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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 metres 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 = litres
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, nautical miles (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 kilometres

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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 colours.

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 coloured sheens.

Mousse

Water-in-oil emulsion often formed as oil weathers: colours can range from orange or tan to dark brown.

Black Oil

Area of black coloured 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 fucus. 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 metres across to hundreds of metres in diameter. Sheen may or may not be present.

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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 kilometres long and 50 metres wide.

How much oil in litres would there be in the spill?

(Remember that to produce a black to dark brown colour the oil would have to be at least 100 microns thick.)

Question 2

A Coastwatch 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 metres.

An oil spill on the water that gives a silvery sheen is approximately 1 micron in thickness.

How much oil in litres 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 litres of heavy fuel waste oil during a bilge pumpout which is mixed with 100 tonnes 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.

Approximate Layer Thickness Graph

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Answers:

Answer 1

1.5 kilometres = 1500 metres.
1500 metres long x 50 metres wide = 75,000 square metres of the slick area.
75,000 x 100 x 0.000001 (conversion of microns to metres) = 7.5 cubic metres.
1 cubic metre is 1000 litres therefore there is 7500 litres of oil in the spill.

Answer 2

13.5 nautical miles x 1.852 (metric conversion to kilometres) = 25.002 kilometres long slick (25,002 metres long).
25,002 metres long x 37.5 metres wide = 937,575 square metres of slick area.
937,575 x 1 x 0.000001 (conversion of microns to metres) = 0.9376 cubic metres of oil in the slick.
That is 937.6 litres of oil in the spill.

Answer 3

100 tonnes of sea water = 100,000 litres of sea water.
1 part per million (ppm) = 1 litre of oil in 1 million litres of sea water.
So if the ship stated it discharged 10 litres of oil in 100,000 litres 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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last updated:2 March 2004