How Big Is the Leak?

The question of the week seems to be just how much oil is leaking from the damaged well in the Gulf of Mexico. I have steered away from the controversy over these dueling estimates until now, because I didn't think I had anything relevant to add. But this mystery has intrigued me for days, particularly as the gap between the official estimate and those from outside scientists grew to alarming--and suspicion-provoking--proportions. How can there be such a wide disparity on something that seems like it should be so simple, and who is right, or a least closer to right? Two numbers in a report yesterday on BP's efforts to siphon off part of the flow provided a key data point for interpreting some of the higher estimates.

The most-frequently cited external estimate I've seen comes from Steven Werely, Ph.D., an Associate Professor of Mechanical Engineering at Purdue University. Dr. Werely is an expert in fluid mechanics--one of the tougher disciplines I encountered in my chemical engineering curriculum, long ago. He has applied a technique called "particle image velocimetry" to the video of the oil leaking from the broken well and derived a flow estimate of 95,000 barrels per day, plus or minus 20%. He has shared this result in front of Congress and with a number of news outlets. It's a frightening number, and he presents it very credibly, though when I saw him interviewed last week on BBC America World News, he was careful to point out that he didn't have an oil and gas background, and thus lacked some context for framing his estimates.

My reaction to this figure was that it was so far beyond the range of my knowledge of what oil wells typically produce that it seemed incredible. For example, Chevron's Tahiti deepwater platform in the Gulf produces a total of 125,000 bbl/day of oil from six wells with none of the constrictions, obstacles and other problems that BP's Macondo well has. It also occurred to me that Dr. Werely's technique really measures what engineers would call "space velocity", or the total volume of fluid moving past a reference point, whatever its composition. If the fluid consisted entirely of oil, then the space velocity and oil flow rate would be identical. However, we know that at least some of that fluid is natural gas, affecting its density. But until I saw the latest report on BP's efforts to collect some of the flow with the "straw" they inserted into the end of the riser, I had no way to gauge that--nor perhaps did Dr. Werely.

I realized that if 5,000 bbl/day of oil are now being collected at the surface along with 15 million cubic feet per day of natural gas being flared, then roughly that same ratio of gas to oil should apply to the fluid we see coming out of the well, adjusted for the effects of depth. Under 5,000 feet of seawater with a pressure gradient of 0.445 psi/foot, that gas will behave differently and take up a much smaller, but still not insignificant volume. At this point in my logic some dormant engineering brain cells sprang to life and I started figuring out the volume that the gas being measured at the drill-ship, at atmospheric pressure and temperature, would occupy at 2,225 psi and a degree or two above freezing, using standard pressure-volume-temperature relationships. My back-of-the-envelope calculation indicates that this amount of natural gas would equate to 16,600 barrels per day (of compressed gas , not oil) at the depth of the broken well and riser: in other words, a higher apparent volume than the oil that accompanied it to the surface through BP's "straw".

While I made several simplifying assumptions along the way to that result, it at least suggests the possibility that the majority--perhaps over 75%--of the visible flow billowing out of that broken pipe, and upon which scientists are basing their estimates, might consist of gas dissolved in the crude oil and compressed gas that has come out of solution but is mixed into the oil by the turbulence of the flow. I can't tell to what extent Dr. Werely has already factored this in, though his comments in this article in Science News seem to suggest that he regards it as a big uncertainty with the potential to scale down his estimate. If so, his mean 95,000 bbl/day figure might consist of something less than 25,000 bbl/day of actual crude oil, plus a much larger quantity of natural gas that would mostly escape into the atmosphere and couldn't foul any beaches. That's still a lot more oil than BP and the federal government had been quoting, but it's not orders of magnitude higher.

So where does this leave us? Apparently, BP is now conceding that the leak must be larger than their 5,000 bbl/day estimate, because they can measure that much oil going into their drill-ship on the surface, and there's still more leaking. At the same time the gas/oil adjustment could bring the high-end estimates from experts like Dr. Werely into the same general ballpark as the flow rates that other wells are known to produce, albeit under more controlled circumstances. That might give us a much better figure from which to calculate how much oil could eventually reach the shore, after its lighter components, such as propane, butane, and naphtha, have evaporated in the warm Gulf Coast conditions.