Mathematics and Oil Spills
Conversion Factors for oil spills
When an oil spill occurs many different units of measure may be used to describe the size of the spill. This can be very confusing for the public as often media reports use the largest figure to describe the oil spill.
Volumes of Oil
barrels x 35 = imperial gallons
barrels x 42 = US gallons
cubic meters x 264.2 = US gallons
cubic feet x 7.481 = US gallons
metric tons x 294 = US gallons
US gallons x 0.833 = imperial gallons
US gallons x 3.785 = liters
US gallons x 0.0238 = barrels (or divide by 42)
US gallons x 0.0034 = metric tons
The amount of oil on the water
Sometimes ships need to discharge oily bilges at sea. The current legal limit for this oily discharge is 15 parts of oil to one million parts of water (or 15 parts per million (ppm)).
A discharge of 15ppm cannot be seen on the water therefore if you can see an oil spill it is an illegal discharge.
When bringing a case to court, authorities need to estimate the amount of oil which may be in the discharge.
Oil spills spread quickly on the surface of the sea and the area of the spill is key information which is reported to authorities. In maritime language, a nautical mile (nm) is used to describe distance travelled by vessels. You will often need to convert this measurement to metric units to then calculate the amount of oil in the spill.
Nautical miles x 1.852 = metric conversion to kilometers
General Glossary of Terms Used in Oil Spill Observations
Spill characteristics appear differently under low light conditions and under strong winds conditions.
Light Sheen
A light, almost transparent, layer of oil.Sometimes confused with windrows and natural sheen resulting from biological processes. (eg coral spawning or algal bloom).
Silver Sheen
A slightly thicker layer of oil that appears silvery or shimmery.
Rainbow Sheen
Sheen that reflects colors.
Brown Oil
Typically a 0.1 mm - 1.0 mm thick layer of water-in-oil emulsion. (Thickness can vary widely depending on wind and current conditions). May be referred as heavy or dull colored sheens.
Mousse
Water-in-oil emulsion often formed as oil weathers: colors can range from orange or tan to dark brown.
Black Oil
Area of black colored oil sometimes appearing with a latex texture.Often confused with kelp beds and other natural phenomenon.
Windrows
Oil or sheen oriented in lines or streaks. Brown oil and mousse can be easily confused with algae scum collecting in convergence lines, algae patches, or mats or kelp or focus. Sometimes called streaks, stringers or fingers.
Tarballs
Weathered oil that has formed a pliable ball. Size may vary from pinhead to about 30 cm. Sheen may or may not be present.
Tar Mats
Non-floating mats of oily debris (usually sediment and/or plant matter) that are found on beaches or just offshore.
Pancakes
Isolated patches of oil shaped in a mostly circular fashion. Pancakes can range in size from a few meters across to hundreds of meters in diameter. Sheen may or may not be present.
Calculate the amount of oil in this spill
Question 1
An oil spill, with the appearance of black to dark brown, is sighted by a commercial airline flying over the Great Barrier Reef. The spill is estimated to be 1.5 kilometers long and 50 meters wide.
How much oil in liters would there be in the spill? (Remember that to produce a black to dark brown color the oil would have to be at least 100 microns thick.)
Question 2
A Coast guard surveillance aircraft photographs a ship trailing a silvery oil discharge from its stern. The discharge is 13.5 nautical miles and at least the width of the vessel which is 37.5 meters.
An oil spill on the water that gives a silvery sheen is approximately 1 micron in thickness.
How much oil in liters has the ship discharged into the sea?
Question 3
A fisherman reports an oil spill near a ship to the local maritime authority. The ship is radioed and asked if oil was being discharged from its vessel.
The captain reports that the ship has discharged only 10 liters of heavy fuel waste oil during a bilge pump out which is mixed with 100 tons of sea water.
Has the ship exceeded the legal limit of oil discharge of 15 parts per million (15 parts of oil to 1 million parts of water)?
Assume oil and sea water has same density for the calculation.
Answers:
Answer 1
1.5 kilometers = 1500 meters.
1500 meters long x 50 meters wide = 75,000 square meters of the slick area.
75,000 x 100 x 0.000001 (conversion of microns to meters) = 7.5 cubic meters.
1 cubic meter is 1000 liters therefore there is 7500 liters of oil in the spill.
Answer 2
13.5 nautical miles x 1.852 (metric conversion to kilometers) = 25.002 kilometers long slick (25,002 meters long).
25,002 meters long x 37.5 meters wide = 937,575 square meters of slick area.
937,575 x 1 x 0.000001 (conversion of microns to meters) = 0.9376 cubic meters of oil in the slick.
That is 937.6 liters of oil in the spill.
Answer 3
100 tons of sea water = 100,000 liters of sea water.
1 part per million (ppm) = 1 liter of oil in 1 million liters of sea water.
So if the ship stated it discharged 10 liters of oil in 100,000 liters of sea water the ppm is 10 x 10.
This is 100 ppm concentration of oil in sea water which exceeds the 15 ppm discharge limit.
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