American Journal of Environmental Engineering 2013, 3(5): 236-252 DOI: 10.5923/j.ajee.20130305.05

Assessment and Modeling of Oil Spill Dispersion in Mediterranean Sea on the North East Coast of Egypt and the Arabian Gulf

A. Amr M. Sabry1,*, M. Naguib1, Alya Badawi1, Tarek Nagla2

1Nuclear & Radiation Engineering Department, Alexandria University, Alexandria, Egypt 2Nuclear Power Plants Authority (NPPA), Cairo, Egypt

Abstract This paper aims assessing the environmental impact of oil spills which are caused by hypothetical oil tankers and offshore nuclear power plants accidents; where the effect of the changes in wind and water current on the oil spill movement and fate is studied. In case (a), multiple oil spills which are caused by a tanker accident near to the north coast of Egypt in the Mediterranean Sea are simulated by MEDSLIK[1] software. In this case, variable wind data is documented every 24 hours for 10 days[5] of simulation and non-uniform current input[4] were used. In case (b), the "best guess"[2] of oil spill trajectory and the associated uncertainty of an oil spill occurred on the Iranian coastline in the Arabian Gulf after an accident in Bushehr Nuclear Power Plant, which is caused by an earthquake, are calculated by using GNOME[2] software. In this case, wind forecast data from Bushehr Airport meteorological station[3] and three current patterns[2] are used to simulate the oil spill dispersion. These cases give decision-makers critical guidance in predicting the behavior of oil spills in the studied regions. Moreover, they show the effect. Ke ywo rds MEDSLIK, GNOME and Trajectory Analysis

Ta b l e ( 1 -a). Input data 1. Introduction Type of accident A tanker accident Type of pollutant Basrah medium Accidental and illegal marine pollution in the Sea water Lat it ude : 31°38.17 (N) 1st spill constitutes a major threat to the marine environment. Longit ude : 31°49.95 (E) nd Lat it ude : 31°28.15 (N) Previous incidents in the Mediterranean Sea and the Arabian Posit ion of accident 2 spill Gulf have resulted in environmental and economic damages Longit ude : 32°9.06 (E) Lat it ude : 31°21.71 (N) to fisheries, to the tourist industry and to coastal marine 3rd spill Longit ude : 32°17.63 (E) ecosystems. Oil-pollution discharges from ships and Dat e 9, January, 2012 offshore power plants in the Mediterranean and Arabian Gu lf 1st spill 9 AM have been described as significant and are a cause of Time of spill 2nd spill 13 PM environmental degradation in the seas of the Middle East 3rd spill 15 PM region. To prevent the major impact of accidental oil spills, Durat ion of spill 0.0 hrs ( instantaneous spills ) 0.0 tons per hr (immediate leakage local and regional preparedness and response plans Rate of spillage assumed) recommend the use of computer-aided support systems 1st spill 2000 tons based on operational oceanography and real-time ocean Volume of spill 2nd spill 1500 tons forecasts and real-time ocean forecasts coupled with 3rd spill 3000 tons satellites images and oil spill models. In this case variable wind data each 24 W in d hrs for 10 days of simulat ion used.[5] In this case a non-uniform current input 2. Materials and Methods used from Nat ional Instit ute of Oceanography and Fishers (NIOF) study, W at er current shows the current patterns of the Egyptian Mediterranean coasts in * Corresponding author: win t er.[4] [email protected] (A. Amr M. Sabry) Published online at http://journal.sapub.org/ajee Sea surface temp. (SST) 17.4°C Copyright © 2013 Scientific & Academic Publishing. All Rights Reserved Int erval for output 2 hrs

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Fi gure (1-a). Levantine Basin map by MEDSLIK

a) MEDS LIK incorporates the use of forecasts developed simu late an oil spill occurs on the Iranian coastline on the under MFS (Mediterranean forecasting system) program for Arabian Gulf after an accident in Bushehr Nuclear Power the whole Mediterranean Sea and its sub-regions such as Plant after an earthquake occurred. The following are input Levantine Basin (figure (1-a)). This program was used to data: simu late a mult iple o il spills occurred by a tanker near to the Ta b l e ( 3 -b). GNOME input dat a north coast of Egyptian. MEDSLIK uses a modified version of Mackay's fate algorithms for evaporation and A nuclear power plant accident; an explosi on emulsification and the dispersion algorithm of Buist and Type of in fuel tanks used to feed the emergency diesel Mackay[1]. The following is the typical data and information accident generators after an earthquake struck the region.(Bushehr Station) required as inputs for MEDSLIK: Type of Diesel Ta b l e ( 2 -a). Wind data for MEDSLIK pollutant Speed Vo lume 10,000 tons Dat e hour Direction (°) (m/s) Position of Lat it ude : 28°49'48.13'' (N) 1 9/1/2007 9 AM 2 70 accident Longit ude : 50°53'9.77'' (E) 2 10/1/2007 1 PM 3 240 Dat e 9, April, 2013 3 11/1/2007 1 PM 2 120 Time of spill 16:22 4 12/1/2007 1 PM 3 150 Release end 10, April, 2013 at 22 PM 5 13/1/2007 1 PM 4 70 dat e and time 6 14/1/2007 1 PM 2 40 Wind forecast dat a from Bushehr Airport W in d 7 15/1/2007 1 PM 5 240 meteorological station[3] 8 16/1/2007 1 PM 4 180 Three current patterns are used to simulate the 9 17/1/2007 1 PM 4 260 circulat ion in the inner Regional Organizat ion for 10 18/1/2007 1 PM 4 180 the Protect io n of the Marine Environment

11 19/1/2007 1 PM 3 180 (ROP ME) Sea Area. These include a reverse

12 20/1/2007 1 PM 4 70 estuarine flow, river flow, and a wind-driven

circulation derived with NNW winds. Tidal flows W at er current b) GNOME (General NOAA Oil Modeling Environment) are not simulat ed in the Locat ion File because it is was developed by the Hazardous Materials Response concerned with a large scale (>10 km) region and Division (HAZMAT) of the National Oceanic and long (> 1 day) timescale simulations[2]. Model run Atmospheric Administration Office of Response and 72 hrs. (3 days) Restoration (NOAA OR&R)[2]. The program was used to durat ion

238 A. Amr M. Sabry et al.: Assessment and Modeling of Oil Spill Dispersion in Mediterranean Sea on the North East Coast of Egypt and the Arabian Gulf

Fi gure (2-a). Distribution of current s at 30 m dept h off the Egypt ian coast in wint er

Fi gure (3-a). Locations of three oil spills and the tanker path in north eastern direction of egyptian coasts

Fi gure (4-b). Wind direct ion distribut ion for April, 2013

Fi gure (5-b). Average wind speed and dominant wind distribut ion in 2013

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Fi gure (6-b). Wind data by the met eorological St ation in Bushehr Airport on 9 th , 10 th , 11 th and 12th of April, 2013

Fi gure (7-b). Wind map on 9th April, 2013 for Arabian Gulf region

240 A. Amr M. Sabry et al.: Assessment and Modeling of Oil Spill Dispersion in Mediterranean Sea on the North East Coast of Egypt and the Arabian Gulf

Fi gure (8-b). Location of Bushehr Nuclear Power Plant in Iran

Fi gure (9-b). Bushehr nuclear power plant

(Bushehr nuclear power plant accident on the Arabian Gu lf) 3. Results and Discussions and the outputs are presented and summarized as follows: All the above data are inputted to MEDSLIK (tanker a) The output of MEDS LIK( tanker accident on north accident on the north east coast of Egypt) and GNOME east coast of Egypt):

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Fi gure (10-a). Surface oil by MEDSLIK Figure (11-a ) (Dispersed oil after three, five and ten days) shows that the dispersed oil propagates in the north direction away from the coastline and there's no coast impact. We used daily wind forecast data for eleven days (table (2-a)) covering the timeline of the accident simulation period (10 day), this may provide more accurate output. Figure (9-a) shows the surface oil for 10 days (240 hrs.) as wind changes as following:

242 A. Amr M. Sabry et al.: Assessment and Modeling of Oil Spill Dispersion in Mediterranean Sea on the North East Coast of Egypt and the Arabian Gulf

Fi gure (11-a). Dispersed oil by MEDSLIK

Ta b l e ( 4 -a). Changes in the propagat ion direct ion of the surface oil for 240 ο (26 to 240 hrs.), constant = 100.45 kg/(s · m). hrs d. Oil viscosity of the oil last released (min imu m Time range (hrs.) Surface oil propagation di rection viscosity): 8 to 16 SW ο (O to 32 hrs.), increases. 18 to 40 NE ο (32 to 240 hrs.), constant = 100.45 kg/(s · m). 42 to 64 NW 66 to 88 NNW Figure (14-a) oil density after 10 days (240 hrs.): 90 to 112 W SW a. Density of first oil released as percentage of density of 114 to 136 SW sea water (maximum density ratio): 138 to 160 NE 162 to 184 N ο (0 to 68 hrs.), increases. 186 to 208 ENE ο (0 to 240 hrs.), constant = 96.9%. 210 to 240 N b. Density of last oil released as percentage of density of sea water (minimum density ratio): Figure (12-a) oil fate parameters after 10 days (240 hrs.): ο (0 to 84 hrs.), increases. a. Percentage of oil on the sea surface: ο (84 to 240 hrs.), constant = 96.9%. ο (0 to 28 hrs.), decreases sharply. c. Percentage of water emulsified in the oil-water mousse ο (28 hrs. to 240 hrs.), decreases slowly. of first oil released (maximum water fraction): b. Percentage of oil evaporated: ο (0 to 68 hrs.), increases. ο (0 to 32 hrs.), increases. ο (68 to 240 hrs.), constant = 72.5%. ο (32 to 240 hrs.), constant = 33.68%. d. Percentage of water e mu lsified in the oil-water mousse c. Percentage of oil dispersed in water column: of last oil released (minimum water fraction): ο (0 to 240 hrs.), slightly increase to become 3.4427% ο (0 to 71 hrs.), increases. after 240 hrs. ο (71 to 240 hrs.), constant = 72.5%. d. Total percentage of oil on the coast: Figure (15-a) slick volume after 10 days (240 hrs.): ο Constant = 0.0%. a. Volume of oil released in: e. Percentage of oil on the coast but potentially releasable: ο (0 to 4 hrs.), constant = 2000 tons (first spill). ο Constant = 0/0%. ο (At 5th hrs.), step change to 3500 tons (second spill). Figure (13-a) oil viscosity after 10 days (240 hrs.): ο (5 to 6 hrs.), constant = 3500 tons a. Viscosity of the oil-water mousse from the oil first ο (At 7th hrs.), step change to 6500 tons (third spill). released (maximum viscosity): ο (7 to 240 hrs.), constant = 6500 tons. ο (0 to 110 hrs.), increases. b. Total volume of e mulsified o il in surface slick in : ο (110 to 240 hrs.), constant = 3111.71 kg/(s · m) . ο (0 to 4 h rs.), almost constant ≈ 2000 tons, but slightly b. Viscosity of the oil-water mousse from the oil last increase (first spill). released (minimum viscosity): ο (At 5th hrs.), step change to 3500 tons (second spill). ο (0 to 114 hrs.), increases. ο (5 to 6 hrs.), almost constant =3500 tons, but slightly ο (114 to 240 h rs.), constant = 3111.71 kg/(s · m) . increases. c. Oil viscosity of the oil first released (maximum ο (At 7th hrs.), step change to 65000 tons (third spill). viscosity): ο (7 to 77 hrs.), increases. ο (0 to 26 h rs.), increases. ο (77 to 240 hrs.), decreases.

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Fi gure (12-a). Oil fate parameters

Fi gure (13-a). Oil viscosity

244 A. Amr M. Sabry et al.: Assessment and Modeling of Oil Spill Dispersion in Mediterranean Sea on the North East Coast of Egypt and the Arabian Gulf

Fi gure (14-a). Oil density

Fi gure (15-a). Slick volume

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Fi gure (16-a). The three spills pat hs for 10 days (240 hrs.) a) The output of GNOME ( Bushehr nuclear power plant accident on the Arabian Gulf: The oil spill's propagation direction during the first day is mostly south-east (figure (17-b)) and there is a large coastal impact on the coasts of Bushehr facility region. The wind directions in day 9, April, 2013 at 16 PM, 19 PM and 22 PM were W, WNW and W respectively. The directions during 10th of April are N, NW and NNE at 1AM, 4AM and 7AM respectively. It remained in WSW direction fro m 10 AM to 16 PM. (figure (6-b)). Later in the day, the response team is able to conduct an over flight of the spill area to visually locate slicks and sheens of oil on the water. They made aerial observations fro m a helicopter to spot oil on the water. One large area of black oil and three smaller areas of brown oil were spotted with silver-to-rainbow sheens trailing them to the East (figure (18-b) and figure (19-b)). The black s plo ts (figure (17-b) and figure (19-b)) represent best guess trajectory estimate of the oil spilled from the tanker. To make this best guess, we assume that: a. The data input on the wind file accurately represent the wind directions in the timeline of the simulation for the next 3 days after the accident which is measured every 3 hours provided by the meteorological station in the Bushehr Airport (figure (3-b)). b. The data in the Location File accurately represent the current patterns during the time of the spill.

246 A. Amr M. Sabry et al.: Assessment and Modeling of Oil Spill Dispersion in Mediterranean Sea on the North East Coast of Egypt and the Arabian Gulf

Fi gure (17-b) . Oil spill by GNOME after 1, 2 and 3 days

Fi gure (18-b) . Ov erflight map by GNOME

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Fi gure (19-b) . Oil spill by GNOME after 1, 2 and 3 days after conducting an overflight

248 A. Amr M. Sabry et al.: Assessment and Modeling of Oil Spill Dispersion in Mediterranean Sea on the North East Coast of Egypt and the Arabian Gulf

The red s pl ots (figure (17-b) and figure (19-b)) represent After about 2 days (48 hrs) there is coast impact on the the model’s larger minimum regret trajectory estimate for coasts of Delvar (fig.(17-b) and fig.(19-b)) which is a city the same spill. To predict this trajectory, the model accounts and the capital of Delvar District, in Tangestan County, for uncertainty in the wind and current information that we Bushehr Province, Iran. Delvar is located near the coas t. At entered. As a very rough rule of thumb—assuming a “typical” the 2006 census, its population was 3,201, in 723 families. degree of uncertainty in the wind and current information, The oil spill also starts to propagate in the northern direction we use in modeling a spill scenario the chance that the spilled of Delvar (figure (21-b)) causing coast impact. oil will remain within the area covered by the red splots is on the order of 90%. It is impossible to assign a more precise probability, because little is yet known about uncertainties in wind and current forecasts. The assumed accident scenario as follo ws: Immediately after the earthquake, the Bushehr reactors shut down automatically and emergency generators came online to power electronics and coolant systems. However, the earthquake had caused deformations in the earth's crust in Bushehr station region which caused seawater to flood the low-laying rooms in which the emergency generators were housed. The flooded generators failed, cutting power to the critical pumps that must continuously circulate coolant water through a nuclear reactor for several days in order to keep it from melting down after being shut down. As the pumps stopped, the reactors overheated due to the normal high Fi gure (21-b) . Coast impact on Delvar city shoreline after about 2 days radioactive decay heat produced in the first few minutes after (48 hrs) nuclear reactor shutdown. In the high heat and pressure of the reactors, a reaction between the nuclear fuel metal cladding, and the water surrounding them, produced 4. Conclusions explosive hydrogen gas. The pool overheated, sparking fires 1. Accidental and illegal marine pollution in the in the building over the next hours. These massive Mediterranean Sea and the Arabian Gulf constitutes a major explosions and fires reached the diesel tanks used to feed the threat to the marine environment. Previous incidents in the emergency diesel generators which causes a huge leakage of Mediterranean Sea and the Arabian Gulf have resulted in oil to the sea water. About 10,000 tons of diesel was released environmental and economic damages to fisheries, to the to the sea, which caused a large oil spill in the Arabian Gulf. tourist industry and to coastal marine ecosystems. On April 9, 2013,anearthquake struck the Iranian province 2. To prevent the major impact of accidental oil spills, of Bushehr, near the city of Khvormuj and the towns of Kaki local and regional preparedness and response plans and Shonbeh. Seismologists said the quake struck at 16:22 recommend the use of computer-aided support sys tems (11:52 GMT) at a depth of 10 km (6.2 miles) near the town of based on operational oceanography and real-time ocean Kaki, south of Bushehr - a Gulf port city that is home to forecasts and real-time ocean forecasts coupled with Iran's first and only nuclear power plant (figure (20-b)). satellites images and oil-spill models. 3. Knowing the trajectory of the spill gives decision-makers critical guidance in deciding how best to protect resources and direct cleanup. However, it is often very difficult to predict accurately the movement and behavior of an oil spill. This is due, in part, to the interaction of many different physical processes about which information is often incomplete at the start of a response. 4. The modeler must thus continuously update pre-dictions with new data and explore the consequences and likelihood of other possible trajectories, a procedure called “trajectory analysis.” The end product of trajectory analy s is is often a map showing the forecast and probable uncertainty bounds of the slick movement. 5. Forecasting the movement of an oil spill is often hampered by insufficient input data, particularly in the first Fi gure (20-b) . Epicenter of the earthquake and the seismic activity fault few hours of the release. Detailed spill data (location, line volume lost, product type) are often sketchy and

American Journal of Environmental Engineering 2013, 3(5): 236-252 249

environmental data (wind and current observations and coefficients. forecasts) are often sparse or unavailable. Nonetheless, the Probability of washing back on each time step τ is given by: modeler must examine the data and attempt to understand the = 1 0.5 𝜏𝜏 physics and chemistry that will likely affect the oil Tw is the half-life for oil to remain�𝜏𝜏𝑤𝑤 on the beach before movement and fate of the particular spill. 𝑃𝑃washing𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑃𝑃off𝑃𝑃𝑃𝑃𝑃𝑃 again𝑜𝑜𝑜𝑜 𝑟𝑟𝑟𝑟. 𝑟𝑟The𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 random− number generator is called 6. As the spill unfolds, the forecast of oil movement and and the parcel is released back into the water if fate improves because the quality and quantity of the Rand (0, 1) < Probability of release on-scene observational data improves (while initial spill data Tw is assigned to each coastal segment depending on the becomes relatively less important). coastal type. On each time step it is assumed that the fraction 7. Trajectory analysis should include not only the “best of a beached parcel seeping is guess” of the oil movement and fate but also some = 1 2 −𝜏𝜏 representation of the uncertainty in the spill and �𝑇𝑇𝑠𝑠 Ts is a half-life for seepage or other mode of permanent environmental data used to make the forecast. The 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 − attachment. uncertainty in a trajectory forecast depends on the length and time-scale of the spill. = 1 2 exp( 0) −𝜏𝜏� Where d is the existing density of oil𝜏𝜏𝑠𝑠 on the segment (bbl 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � − � −𝑑𝑑⁄𝑑𝑑 /km) and d0 is a parameter. The half-life Ts for heavy oils:

5. Appendix = 0 [1 + (30 )] > 30 (8) Where Ts0 is the default half-life 5.1. Advection and Diffusion of the Slick 𝑇𝑇𝑠𝑠 𝑇𝑇𝑠𝑠 𝐶𝐶𝐻𝐻 − 𝐴𝐴𝐴𝐴𝐴𝐴 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 It is assumed that the surface oil is transported at a speed 5.2. Technical Description of the Fate Models that is a certain fraction α of the wind speed and at a certain For any sub-spill at any time step, let Vtk and Vtn be the angle β to the right of the wind direction. volumes of oil remaining respectively in the thick and the In M EDSLIK, the oil spill is modeled using a Monte Carlo thin slic ks, Atk and Atnt heir two surface areas and Ttk and Ttn method. The pollutant is divided into a large number of their thicknesses. It is assumed that the thickness Ttn of the Lagrangian parcels of equal size. At each time step, each thin slic k is constant equal to 10 microns, which is a typical parcel is given a convective and a diffusive displacement as th observed value for the final thickness of the sheen. On any follows. Let (Xi, Yi, Zi ) be the position of the i parcel at the time step, the two volumes are updated as beginning of a particular step, Z being measured vertically ( ) ( ) ( ) = upwards from the bottom. Then at the end of the time step of (9) (𝑒𝑒 ) (𝑑𝑑 ) (𝑠𝑠 ) ′ = length τ the parcel is displaced to the point 𝑉𝑉𝑡𝑡𝑡𝑡 𝑉𝑉𝑡𝑡𝑡𝑡 − ∆𝑉𝑉𝑡𝑡𝑡𝑡 − ∆𝑉𝑉𝑡𝑡𝑡𝑡 − ∆𝑉𝑉𝑡𝑡𝑡𝑡 (10) Where u(x, y, z) and v(x, y, z) are the water velocity (′ ) ( ) 𝑒𝑒 𝑑𝑑 𝑠𝑠 Where 𝑡𝑡𝑡𝑡 , 𝑡𝑡𝑡𝑡 are𝑡𝑡𝑡𝑡 the volumes𝑡𝑡𝑡𝑡 lost by𝑡𝑡𝑡𝑡 evaporation, components in the x and y directions, ( ) ( 𝑉𝑉) 𝑒𝑒 𝑉𝑉 𝑒𝑒− ∆𝑉𝑉 − ∆𝑉𝑉 − ∆𝑉𝑉 ( ) , 𝑡𝑡𝑡𝑡 are the𝑡𝑡𝑡𝑡 volumes lost by dispersion and Wx and Wy the components of wind velocity and 𝑑𝑑 ∆𝑑𝑑𝑉𝑉 ∆𝑉𝑉 𝑠𝑠 ( ) ( ) ( ) is the amount flowing from the thick to the thin parts of the ∆ , , are the diffusiveDisplacements in the ∆𝑉𝑉𝑡𝑡𝑡𝑡 ∆𝑉𝑉𝑡𝑡𝑡𝑡 ∆𝑉𝑉𝑡𝑡𝑡𝑡 slick. These transfers of oil are illustrated in Figure 21. three𝑑𝑑 directions.𝑑𝑑 The𝑑𝑑 vertical velocity w is not included in the 𝑖𝑖 𝑖𝑖 𝑖𝑖 Having updated the volumes of the two parts of the slick, model𝑋𝑋 since∆𝑌𝑌 it∆ is𝑍𝑍 generally very small. their areas are also updated on each step using = + , , + cos + sin s emi-empirical spreading formulas (see below). Then the ′ ( ) new thickness of the thick slick is computed: 𝑋𝑋𝑖𝑖 𝑋𝑋𝑖𝑖+ �𝑢𝑢 � 𝑋𝑋 𝑖𝑖 𝑌𝑌 𝑖𝑖 𝑍𝑍 𝑖𝑖 𝑎𝑎 � 𝑊𝑊 𝑥𝑥 𝛽𝛽 𝑊𝑊 𝑦𝑦 𝛽𝛽 � � � 𝜏𝜏(1) 𝑑𝑑 = (11) = + 𝑖𝑖 , , + sin + cos ∆𝑋𝑋 In the following sections,𝑡𝑡𝑡𝑡 expressions𝑡𝑡𝑡𝑡 𝑡𝑡𝑡𝑡 based on MacKay's ′ ( ) 𝑇𝑇 𝑉𝑉 ⁄𝐴𝐴 𝑌𝑌𝑖𝑖 𝑌𝑌𝑖𝑖 +�𝑣𝑣 �𝑋𝑋𝑖𝑖 𝑌𝑌 𝑖𝑖 𝑍𝑍 𝑖𝑖 𝑎𝑎 � − 𝑊𝑊 𝑥𝑥 𝛽𝛽 𝑊𝑊 𝑦𝑦 𝛽𝛽 � � � 𝜏𝜏(2) algorithms will be developed for all the volume and area 𝑑𝑑 ( ) increments. = + + ∆𝑌𝑌𝑖𝑖 (3) ′ 𝑑𝑑 The diffusive displacements𝑖𝑖 𝑖𝑖 are given𝑖𝑖 by: ( ) 𝑍𝑍 𝑍𝑍 ∆𝑍𝑍 = [2 (0,1) 1] 6 (4) (𝑑𝑑 ) = [2 (0,1) 1] 6 (5) ∆𝑋𝑋𝑖𝑖 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − � 𝐾𝐾ℎ 𝜏𝜏 (𝑑𝑑) = [2 (0,1) 1] 6 ℎ ∆𝑌𝑌𝑖𝑖 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − � 𝐾𝐾 𝜏𝜏 (6) 𝑑𝑑 Where Kh and Kv are the horizontal and vertical ∆𝑍𝑍𝑖𝑖 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − � 𝐾𝐾𝑣𝑣𝜏𝜏 diffusivities and rand (0, 1) is a uniform random number lying between 0 and 1. ( ) ( ) ( ) . . . , , = Fi gure 20. Volume transfers from the thick and thin slicks 2 𝑑𝑑 , 2 𝑑𝑑 , 2𝑑𝑑 (7) 𝑟𝑟 𝑚𝑚 𝑠𝑠 �∆𝑋𝑋 ∆𝑌𝑌 ∆𝑍𝑍 � K and K are the horizontal and vertical diffusion 5.2.1. Evaporation h v �� 𝐾𝐾ℎ 𝜏𝜏 � 𝐾𝐾ℎ 𝜏𝜏 � 𝐾𝐾𝑣𝑣𝜏𝜏�

250 A. Amr M. Sabry et al.: Assessment and Modeling of Oil Spill Dispersion in Mediterranean Sea on the North East Coast of Egypt and the Arabian Gulf

First, for the oil in the thin slick, it is supposed that the the fraction fmax of light component in the original oil. light component evaporates immediately. The volume Evaporation leads to an increase in the viscosity of the oil, evaporating on each time step from the thin slick equals the and the formula used for this is ( ) total content of light component in the thin slick: = 0 (20) ( ) 𝑒𝑒 = ( ) (1 ) (12) Where η0 is the initial v iscosity and K (e) a constant that 𝜂𝜂𝑜𝑜𝑜𝑜𝑜𝑜 𝜂𝜂 𝑒𝑒𝑒𝑒𝑒𝑒�𝐾𝐾 𝑓𝑓𝑡𝑡𝑡𝑡 � Where f is the𝑒𝑒 fraction of the oil in the thin slick that has determines the increase of viscosity with evaporation tn ∆𝑉𝑉𝑡𝑡𝑡𝑡 𝑉𝑉𝑡𝑡𝑡𝑡 𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑓𝑓𝑡𝑡𝑡𝑡 ⁄ − 𝑓𝑓𝑡𝑡𝑡𝑡 already evaporated at the beginning of the step and fmax is the (default value 4.0) initial fraction of evaporative component, which represents 5.2.2. Emulsificat ions the maximum value that ftn can attain. For the thick slick, the increment in the fraction ftk of the Emulsification refers to the process by which water oil that has evaporated is expressed as a product of the vapor becomes mixed with the oil in the slick. Let fw be the fraction pressure, Poil, and the change in an evaporative exposure, of water in the oil-water mousse. Then Mackay's model for Δ the change in this fraction per time step is[16] = ( ) ( ) 𝑡𝑡𝑡𝑡 (13) = 1 𝐸𝐸 2 3 (21) 𝑚𝑚 𝑚𝑚 The vapor pressure is 𝑡𝑡expressed𝑡𝑡 𝑜𝑜𝑜𝑜𝑜𝑜 in𝑡𝑡𝑡𝑡 the form ( ) ( ) ∆𝑓𝑓 𝑃𝑃 ∆𝐸𝐸 Where and 𝑤𝑤 are constants. This𝑤𝑤 model is based = ( ) (14) 2 Δ𝑓𝑓 3 𝐶𝐶 � − 𝐶𝐶 𝑓𝑓 �𝜏𝜏 0 on assuming𝑚𝑚 mousse formation𝑚𝑚 is a first-order process with P0 is the initial vapor pressure and c a constant that 𝐶𝐶 𝐶𝐶 ( ) 1 𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜 𝑃𝑃 𝑒𝑒𝑒𝑒𝑒𝑒 −𝑐𝑐𝑓𝑓𝑡𝑡𝑡𝑡 the water-in-oil fraction having an upper limit of measures the rate of decrease of vapor pressure with fraction 3 − 𝑚𝑚 already evaporated. The increment in exposure is expressed (default value taken as 75% for light oils but decreasing with 𝐶𝐶 as a product of a mass transfer coefficient Km, the time step τ, API number for heavy oils). The principal effect of emulsification is to create a mousse the slick area Atk and the molar volume of the oil Vmo l , divided by the gas constant R, the temperature T in °K and with greatly increased viscosity. It is supposed that the the initial volume of the sub-spill, V (0): viscosity ηem of the mousse is given by ( ) (1 ) = 2.5 / 1 = = (15) 1 (22) (0) 𝑚𝑚 𝐾𝐾𝑚𝑚 𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚 𝐴𝐴𝑡𝑡𝑡𝑡 𝜏𝜏 𝑘𝑘𝑚𝑚 𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚 𝐴𝐴𝑡𝑡𝑡𝑡 −𝑓𝑓𝑡𝑡𝑡𝑡 𝜏𝜏 ( ) Where 𝑒𝑒𝑒𝑒 a𝑜𝑜𝑜𝑜𝑜𝑜 constant that𝑤𝑤 determines the𝑤𝑤 increase of Where Vtk is𝑡𝑡𝑡𝑡 the current𝑅𝑅𝑅𝑅𝑉𝑉 volume of oil𝑅𝑅𝑅𝑅 𝑉𝑉 in𝑡𝑡𝑡𝑡 the thick slick, 𝜂𝜂1 𝜂𝜂 𝑒𝑒𝑒𝑒𝑒𝑒� 𝑓𝑓 � − 𝐶𝐶 𝑓𝑓 �� Δ𝐸𝐸 𝑚𝑚 equal to V (0) (1 – ftk) in the program, the various quantities viscosity with e mulsification 𝐶𝐶 𝑖𝑖𝑖𝑖 are given the values Vmo l = 0.0002, R = 0.000082 and 5.2.3. Dispersion = ( ) (16) 𝑦𝑦 The model of dispersion of oil into the water column is 𝑒𝑒 Where Wkph is the wind speed in kilometers per hour and 𝐾𝐾𝑚𝑚 𝐶𝐶 �𝑊𝑊𝑘𝑘𝑘𝑘ℎ � based on the work of Buist[17] and Mackay et al[16]. The C(e) and γ are coefficients with default values 0.00067 and process is illustrated in Figure 22. Wave action drives oil into 0.78 respectively. the water, forming a cloud of droplets beneath the spill. The Then the volume loss by evaporation per time step is equal droplets are classified as either large droplets that rapidly rise to the increment in the fraction evaporated multiplied by the and coalesce again with the spill, or s mall droplets that rise original volume: more slowly, and may be immersed long enough to diffuse ( ) = (0) = (1 ) (17) into the lower layers of the water column. In the latter case 𝑒𝑒 Although the evaporative component in the thin slick has they are lost from the surface spill and considered to be Δ𝑉𝑉𝑡𝑡𝑡𝑡 Δ𝑓𝑓𝑡𝑡𝑡𝑡 𝑉𝑉 Δ𝑓𝑓𝑡𝑡𝑡𝑡 𝑉𝑉𝑡𝑡𝑡𝑡 ⁄ − 𝑓𝑓𝑡𝑡𝑡𝑡 been assumed to disappear immediately, the thin slick is fed permanently dispersed. The criterion that distinguishes the by oil from the thick slick that has not in general fully small droplets is that their rising velocity under buoyancy evaporated. Thus the fraction ftn of oil in the thin slick that forces is comparable to their diffusive velocity, while for has evaporated must be reduced from the maximum value large droplets the rising velocity is much larger. fma x. Equating the oil content of the thin slick before and after the inflow, we have ( ) (1 ) = (1 ) 𝑠𝑠 ′ ′ ( ) ( ) 𝑉𝑉𝑡𝑡𝑡𝑡 − 𝑓𝑓𝑡𝑡𝑡𝑡 +�𝑉𝑉𝑡𝑡𝑡𝑡 − Δ1𝑉𝑉𝑡𝑡𝑡𝑡 � − 𝑓𝑓𝑚𝑚 𝑚𝑚𝑚𝑚 (18) Where is the updated volume,𝑠𝑠 this leads to the formula Δ𝑉𝑉𝑡𝑡𝑡𝑡 − 𝑓𝑓𝑡𝑡𝑡𝑡 ′ = ( ) ( ) 𝑉𝑉𝑡𝑡𝑡𝑡 (19) 𝑠𝑠 ′ Fi gure 22. The dispersion model Having updated�𝑓𝑓𝑡𝑡𝑡𝑡 𝑓𝑓 𝑚𝑚the𝑚𝑚𝑚𝑚 volumes− Δ𝑉𝑉𝑡𝑡𝑡𝑡 𝑓𝑓evaporated𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑓𝑓𝑡𝑡𝑡𝑡 �from�𝑉𝑉𝑡𝑡𝑡𝑡 the thick and thin slicks, the total fraction of the oil that has been lost Consider first the thick slick. At a given instant, let RL and by evaporation can be computed. This lost fraction is RS be the downward volume fluxes of oil per unit area of the assumed to apply to all the parcels in the particular sub-spill slick entering the water as large and small droplets and their fraction of light component is adjusted accordingly. respectively. Let the corresponding concentrations be cL and

Evaporation is stopped when the fraction evaporated reaches cS. If the rising velocities of the large and small droplets are vL

American Journal of Environmental Engineering 2013, 3(5): 236-252 251

( ) ( ) (0) and vS, then for a quasi-steady state we can equate the = (36) downward and upward fluxes: For each parcel the 𝑑𝑑random number𝑑𝑑 generator is called, 1 ( ) 𝑝𝑝 Δ𝑉𝑉 ⁄𝑉𝑉

= = + 1 (23) and the parcel is dispersed if 2 ( ) ( ) 𝑑𝑑 (0,1) < Where (>>𝐿𝐿vS ) is𝐿𝐿 the𝐿𝐿 (upward)𝑠𝑠 𝑠𝑠 diffusive𝑠𝑠 velocity of the 1 𝑅𝑅 𝑐𝑐 𝑣𝑣 𝑅𝑅 𝑐𝑐 �𝑣𝑣 𝐶𝐶 � Dispersion is assumed to stop when𝑑𝑑 the viscosity ηem of s mall droplets.𝑑𝑑 Thus, the mousse reaches a𝑟𝑟 value𝑟𝑟𝑟𝑟𝑟𝑟 ηmax . 𝑝𝑝 𝐶𝐶 1 ( ) = = + (24) 2 1 𝑑𝑑 5.2.4. Spreading The total volumes𝑐𝑐𝐿𝐿 𝑅𝑅of𝐿𝐿 ⁄oil𝑣𝑣 𝐿𝐿beneath𝑐𝑐𝑠𝑠 𝑅𝑅 the𝑠𝑠 ⁄ �thick𝑣𝑣𝑠𝑠 slick𝐶𝐶 in� the form of large and small droplets are then given by To complete the algorithms we need models for the = (25) changes in areas of the thick and thin slicks and the rate of ( ) flow of oil from the one into the other[18, 19]. For the thick = 𝐿𝐿 = 2𝐿𝐿 𝑚𝑚 𝑡𝑡𝑡𝑡 / 1 + (26) 𝑋𝑋 𝑐𝑐 𝑢𝑢 𝐴𝐴 𝑑𝑑 slick, spreading consists of two parts, one a loss of area due Where um is the vertical thickness of the droplet cloud. On 𝑋𝑋𝑠𝑠 𝑐𝑐𝑠𝑠𝑢𝑢𝑚𝑚 𝐴𝐴𝑡𝑡𝑡𝑡 𝑅𝑅𝑠𝑠𝑢𝑢𝑚𝑚 𝐴𝐴𝑡𝑡𝑡𝑡 �𝐶𝐶 𝑣𝑣𝑠𝑠 � to oil flowing from the thick to the thin slicks and a second each time step, a fraction of the small droplets is assumed to corresponding to Fay’s gravity-viscous phase of the be lost by diffusion to the lower layers of the water column. spreading[9]. Thus the change of area of the thick slick per The total volume lost on each step is taken as ( ) time step is 1 ( ) 1 ( ) 1 4 ( ) ( ) = = ( ) 𝑑𝑑 (27) 3 3 2 1 � + � = 𝑠𝑠 + (37) 𝑑𝑑 𝑅𝑅𝑠𝑠 𝐴𝐴𝑡𝑡𝑡𝑡1𝜏𝜏 𝐶𝐶 −𝑣𝑣𝑠𝑠 2 𝑠𝑠 ∆𝑉𝑉𝑡𝑡𝑡𝑡 𝑠𝑠 � � 𝐿𝐿𝐿𝐿 𝑠𝑠 ( ) 𝑠𝑠 𝑡𝑡𝑡𝑡 𝑑𝑑 ( ) ( ) Δ𝑋𝑋 𝑐𝑐 �𝐶𝐶 − 𝑣𝑣 �𝐴𝐴 𝜏𝜏 �𝐶𝐶 𝑣𝑣𝑠𝑠� 𝑡𝑡𝑡𝑡 𝑡𝑡𝑡𝑡 𝑡𝑡𝑡𝑡 Where again 1 is the diffusive velocity of the small Where 2 ∆ 𝐴𝐴is a constant− 𝑇𝑇𝑡𝑡𝑡𝑡 𝐶𝐶and 𝐴𝐴 𝑇𝑇 is𝜏𝜏 the volume droplets. The total 𝑑𝑑volume ofdispersed oil beneath the thick increment flowing𝑠𝑠 from thick to thinslick.𝑠𝑠 This volume is 𝑡𝑡𝑡𝑡 slick is then incremented𝐶𝐶 according to related to the𝐶𝐶 increment in area of the thin𝑉𝑉 slick: ( ) ( ) ( ) = + ( ) (28) = (38) 𝑑𝑑 Where the last term represents the′ change in the small 𝑠𝑠 𝑠𝑠 ( ) Δ𝑉𝑉𝑡𝑡𝑡𝑡 Δ𝑋𝑋𝐿𝐿𝐿𝐿 𝑋𝑋𝑠𝑠 − 𝑋𝑋𝑠𝑠 Thus, once we have a 𝑡𝑡𝑡𝑡value for𝑡𝑡𝑡𝑡 𝑡𝑡𝑡𝑡 , we can update the ( ) ∆𝑉𝑉 ∆𝐴𝐴 𝑇𝑇 droplet cloud during the time step due to changing conditions area, of the thick slick. 𝑠𝑠 (The large droplets are not regarded as dispersed since they ∆𝐴𝐴𝑡𝑡𝑡𝑡 Mackay𝑠𝑠 approximates the increment in area of the thin eventually re-coalesce with the slick.) 𝑡𝑡𝑡𝑡 slick by∆ 𝐴𝐴a formula similar to the Fay formula: proportional to To complete this part of the model, expressions are the cube root of the area times the time step times an required for the downward fluxes, RL and RS. For this, the exponential function of the thickness of the thick slick that fraction of the oil in either the thick or the thin slick that is reflects the tendency of the slicks to stop spreading when dispersed each time step is taken as they become very thin: ( ) 2 = / + 1 (29) 3 1 ( ) 𝑑𝑑 ( ) ( ) 3 3 Where Wm/s is wind𝑑𝑑 speed in m/s.𝑚𝑚 𝑠𝑠 For the thick slick, the = 1 𝑠𝑠 ( ) (39) Δ𝑓𝑓 𝐶𝐶 �𝑊𝑊 � 𝜏𝜏 � + 0.00001 fraction of this that consists of small droplets is taken as 𝑠𝑠 𝑠𝑠 −𝐶𝐶 11 𝑡𝑡𝑡𝑡 𝑡𝑡𝑡𝑡 � ( ) ∆𝐴𝐴 𝐶𝐶 𝐴𝐴 𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏 � 𝑡𝑡𝑡𝑡 � = 1 + ( 10)1/2( /0.001)( 24 ) (30) Mechanical spreading is considered𝑇𝑇 to occur for an initial 4 − 𝑑𝑑 period of 48 hours after the release of each sub-spill or until Where𝑠𝑠 σ is the interfacial𝑒𝑒𝑒𝑒 surface𝑡𝑡𝑡𝑡 tension between the oil 𝑓𝑓 � 𝐶𝐶 𝜂𝜂 ⁄ 𝑇𝑇 𝜎𝜎⁄ � the thickness of the thick part of the slick becomes equal to and sea water, the downward fluxes per unit area of slick per that of the thin slick if this occurs first. time step are then given by = ( ) (31) = (1 )( ) (32) 𝑅𝑅𝑠𝑠 𝑓𝑓𝑠𝑠 Δ𝑓𝑓𝑑𝑑 ⁄𝜏𝜏 ACNOWLEDGEMENTS For the thin slick, the following simpler expression is used 𝑅𝑅𝐿𝐿 − 𝑓𝑓𝑠𝑠 Δ𝑓𝑓𝑑𝑑 ⁄𝜏𝜏 for the fraction of small droplets: I would like to express my sincere gratitude and 1 ( ) appreciation to Dr. Nagwa Nassar for all o f her help and = 1 + ( 24) (33) 5 − valuable resources which proved to be essential while 𝑑𝑑 writing my paper. And it is assumed𝑓𝑓𝑠𝑠 that� all the𝐶𝐶 small𝜎𝜎⁄ droplets� below the thin slick are permanently dispersed. Thus the volume loss is given by ( ) ( ) = (34) 𝑑𝑑 𝑑𝑑 The total volume of oil dispersed from both thick and thin REFERENCES Δ𝑉𝑉𝑡𝑡𝑡𝑡 𝑓𝑓𝑠𝑠 Δ𝑓𝑓𝑑𝑑 𝑉𝑉𝑡𝑡𝑡𝑡 slicks, V(d) is then incremented according to [1] MEDSLIK Version 5.1.3 User's Manual, 2004, 2006, R. W. ( ) ( ) ( ) = + (35) Lardner, B.A., Ph.D., Sc.D., Cambridge, UK. 𝑑𝑑 𝑑𝑑 This gives a probability𝑑𝑑 of any particular Lagrangian Δ𝑉𝑉 Δ𝑉𝑉𝑡𝑡𝑡𝑡 Δ𝑉𝑉𝑡𝑡𝑡𝑡 [2] GNOME (General NOAA Oil Modeling Environment) User's parcel being dispersed into the water column on the given Manual, 2002, National Oceanic and Atmospheric time step equal to Administration, Office of Response and Restoration,

252 A. Amr M. Sabry et al.: Assessment and Modeling of Oil Spill Dispersion in Mediterranean Sea on the North East Coast of Egypt and the Arabian Gulf

Hazardous Materials Response Division, United States of [5] N. Nassar, 2012 "Assessment and modeling of radiation level America. over North Western Coast of Egypt" Thesis; PhD; Nuclear and Radiation Engineering Department, Alexandria [3] Website for wind, waves and weather forecasts: University, Egypt. http://www.windfinder.com. [6] A. Amr M. Sabry, 2013" Assessment and Modeling of oil spill [4] M. S. Kamel, 2010 "Geostrophic current patterns off the Dispersion on north east coast of Egypt & the Arabian Gulf" Egyptian Mediterranean coast" study; National Institute of Thesis; Master; Nuclear and Radiation Engineering Department, Oceanography and Fisheries, Kayt-Bay, Alexandria, Egypt. Alexandria University, Egypt.