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2. Introduction.
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1. 1 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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8. 8
9. 9 The Currents in the Caspian Sea: And the role it plays in oil spills and sturgeon spawning.
10. 10 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).
11. 11 Surface Water Temperatures for Summer 2002
12. 12 The Caspian Sea January Mean Surface Water Temperatures
13. 13 The Caspian Sea August Mean Surface Water Temperatures
14. 14 Contaminant loading into the Caspian Sea
15. 15 Sources of oil loading into the Caspian Sea (T/y)
16. 16 Petroleum Hydrocarbon Input into the Caspian Sea
17. 17 Hydrocarbon loading from rivers
18. 18 Discharge of oil from industry in % of total.
19. 19 Total pollution load to the Caspian Sea from municipalities
20. 20 Municipal wastewater discharge to the Caspian in % of the total.
21. 21 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.
22. 22 Contaminant migration processes Spreading
Advection
Dispersion
Turbulent diffusion
Evaporation
Emulsification
Density changes
23. 23 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.
24. 24 Spreading of a thin slick
25. 25 Spreading of a thick slick
26. 26 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.
27. 27 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@10m
(Elliott, 1986; Reed et al., 1989)
28. 28 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)
29. 29 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.
30. 30 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)
31. 31 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:
32. 32 Turbulent diffusion Horizontal 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)
33. 33 Vaporization Mass transfer rate due to evaporation:
34. 34 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)
35. 35 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)
36. 36 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)
37. 37 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)
38. 38 Other processes Dissolution < 1% Biodegradation<1%
Photolysis
B – sun’s radiation angle
C – fractional cloud cover
CA = f(h)
(Cochran & Scott, 1971)
39. 39 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)
40. 40 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
41. 41 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.
42. 42 The hybrid model flow-chart
43. 43 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.
44. 44 The hybrid model flow-chart
45. 45 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.
46. 46 The hybrid model flow-chart
47. 47 Model blocks 3 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
transformation to the Gaussian law (Block 3).
48. 48 The hybrid model flow-chart
49. 49 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).
50. 50 The model dialog
51. 51
52. 52 Southward wind 6.0 m/s
53. 53 Southeastward wind 6.0 m/s Eastward wind 6.0 m/s
54. 54 Southwestward wind 6.0 m/s Southward wind 6.0 m/s
55. 55 Time-distribution of oil spill
56. 56 Time-simulation of an oil spill
57. 57 Time-simulation of an oil spill
58. 58 Domestic and industrial waste release in Baku region Southward wind 8.0 m/s Westward wind
59. 59 The model dialog
60. 60 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
61. 61 Conclusions (2) The simulated processes include:
Advection
Turbulent diffusion
Evaporation
Decay, representing all the biochemical and physical mechanisms that decompose oil
62. 62 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.
63. 63 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
