# Oil in the Gulf of Mexico? The calculator speaks

Where is the Deepwater Horizon oil? This question fascinates a number of scientists who dispute the official figures published by US administration who asserts that only 25% of the 545,000 metric tons of oil released in the Gulf of Mexico, are still in the ocean. One of the relevant question is: how much oil is floating deep under the surface, dispersed in a plume of small droplets formed at a 1000 meters depth? The NOAA refused first to admit the existence of such a plume, before publishing a report in june, with numerous experimental data.

To refresh my mathematical souvenirs and try to answer this question, I tried a small back-of-an-envelope calculation, partly based on NOAA informations, to evaluate some orders of magnitude, considering that the plume is about a hundred meters in depth. NOAA scientists measured a few parts-per-million oil concentration near the rig, about few gram per cubic meter, decreasing with distance. I have to say that the hypothesis I took for my calculations are somewhat false. But, remember, my intent is only to get some orders of magnitude.

If we consider that the concentration is homogeneous and isotropic, in a disc of 160 kilometers in diameter (1) with a 100 meters height, I’s easy to calculate that the plume may contain from 2,000 metric tons (for a 1 part-per-billion mean oil concentration, ppb) to 2 million metric tons (@ 1 ppm mean concentration). This is not a useful interval!

I made a brainstorm in my memory —does mathematical integration speaks to you? (2)— and considered that oil concentration exponentially decreases when distance from rig increases. Let’s say from 1 ppm above the rig, to 1 ppb at 80 kilometers. This gives me a figure of 83,000 metric tons of oil in the famous plume. It’s about 15% of the oil released in the Gulf of Mexico. As oil is also hidden elsewhere, in sediments for example, this is not light-years ahead of official figures!

(1) Why 160 kilometer diameter? Why not!!!
(2) This calculation won’t change the course of the universe, but it is not so stupid. And it’s always good to refresh some souvenirs. I didn’t fight with mathematical integration since I finished my PhD, in 1989!