Mathematical Model to Evaluate Behavior of Oil Spill Discharged into Tigris River

لاخلا ةص  ةلجد رهن ىلإ ةيطفن ةعقب برست كولس نهكتل يضاير ليدوم ءانب ثحبلا نمضتي رهنلا راسم لوط ىلع ةعقبلا كلت ريصمو .  ليدوملا لدعمو رخبتلا لدعمو ءاملا حطس ىلع ةيطفنلا ةعقبلا راشتنا لماع لثم لماوعلا نم ةعومجم ةجلاعم رابتعلاا رظنب ذخأ يضايرلا ىلإ ةفاضإ ،رهنلا ءام يف تيزلل بلاحتسلاا راشتنا ب تدمتعا ليدوملا تاباسح نا .رهنلا ةفاح ىلع ةعقبلا لماوعلا ىلع يساسا لكش ىلع اهريثأتو رهنلا ةعرس نهكت ىلع رداق ليدوملا نأف كلذك ،رهنلل يسدنهلا عقاولا ىلعو قارعلا يف ةلجد رهن راسمل ةيفارغجلا رهنلا لوط ىلع ةعقبلا دادتما .  نم ةعومجم نمضتي نكلو ةعقبلا ةلاح فصول ةدحاو ةلداعم ىلع لمشي لا يضايرلا ليدوملا تلاداعملا  دامتعلااب ممصُ يبوساح جمانرب مادختساب تلاداعملا كلت لح مت دقل .ةدحاو ةيئاهن ةجيتن ءاطعلإ ضعبلا اهضعبب ةطبترم .مدختسم يأ لبِق نم جئاتنلا ىلع لوصحلا ليهستل (كسيب لوجِف) ةيجمرب هغل ىلع  Abstract This study included first attend in Iraq to built a mathematical model predicting the behavior oil spill discharged into Tigris river and the fate of spill along the river. The model included many factors such as spreading & oil spill, evaporation; emulsion shoreline closes in river sedge. The calculations based on the geographical location of the spill & geometry of the river section also, the model predicts the speed of Water River and its effect on the oil. Spill spreading along the river. The model did not describe the oil spill in one equation but, it divided to steps related together to give the single results. The model equation can be solved by computer software designed using visual basic program to facility getting result by any use.


Introduction
Mathematical model of prediction the oil spill fate in river Tigris is achieved in this work , after that the model applied by a computer program designed by Visual Basic language ,to simplify the use of the mathematical model to any user [1].

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River Tigris representing an important source of water for many governors in Iraq , it has long path from north to south , and it is very important to prevent and control any pollution accidents occurs in the river . oil spill one of most possible event in the river , this belong to the fact of many oil projects , like refineries storages and others are founded in different areas of Iraq close to the river and also many pipelines pass near it . In the past time there is no any record or archives for such events and there is no any scientific data about the oil spill happened in the river Tigris.
Therefore, it is very important to build a mathematical model to control, predict and record all oil spill can occur in the future. The model cover the whole path of the river across Iraq lands from the entering point in the north Duhuk to the last point in the south Basra. Taking into account the weather effect, river water conditions, geometry of the river and oil spilled type and properties [2].
There are many oil spill studies and models. Almost all these models were developed for marine environment. For rivers, limited models were developed and the model can be applied for the specific river and this is the fact that each river differ than other rivers which required a limited oil spill mathematical model [3].
The oil spill in the river will take many directions, at the minute it starts, under the effect of the river conditions at the area of spill. First, advection under effect of river water velocity and wind speed take place,, the velocity of oil and flow direction will determine the time required to reach specific place. Known this time will very important to treatment work. Second, the horizontal flow of the oil across the river and maximum diameter of the oil spill can give the idea about the area will be cover by the oil. Third, the effects of loss some hydrocarbons due to evaporation will be calculate by the mathematical model, which represent an important factor in the air pollution. The loss in the shorelines (river cliff) according to the nature and constituent the river cliff also the emulsion effect on oil properties with time to be evaluate mathematically [3].
Most of the above factors are calculated from experimental models used previously and derived from the basic of scientific resources. The final result of the work is a simple and clear computer application fed with oil spill data like location, date, oil spill amount , type of the oil, wind speed and weather conditions. All of this information are easy to collect and fed to the program [4].
Then the computer will provide results of spreading velocity and area, time to reach any area will be known, amount evaporated after time, the loss at river cliff, and changing in oil properties aftertime. Normally, the calculations is made for the first twelve hours due to the fact that the oil spill spreading will take its final limit within this time and the treatment work will be started at this period specially in the oil spill river it is more easier than oil spill in the sea [5].

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At the end the program will keep a record of all details for this oil spill and this will be a basic archive to any future study or observation of oil spill pollution in the river Tigris [6].

The Mathematical Model
The mathematical model dialed with four points: 1. Evaluation of oil spill speed.

Evaluation of oil loss by evaporation.
3. Evaluation of oil deposed on river beaches.

Evaluation of oil residue.
In general, the state of oil spill transported on river water can be described by equation 1: So, the quantity of oil transferred with river is calculated using equation 2:

Transport and Diffusion
When volume of oil discharged to river water, the first stage that described the behavior of the oil spill formed is the transport of oil spill with river current associated with diffusion of oil in river water.
The overall speed of oil spill transported over river water is yield of spill velocity with river current direction and molecular diffusion velocity of oil as shown in equation 3 Spill velocity with river current direction depending on wind direction and illustrated by The velocity of river is graduated from zero in river bottom to maximum value at river surface and can be represented mathematically depending on fluid flow phenomena as shown in Fig. (2).

River Surface
River Water Velocity To evaluate molecular diffusion velocity it is important to evaluate random function as shown in

Fig. (7)
The water cut emulsified in oil phase must evaluated in order to know the fate of the spill:

Oil Deposited on River Beaches
When oil discharged to water river, the oil spill is expanded in two dimensions as show in Fig. (8). The rate of oil deposited on the beaches of river can be evaluated as follows: