# Some numbers for the BP leak

The Deepwater Horizon well is situated 1500 m below the surface of the Gulf of Mexico.  The hydrostatic pressure is approximately given by  the simple formula of $P_a+ g\rho h$ where $P_a = 100 \ kPa$ is the pressure of the atmosphere, $\rho = 1 \ g/ml = 1000 \ kg/m^3$   is the density of water, and $g = 10 \ m/s^2$ is the gravitational acceleration.  Putting the numbers together gives $1.5\times 10^7 \ kg/m s^2$, which is $15000 \ kPa$ or about 150 times atmospheric pressure.  Hence, the oil and natural gas must be under tremendous pressure to be able to leak out of the well at all.  It’s no wonder the Top Kill operation, where mud was pumped in at high pressure, did not work.

Currently, it is estimated that the leak rate is somewhere between 10,000 and 100,000 barrels of oil per day.  A barrel of oil is 159 litres or 0.159 cubic metres.  So basically 1600 to 16000 cubic metres of oil is leaking each day.  This amounts to a cube with sides of about 11 metres for the lower value and 25 metres for the upper one, which is about the length of a basketball court.  However, assuming that the oil forms a layer on the surface of the ocean that is 0.001 mm thick, this then corresponds to a slick with an area between 1,600 to 16,000 square kilometres.  Given that the leak has been going on for almost two months and the Gulf of Mexico is 160,000 square kilometres, this implies that the slick is either very thick, oil has started to wash up on shore, or a lot of the oil is still under the surface.

## 6 thoughts on “Some numbers for the BP leak”

1. Greg says:

Excellent and well explained. Overcoming the static pressure of the ocean at 5000 ft. That is quite an oil well. You would think that a probe could be inserted down the pipe and measure the pressure in the column. At different depth the real flow could be determined accurately. Of course the well casing could be cracked with in the earth. And the leaks cannot be seen.
Get ready for a lot more oil!

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2. Hugh Riddle says:

Entirely misguided explanation. It is the DIFFERENCE between the sea and oil pressures that is relevant and this will be much smaller than the absolute sea pressure figure given.

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3. True, but I believe the reason they stopped was because they were afraid that the casings would burst and make the spill worse and that is a function of the absolute pressure isn’t it?

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4. Greg says:

I did not quite comprehend what Hugh is saying.
There are too many unknowns to explain the whole scenario. I’d prefer to assume that this well had the capability to produce 60,000 BPD or it would of been abandoned long ago.
Now its a matter to determine the efficacy of the well casing by other methods including the observation of the sea floor in search of plumes of oil. You got to wonder what the guy on top are thinking with their access to privied information. Just fun and game for us in the blog world

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5. Hugh Riddle says:

Sorry Greg, I apologise for being too sweeping. My objection was only to presenting the absolute pressure as driving the leak flow. The oil will be at 150 atmospheres because it’s part of the sea bed but the sea is ‘pushing it back in’ with a similiar absolute pressure. For oil to flow out, the oil pressure must be a bit higher than the sea pressure and that pressure DIFFERENCE determines the flow rate. My guess is somewhere between 5 and 20 atmospheres difference.

Carson, I’m not clear which casings you are referring to. The most dramatic example is probably that of the remote-controlled undersea vehicles that are presumably groping around down there right now. They are quite likely near atmospheric pressure INSIDE their casings which have to be extremely strong not to be crushed by the 150 atmosphere sea pressure. I don’t think that’s the situation for the drilling casings etc.

I did a little exercise to get a sense of proportion about the leak rate – 60000 barrels per day appears equivalent to one (big: 2 million barrels) full supertanker breaking up a month. I remember the ‘Brer’ supertanker grounding on a rocky Scottish Island some years ago. It was blowing Force 12 and the waves smashed it up very quickly and completely and there wasn’t a bad problem. Presumably when the oil gets spread around like that, the existing microbe populations are able to do a pretty good final clean-up job!

I’m enjoying this site, not least because of your very gentlemanly reactions to my over-sweeping assertions. Best wishes to all.

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6. Hi Hugh,

I calculated the absolute pressure just to show how much pressure the oil must overcome to escape. I didn’t mean to imply that this determined the flow rate. Secondly, I then argued that for top kill to work, the pressure of the mud sent down the pipe must at least be as high as the absolute pressure. What I was thinking, and I may be mistaken, was that you have are putting a plug into a pipe that is under 150 atmospheres so the pipe has to be pretty strong to contain that pressure. I think what they were worried about is the integrity of the pipe casing in the sediment under the sea floor. They didn’t want plugging the well head to cause it to burst underneath and then the leak would not be containable at all.

Carson

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