Volume Voodoo: Relative Volumes of the Gulf of Mexico and Dispersant

Given today's earlier post, this one would seem to fit right in.

A Tweet rolled across my screen the other day. I can't recall the exact verbiage but it was something like this:

Gulf volume: 643 quadrillion gallons; dispersant volume: 1.5 million gallons. What's the problem?

Sounds like the Tweeter had a point: the volume of the Gulf is so huge relative to the volume of dispersant that the dispersant is unlikely to be a threat to Gulf life.

Let's do some arithmetic. If you divide the dispersant volume by the Gulf's volume (6.43E+17 gallons)  you find the former represents something like 2E-12 (or 0.0000000002 %) of the Gulf's total volume. Put another way, it is about 2 parts dispersant per one trillion parts of Gulf water, or 2 pptr. I have trouble imagining that small of an amount. Nevertheless, if you are trying to demonstrate that the dspersant is not a problem because its relative volume so small, the reasoning is specious.

The dispersant is not uniformly distributed ('perfectly mixed' in chemical engineering jargon) throughout the Gulf's entire volume.  There's more of it some parts of the Gulf, and less of it in other parts. Recall the Gulf is not like a big fish tank with relatively uniform or regular dimensions. About 38% of the Gulf's area consists of shallow intertidal zones, followed by 22% for the continental shelf (<200 m or <650 feet depth), 20 % for the continental slope (depths between 200-300m or 650 - 1,000 feet), and 20% for the abyssal regions (depths >3,000m or >10,000 feet). The greatest depth in the Gulf is 4,384m or 14,400 feet. Because of depth variations and currents, the dispersant is not likely to be evenly distributed. So the 2 pptr figure is likely a fiction.

Perhaps more importantly, keep in mind that this analysis does not consider the toxicity of the dispersant, how it degrades, and the effects of the dispersed (smaller particle size) oil. And some compounds can be toxic in extremely small amounts.

You can play the same game with the total volume of oil leaked. It is far greater than the dispersant volume, but it will still be small relative to the Gulf's volume., So it's not a problem, right?

See my comment below for a similar analysis of the total volume of oil released relative to the Gulf's volume.

As an aside, a fascinating book is How to Lie with Statistics, first published in 1954.

"If your experiment needs statistics, you ought to have done a better experiment." -- Ernest Rutherford

Comments

[Michael]

Thanks for commenting, David.

Your conversion is incorrect:

50,000 bbl/day = 2.1 Mgd = 8,000 cubic meters per day = 0.000008 cubic km/day or 8E-6 cubic km/day. There are 1E+9 cubic meters per cubic kilometer.

Assuming that the leak existed for about 90 days at that constant rate, we have a total volume of leaked oil of 0.00072 cubic km.

Since the volume of the Gulf is 2,434,000 cubic kilometers, the amount of oil leakage expressed as a fraction of the Gulf's volume is 3E-10 or 3E-8 %, or 300 parts per trillion by volume.

I did some rounding off, so these numbers are approximate.

[David Zetland]

Agreed. My current estimate is that Deepwater was polluting 0.8km^3 per day (@50,000bbl/day leak). That's a lot or a little. Take your pick