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

2. Introduction.

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

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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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    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

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