A 3D Model for Predicting the Fate of Contaminants Released in the Caspian Sea

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A 3-D Model for Predicting the Fate of
Contaminants Released in the Caspian Sea

• Yoram Eckstein CRDF Grant No 2284
• Department of Geology
• Kent State University, Kent, Ohio 44242, U.S.A.
  
• Ramiz M. Mamedov
• Institute of Geography
• Azerbaijan Academy of Sciences, Baku,
  Azerbaijan
• Konstantin A. Korotenko
• Shirshov Institute of Oceanology
• Moscow, Russian Federation

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Introduction

• Petroleum companies from around the globe have
  descended on the independent countries that
  border the oil-rich Caspian Sea to develop new
  and old fields. They have signed contracts worth
  tens of billions of dollars in what is the
  centurys last big oil bonanza.
• Steve LeVine A cocktail of oil and politics
• New York Times, November 19, 1999

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The Caspian Lake
May, 2002
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The Caspian Sea Drainage Basin
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The Volga is the largest river system in Europe.
Its watershed covers about 1,450,000 sq. km
(about 560,000 sq. mi). It rises northwest of
Moscow in Valday Hills, and flows some 3,700 km
(2,300 mi), discharging annually about 230 cu.km
of water into the Caspian Sea.
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Annual flow of rivers calculated in of
the total inflow into the Caspian Sea
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The Currents in the Caspian Sea And the role it
plays in oil spills and sturgeon spawning.
    The Caspian Sea Currents The currents in
the Caspian Sea are caused by several factors.
First, the inflow from the Volga and Ural rivers
push the water to the south. Second, the shallow
areas in the Caspian Sea, particularly in the
Baku region, mark areas where there is more wave
action. Probably, the most important factor is
the winds.  The Caspian Sea, especially Baku, is
subject to many storms and high winds, which
create large onshore waves. The currents, in the
event of an oil spill, would keep the oil from
flowing up to the north where the sturgeon graze
and spawn.
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Chemical composition of the 2001-2002 Caspian Sea
water sampled at 1 m depth in the south-eastern
portion, near the coast of Turkmenistan
(concentrations in g/L).
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Surface Water Temperatures forSummer2002
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The Caspian Sea January Mean SurfaceWater
Temperatures
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The Caspian Sea August Mean SurfaceWater
Temperatures
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Contaminant loading into the Caspian Sea
 
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Sources of oil loading into the Caspian Sea
(T/y)
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Petroleum Hydrocarbon Input into the
Caspian Sea

• 
  

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Hydrocarbon loading from rivers

• 
  

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Discharge of oil from industry in of
total.

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Total pollution load to the Caspian Sea from
municipalities
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Municipal wastewater discharge to the
Caspian in of the total.
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Modeling of contaminant fate and migration in
an open body of water

• Modeling of fate and migration of contaminants
  in an
• open body of water must take into account
  both the
• mechanical spreading and drift of the
  contaminant,
• and the processes that determine the
  behavior of
• the contaminant and its components
  in the sea
• water. To that effect we use
  particle tracking,
• a technique based on the Monte
  Carlo method.
• In this method, each particle
  represents a
• fraction of the total mass of
  the contaminant,
• and their 3-D movement is
  simulated taking
• into consideration all the
  physical, chemical
• and biochemical processes.

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Contaminant migration processes

• Spreading
• Advection
• Dispersion
• Turbulent diffusion
• Evaporation
• Emulsification
• Density changes

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Spreading

• Spreading process is particularly important
• when an immiscible contaminant forming a
• separate phase, e.g. oil is involved.
• Spreading of oil on water is
  controlled by
• the driving forces of gravity and
  surface
• tension and retarding effects of
  inertia and
• viscosity, leading to an extension
  of the oil
• spill and the formation of a
  slick on the
• sea surface.

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Spreading of a thin slick
(Mackay et al. 1979)
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Spreading of a thick slick
(Mackay et al. 1979)
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Advection

• Advection is accounted for by simulation of
• the movement of the centroid of the oil slick
• resulting from the large-scale sea water
• circulation, tidal, and buoyancy driven
• and wind-induced transient currents.

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Advection

• Vi Viwind Viwave Vid Vic ViT ViB
• Viwind velocity due to wind drift
• Viwave velocity due to wave (Stokes)
  drift
• Vid - wind-induced component
• Vic large-scale component
• ViT tidal component
• ViB buoyancy-driven component
• Viwind Viwave 0.03 Vwind_at_10m
• (Elliott, 1986 Reed et al., 1989)

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Vertical dispersion

• Vertical dispersion results from wind-generated
  breaking
• waves dispersing oil vertically in the water
  column.
• In high sea states where a slick is
  subject to
• continuous turbulence by wind shear
  and breaking
• waves, the oil may be rapidly
  dispersed into
• small, less than 1 mm drops, which
  hover within
• certain depth interval below the
  sea surface.
• The shower of oil droplets
  then slowly raise
• to the surface by their
  buoyancy. The simplest
• way to quantify this process
  is based on
• describing dispersion as a
  function of sea
• state and time since the oil
  release
• (Audunson, 1979 Spaulding
  et al. 1988)

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Vertical dispersion

• Yet, some of the smaller drops diffuse downward
• and become permanently incorporated into the
• water layer, which adds the third
  dimension to
• the process of oil migration in the sea.
  In some
• cases quantities of oil have been
  detected as
• deep as 20 m below the sea surface
  (Cretney
• et al., 1981 Sorstrom, 1987
  Genders, 1988)
• The entire process of oil
  dispersion and
• entrainment is very complex, and
  the exact
• nature of the fluid mechanics is not
  too
• well understood. The
  available solutions
• rely more on the empirical than on
• theoretical considerations.

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Vertical dispersion

• The dispersed mass of oil droplets per unit
  surface
• area and per dispersion event (kg/m2) is
  given by
• Md
  Co(DBA)0.57SCOVd0.7Dd
• Mtotal(de)
  Co(DBA)0.57SCOVdmax1.7
• d oil droplet
  diameter Co m(Toil)-1
• DBA 0.0034 rw g
  (Hrms)2
• (average energy
  dissipation per unit
• surface area
  in overturning wave)
• SCOV fraction of the
  sea surface covered by oil
• (Delvigne, 1993)

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Turbulent diffusion
When an oil slick is dispersed, an expanding
cloud of droplets is formed and
diffused horizontally and
vertically due to turbulence. Some larger
droplets may rise and reform
the slick, but, most of them
will become mixed into the subsurface layer.
The vertical distribution of the
oil concentration can be
expressed as
CS surface oil concentration Dv effective
vertical dispersivity (typically 0.0126 m2/s)
(Mackay et al. 1979)
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Turbulent diffusionHorizontal distribution of
the oil concentration

• C(x,y,t) Co erf((D/2 x)/E)
• ((D/2 y)/E)((D/2 y)/E)
• ((D/2 y)/E)
• D the initial cloud diameter
• E (4Kxyt)1/2 where Kxy
  ceL4/3
• Kxy - horizontal diffusivity
  (cm/s2)
• (ce - 0.01 an empirical constant
• dependant on the turbulence
• dissipation rate)
• (Reed, 1989)

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Vaporization Mass transfer rate due to
evaporation
(Reed et al. 1989) Mi molecular
weight (gmol) KE mass transfer coefficient
Pi vapour pressure (atm) KE
0.28VA0.78DS-0.11Sci-0.67 As area of
the spill (m2) VA wind speed R gas
constant DS spillet diameter
Sci Schmidt Number of the ith fraction (f)

(Mackay Matsugu, 1973)
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Changes in oil slick viscosity due to evaporation

• The evaporation process results in an increase of
  oil viscosity.
• m mo(Cm FE)
• FE evaporated fraction
• mo parent oil viscosity
• Cm a constant (1-10) dependant on oil type
• (Mackay et al. 1979)

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Emulsification

• Many oils tend to absorb water to form emulsions
  containing up to 80 water.
• dYw/dt KA(1 VA)2(1 KBYW)
• Yw fractional water content
• 1/ KA final water content (0.8)
• KB empirical coefficient
  (1.43)
• VA wind speed
• (Mackay et al. 1979)

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Increase in the effective oil viscosity due to
emulsification

• Oil-sea water emulsions can be very viscous,
  and
• have density approaching that of sea
  water.
• where Yw is fractional water content
• 
  (Mackay et al. 1979)

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Density increase

• The process of evaporation and formation of
• water-in-oil emulsion leads to an increase
• in the oil density.
• rE Yw rw (1 Yw)(rC CrFE)
• rE oil emulsion density (kg/m3)
• rC density of the original spill
• Cr distillation constant
• Yw fractional water content
• (Buchanan Hurford, 1988)

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Other processes

• Dissolution lt 1 Biodegradationlt1
• Photolysis
• B suns radiation angle
• C fractional cloud cover
• CA f(h)
• (Cochran Scott, 1971)

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Other processes

• Sinking/bottom-settling
• In some cases the process of vaporization may
• increase the oil density to the point of
  conversion
• from a floater to sinker. More
  important is
• the process of sinking due to
  adherence of oil
• droplets to suspended sediments
• dA/dt 1.4 10-12SL(1- 0.023Sa)
• SL sediment load (gm/m3)
• Sa - salinity
• (Kolpack et al. 1977)

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Oil spill migration model

• The description of the transport and dispersion
• of a contaminant spilled at sea may be based
• on the advection-diffusion equation solved
• by finite differences for the concentration
  C
• Ui components of the 3-dimensional
• mean velocity field
• Kij diffusion tensor
• S source or sink term

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Our model

• We use the pre-calculated mean velocity and
• the random walk (Monte Carlo) technique to
• follow the motion of individual particles
• (oil droplets). This approach is much more
• effective, because it exactly describes the
• advection, by far the most important
• transport process for oil slicks. Oil is
• initially divided into fraction in order to
• describe accurately the evaporation
• processes.

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The hybrid model flow-chart
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• The main part of the model is Block 5, where
• displacements of each particle are
  calculated by
• the following expressions
• The displacements
  are defined as the deterministic
• part of the motion due to the
  mean velocity field, Vij,
• and the random
  displacement, (hi)j,k, due to fluctu-
• ations of
  velocity and denote the displacement of
• the k-th
  particle moving along the xi-axis at the j-
• th instant of time Nt is
  the number of time steps,
• ?t is the time
  step, Nf is the number of particles in
• each fraction,
  and the subscript f denotes one of
• the particle
  fractions.

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The hybrid model flow-chart
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Oil droplet generator (block 2)

• The distribution of the number of
  particles in each fraction is
  initially assigned and distributed randomly
  depending on the type of oil. The total
  number of particles launched in the
  model does not usually exceed 106 nevertheless,
  the behavior of the tracked particles
  proved to be representative of
  the entire spill, even though each 'droplet'
  represents only a small part of the total
  volume of the oil. Within each fraction, each
  droplet is also randomly distributed to
  have its own half-life according to the
  empirical expo- nential laws. In
  practice, those distributions are
  assigned randomly by means of a random
  number generator giving uniform numbers
  chosen uniformly between 0 and 1, and then
  transformed into an exponential
  distribution with a weight dependent
  on wind speed and oil temperature.

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The hybrid model flow-chart
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Modelblocks3 and 4

• In addition to the regular movements due to mean
  current
• velocity, oil droplets experience a random
  diffusion due to
• velocity fluctuations. The distribution law
  of these is
• represented by the term, (hi)j,k, which
  is in general a
• function of time and space. The
  choice of law for (hi)j,k
• is determined by the statistical
  structure of deviations
• (fluctuations) of velocity from
  its mean value at each
• time step ?t. Since these
  fluctuations are
• considered independent, the law for
  (hi)j,k is
• chosen to be Gaussian. In this case, (hi)j,k
  can be
• represented as gj,k(2Ki,j ?t)1/2, where
  gj,k is a
• random vector normally distributed with an
• averaged value of zero and unit standard
• deviation Ki,j represents
  coefficients of diffusion
• along the xi- axis at the time tj
  to j ?t . The
• random vector gj,k is obtained with the
  use of
• the random number generator (Block 4)
  giving
• a homogeneous distribution of random
• numbers between 0 and 1, with
  consequent

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The hybrid model flow-chart
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Princeton Ocean Model (POM)

• The horizontal and vertical diffusion
  coefficients, Kx,j,
• Ky,j and Kz,j, as well as the mean current
  velocity
• Uij are provided by the flow model POM in
• block 8. The horizontal diffusion
  coefficients,
• Kx,j and Ky,j, are calculated in POM from
• the Smagorinsky formula,
  while the
• vertical diffusivity, Kz,j, is obtained
  from
• the level 2.5 turbulence model
  (Mellor Yamada, 1982).

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The model dialog

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Oil release in the Volga River delta
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Southward wind 6.0 m/s
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Southeastward wind 6.0 m/s Eastward wind 6.0
m/s
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Southwestward wind 6.0 m/s Southward wind 6.0
m/s
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Time-distribution of oil spill
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Time-simulation of an oil spill
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Time-simulationofan oil spill
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Domestic and industrialwaste release in Baku
region Southward wind 8.0 m/s
Westward wind
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The model dialog

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Conclusions (1)

• The oil spill prediction procedure is split into
  two parts
• the computation of the current field using POM
  and input of these currents together with winds
  to the oil spill transport model and
• the oil spill model which uses a random walk
  particle-tracking method, together with the
  currents from POM, to predict the 3-D movements
  and fate of the oil droplets

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Conclusions (2)

• The simulated processes include
• Advection
• Turbulent diffusion
• Evaporation
• Decay, representing all the biochemical and
  physical mechanisms that decompose oil

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Conclusions (3)

• The combination of incident-specific
  environmental data and spilled oil
  characteristics, allows conducting diagnostic and
  prognostic simulations of behavior of the oil
  slick in the marine environment.

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Conclusions (4)

• The transport model effectively predicts
• oil slick movement
• the area covered by the oil
• and allows for risk assessment of coastline
  contamination by the beaching of oil spills in
  coastal waters