil
spill have a huge impact on the oil composition and
propertieswithtime.Estimatesofslickareaandfilm
thicknessareusedinthecomputationofevaporation.
Estimates ofevaporativelosses are requiredinorder
to assess the lifetime of the spill. In addition,
these
estimatesarerequiredfor evaluation of thepotential
efficiency of different oil spill combat methods, and
forassessmentsofenvironmentalimpacts.
1.4 Oilspillsimulation
Numerical prediction models have been generally
used to solve the movement and diffusion of water‐
borne pollutants. To simulate oil transported on the
sea
surface there is used the advection‒diffusion
equation,(Choietal.2010).Itisthegeneral Eulerian
equation,commonmathematicalmodeldefinedas:
()
C
UC DC S
t
(1)
whereCisthedensityofoil,Uisthevelocityvector,
Disthediffusivitycoefficient,andSisexternalfluxes.
Equation1iscalculated from Lagrangian formula as
follows:
current wind random
L=(U + U ) t+L
(2)
whereListhemovingdistanceofeachparticleduring
Δt, α is the wind drift factor (usually taken as 0.03),
current
U
istheoceancurrentvelocityattheseasurface,
and
ind
U
w
is the wind velocity at 10 m above the
water surface, respectively. The advection due to
turbulent diffusion
random
L is computed by the
randomwalkmethodforGaussian“spillets”as
random
LR6D/t
(3)
whereRistherandomnumberbetween−1and1.The
empiricaldiffusivitycoefficientDistakenas10m
2
/s.
The oil spill model, Equation 2, calculates the oil
transportation.
Choiinthearticle(Choietal.2010)constructedof
the high resolution oil spill forecast simulation
system. This model was built for the whole routes
between Japan and Middle East, so to verify of the
performance and accuracy of
the simulation system
there was used the accident of the Russian tanker
“Nakhodka” in the East/Japan Sea, in January 1997.
Simulationexperimentofthisaccidentwasconducted
and the simulation results were compared with the
observationandthepreviousstudy.
Figure2.The Yang grid (on the left), the Yin grid (in the
middle), their composition – the Yin‐Yang grid (on the
right)(Choietal.2010)
21
In presented model there is used global grid
system,named“Yin‐Yanggrid”.Thisgridconsistsof
two grid components that have exactly the same
shapeandsize,asshowninFigure 2.Theadoptionof
nestinggridsystemforneighboringJapaneseIslands
and the global ocean model by means
of Yin‒Yang
grid enables us to realize the quick and accurate
response for emergency countermeasures. The
movements of spilled oil are defined by the surface
wind drift and ocean currents which are obtained
fromthegeneralcirculationmodel.
Inthemodeldescribedinthearticle(Moritaetal.
1997)
theexperimentwasusedtoestimatethedegree
ofoilweatheringontheseasurfaceandtodetermine
parameter values of surfacing, sinking, and
resurfacingspeedfortheforecastingmodel.
The Figure 3 presents the laboratory setup. The
wavegeneratorwasmadewithanelectricmotorand
an acrylic board. Five
liters of fresh crude oil was
addedtothewatersurfaceina60litertank.
Figure3. A sketch of the weathering experiment setup
(Moritaetal.1997)
At the beginning of the experiment, after 3, 6, 12
hoursandafter1,2,4,8,12daysthesurfaceoilwas
sampled. The research has shown that the specific
gravityoftheoilincreasedlogarithmicallywithtime
and the viscosity of surface oil increased
exponentiallywithtime.Theoil
dropletswerepatchy.
The surfacing, sinking and resurfacing speed of
emulsion, which was estimated with a video and
photographic camera, increased with droplet
diameter.
2 OILSPILLMODELWITHDECISIONMAKING
2.1 Oilspillmodel
Themodelwidelydescribedin(Mazurek&Smolarek
2012) consists of the model of oil
spill on the grid
graph, the stochastic model of action time of spill
surroundingandthestochasticmodelofoilslickdrift.
Water area is described by a grid, where an every
vertex of grid corresponds torectangulararea of the
sea and an every edge of grid represents contact
between
two areas. The size and the dimensions of
area of the sea related to one vertex depends on
hydro‐meteorologicalconditionandtypeofsubstance
spill.Weconsiderthreegrids:theCartesiangrid,the
triangulargridandthestronggrid,Figures4‐6.
Figure4.TheCartesiangridmodel.
Figure5.Thetriangulargridmodel.
Figure6.Thestronggridmodel.
Thechoiceof gridallowstotakeintoaccountthe
prevailing conditions at the sea, in particula r the
speedofthespillspreading.Inmodelthereisapplied
the algorithm of a spill surrounding, known as
“firefighteralgorithm”,(Fogarty2003).Thisalgorithm
shows how to use available forces and resources to
boundaspill.Themethodologythatwasusedallows
toestimatethetimeofactionpreparation,thetimeof
actionof a spill surrounding, the size of the spillage
andtheamountofresourcesused.
Inrealsituationincompletenessanduncertaintyof
the data do not enable to establish when
start the
rescueoperation. In the stochastic model we assume
that the time since oil spill occurs to starting the
action is composed of two stages. The first stage is
related to information about the spillage and the
second stage depends on the time of share
preparation: collect forces and resources,
locate and
gettothespillspacebytherescueunits.Weusethe
triangular distribution to describe the time of these
stages, because we usually know the shortest time,
thelongesttimeandthemostprobabletimeof these
stages.
The time of the first stage is defined by
parameters
1
a ,
1
m
,
1
b
, denoting minimum time, most
probable time and maximum time, respectively. The
time of the second stage is described by
parameters
2
a ,
2
m ,
2
b . We assume that the time of
sharepreparationisarandomvariabledescribedbya
sumoftwo triangularrandomvariables, (Mridula et
al. 2009). The following formula presents the
22
probability density function of this variable in case
11
mxa
,
22
mxa
21
23
1
26
aa
xx
kxf
212211
2
2
2
1
22
aamama
mm
x
21
2
2
21
2
1
22
aa
m
aa
m
33
3
2
3
1
2121
mm
mmaa
(4)
where
22112211
1
4
amamabab
k
for
12
x
mm
.
The stochastic model of oil slick drift takes into
accountspeedanddirectionofthewindandcurrents.
This model is needed to research the horizontal
movementofoilslick.
2.2 Thedecisionmakingprocessinoilspillmodel
Models described in the first paragraph dissect all
physical and chemical
processes occurring at oil
spills.Themodelproposedinthesecondsectionwas
builttoanalyzetherescueactionforthemanagement
onthetacticalandstrategiclevel.Themainfeatureof
themodelisthedecisionmakingprocess.
Decision making is the process of recognizing a
problem and finding
a solution to it. Many of these
decisions are relatively simple and routine, they are
knownasprogrammeddecisions.However,thereare
nonprogrammed decisions where neither the
appropriate solution nor the potential outcome is
known. Decision making process has a six‐steps,
(French,1998):
identify the problem, the decision maker
must be
sure he or she has an accurate grasp of the
situation,
gatherrelevantinformation,allthefactsgivesthe
decisionmakermuchbetterchanceofmakingthe
appropriatedecision,
developmanyalternatives,
evaluatealternativestodecidewhichisthebest,
decideonand
implementthebestalternative,
follow‐upthedecision.
Most significant are two first steps because it is
important to pinpoint the actual cause of the
situation, which may not always be obviously
apparent.Whenanuninformeddecisionismade,itis
important to know all the facts before proceeding.
People
atdifferentlevelsinacompanyhavedifferent
typesofdecision‐makingresponsibilities.
Strategic decisions, which affect the long‐term
directionoftheentirecompany,aretypicallymadeby
top managers, (French, 1998). Examples of strategic
decisionsmightbetofocuseffortsonanewshipsor
methodsofoil
spillfighting.These typesofdecisions
are complex and uncertain, because available
informationisoftenlimited.
Tactical decisions, which focus on more
intermediate‐term issues, are typically made by
middle managers, (French, 1998). The purpose of
decisions made at this level is to help move the
company closer to reaching
the strategic goal.
Examples of tactical decisions might be to select the
location, deployment of resources to be put into
action.
Decision makers managing rescue services at the
tacticalandstrategicleveltakedecisionswhichhavea
majorinfluenceontheecologicaleffectsofspill.The
use the presented model
to support decision‐makers
work enables a thorough analysis of the rescue
operation.Parametersofthemodelareasfollows:
thetimeofpreparationrescueoperation,
thetimeofrescueoperation,
thesizeofthecontaminatedarea,
forcesandresourcesusedinaction,
and they define the
main criteria for evaluating
decisions. The proposed criteria enable to determine
the set of admissible decision and the set of optimal
decisions. An analysis of all possible strategies and
their evaluation allow for a rational and logical
identificationofanemergencysituation.
3 CONCLUSIONS
The model described in this paper
is a model for
decision‐makersonthestrategicortacticallevel;itis
notaddressedtoaheadofarescueoperation.Inthe
constructionofthemodeltherearetakenintoaccount
the dynamic parameters, e.g. the velocity of the
spread of the oil spill, the hydro‐meteorological
conditions
thataffectthedirectionandthevelocityof
the surface oil slick. Models presented in section1
willbeusedtodeterminethesizeofthemeshgraph
becausetheyincludenotonly physicalandchemical
properties of the spilled substance but also physics
phenomena related to the spill, such
as evaporation,
sedimentation,etc.
The main objective is to create a tool that allows
the decision maker to evaluate the extent to which
availableforcesandresourceswillbeneed.Moreover
their location influence effects of maritime oil spill
disasters at the sea. The model is currently under
constructionandwill
beeventuallysupplementedby
a simulation program for the analysis and
visualization of the development and effects of the
rescueoperation.
REFERENCES
Choi,Y.J.& Abe,A. & Takahashi,K.2010. Developmentof
oil–spill simulation system based on the global ocean–
atmosphere model. Proceedings of The 6th International
Symposium on Gas Transfer at Water Surfaces, Kyoto,
JAPAN,pp559‐570.
Fogarty,P.2003.CatchingtheFireonGrids.MasterofScience
Thesis.Universityof
Vermont.
23
French, Wendell L. 1998. Human Resources Management.
NewYork:HoughtonMifflin.
Mazurek,J.&Smolarek,L.2012.Estimationofsurrounding
the spillage time. Journal of Polish Safety and Reliability
Association3(2),pp245‐250.
Mridula,G.&Choudhary,S.&Kalla,S.L.2009.Onthesum
oftwotriangularrandomvariables.
InternationalJournal
ofOptimization:Theory,MethodsandApplications,pp279‐
290.
Morita, I. & Sugioka, S. & Kojima, T. 1997. Real‐time
forecastingmodelofoilspillspreading.InternationalOil
SpillConferenceProceedings:April1997No.1,pp559‐566.
Reed, M. & Johansen, Ø. & Brandvik, P.J. & Daling, P. &
Lewis,A.&Fiocco,R.&Mackay,D.&Prentki,R.1999.
Oilspillmodelingtowardthecloseofthe20thcentury:
overview of the state of the art. Spill Science and
TechnologyBulletin5(1),pp3‒16.
Technical paper: Use of models in oil spill response.
Industry Technical Advisory
Committee‐
ITAC,http://www.industry‐tac.org/technical_docu‐
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