# volumes of oil

the collapse of the Deepwater Horizon drilling rig in the Gulf of Mexico is making a mess, but a lot of the numbers being bandied about make little sense

partly the problem is units, with news media freely exchanging barrels per day with gallons per minute and rates with integrals

I am but a humble physicist, but that has never stopped me before...
for real info go someplace like The Oil Drum

So, lets take your benchmark guesstimate as the oft quoted 5000 barrels per day.

Now there's a meaningless unit.
A barrel is a whisker under 160 liters, so per day this is 800,000 liters (massing about 750 tons), or about 10 liters per second.

Hmmm.

The size of the hole drilled can be from few inches to couple of feet.
We can estimate the diameter of this one at 8" or so, or 20 cm.
So it has a cross-sectional area of 300 cm2

A liter is 1000 cm3, so we're talking 104 cm3/sec, which implies an mean outflow velocity of about 30 cm/sec.
That is not exactly a gusher.

This is linear in leak rate - so 25,000 barrels per day would imply 50 liters per second, and velocities of order 1.5 m/sec (but see caveat below).

The oil is coming out of three separate leaks in the pipe, one of which has reportedly been plugged. Presumably most of the oil is coming out of one hole, and the holes in the pipe are smaller than the pipe diameter. So actual velocities might be more like a meter per second - still only comparable to slow walking speeds.

The leak is down at about 1500m, so the pressure down there is about 150 atmospheres.
So about 2500 psi - that is a lot, and the oil of course is coming from deeper down, but the pressure is ambient, so the pressure differential at the well head must be small (else the velocity would be higher).

One might therefore conclude that actually capping the well is not physically hard, except for the part where it is at 1500m depth, and dark.
So containment ought to be possible, and once contained extracting the oil into storage should be possible.

The problem is the oil in the water - the Exxon Valdez, the US's worst spill, was about 250,000 barrels (about 30,000 tons), at least.
At the low estimated leak rate, that much oil will come out in 50 days (we're at day 15 already) - at the, arguably more plausible, higher estimated leak rated of 25,000 barrels per day we are already well past the Exxon Valdez leak.

There have been worse oil spills - Kuwait in 1991 was about a million tonnes, or 8 million barrels; the Ixtoc-1 oil well in the Gulf in 1979 was on a similar scale to Deepwater Horizon and took 9 months to control, losing about 500,000 tons, or about 4 million barrels. The Amoco Cadiz in 1978 in the Channel lost 200,000 tons, or about 1.7 million barrels.

If the leak will take 9 months - 200 days - to contain, then at the low estimated leak rate it will spill a million barrels, or little over 100,000 tons. At the higher estimated leak rates the spill would be exactly like Ixtoc-1 - 4 million barrels or half million tons in the ocean.
About 10-12 Exxon Valdez sized spills!

It will be interesting to see which way it goes - technology to cap wells and control them has improved since 1980, but this well is also deeper and harder to work.
Drilling a new well to cut this one off below the surface, by all accounts, will take about 3 months, if it works.

Clearly it will take at least a month to control this - so we're looking at 1-10 months, with
spills of at least 150,000 barrels and possibly as high as 5,000,000 barrels.
If the pipe is eroding and the oil flow is currently constrained by the fittings, then the rate of flow could increase! Which would make it harder to contain.

The wild-ass guesstimate of the size of the field is ~ 100,000,000 barrels and typically it appears ~ 10% of the field will free flow under its own pressure into wells before active extraction is needed, so total leakage as high as 10,000,000 barrels is not implausible for timescales of a year and plausible higher end leakage rates.

That is not good.

Coastal fisheries off the north gulf are likely to be trashed, as a long stretches of beaches.
Oil may end of going both east towards Florida, and west towards Texas, and maybe to some of the islands.
There is a possibility that some oil will get past the Keys into the Gulf Stream and up the US coast, maybe even further, though that will be spotty contamination.
I have no idea what the oil will do if a hurricane enters the gulf before the leak is contained, or while there is a lot of oil on the surface.

A lot of wildlife will die, and extensive ecosystems will suffer multi-year damage.

US oil consumption is 21 million barrels per day.

That leak is order 0.1% of the oil flowing into the US supply chain per day.

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Interesting calculation, but I'm not sure I buy your "not hard to cap" conclusion. If indeed the oil is coming out at a slow walking speed, and if it isn't too viscous, then sure, the pressure difference between just inside the pipe end and just outside are not too great. But that's not the pressure difference that matters for capping the well. What matters there is something like the difference between the pressure deep inside the well and the pressure just outside the pipe. After all, crude oil is fairly viscous stuff, so there is potentially a large pressure drop as it flows from the reservoir to the leak. (I am ignoring the depth-related changes in pressure.) If you outright stop that oil from flowing, there will no longer be a viscous pressure drop and the pressure at the now-stopped leak will rise to that inside the reservoir. So your patch has to stand up to that pressure, not just the pressure difference there is now.

This could be avoided if instead of sealing the holes you had some system that captured all the oil that flowed out; then you'd still have that viscous drop to take the pressure off. Such a system need not even be completely tight to drastically reduce the severity of the spill. But you do need to gather all that oil and put it somewhere, fast enough to keep up with what's coming out of the leak.

I completely agree - just plugging the well would be hard, because the backpressure from 6 km down would build up and be transmitted extremely efficiently by the relatively incompressible oil - the cumulated back pressure must be several hundred atmospheres, or maybe 10,000 psi.

But, as you say, it makes catching the oil relatively "easy",
even at the high end of the estimated leakage rate it is only about 100 kg/sec coming at few m/sec - so like catching a running person (and storing them) every second.
Quite doable, IF they can maneuver to get equipment in place and get the built up stored oil pumped away for recovery.
That ameliorates the pollution significantly and buys time to drill a recovery well sideways into the old well under the breach. IF the well head doesn't erode away in the mean time.

"That leak is order 0.1% of the oil flowing into the US supply chain per day.

It seems we need to build 1000 more offshore wells. More seriously, I was asking myself what type of risk analysis goes into offshore oil drilling. I have to say, what I found is incomprehensible.

The Minerals Management Service is responsible for managing offshore continental oil and gas reserves. I came across their economic and environmental assessment here: http://www.mms.gov/5-Year/PDFs/MMSProposedFinalProgram2007-2012.pdf

Basically this is how they calculate the net value of the oil reserves to society:
Value of Oil
- cost to extract oil
- cost to the 'environment'
and then
+ financial benefits to society (i.e. all the people you pay to extract oil and any other jobs involved).

For the Central Gulf of Mexico, over 40 years, the estimated cost of environmental impact is 337.5 Million Dollars. A very precise estimate, they must know what they are talking about. You can check out all the numbers on page 84.

I'm sure that the law required the analysis to be done like this. But it blows my mind that the cost benefit analysis can be so terrible: The oil industry profit - a made up environmental cost.