Billions of dollars and the future of one the world's lushest ecosystems could all ride on one elusive number: the precise amount of oil gushing from the broken BP well at the bottom of the Gulf of Mexico.
Evidently, it's not an easy number to calculate. Estimates have ranged from a 1,000 barrels a day to 100,000 barrels a day. Some say it depends who's doing the figuring; others point to the unpredictable conditions that go along with drilling for oil deep beneath the seabed.
Whatever the final number is, it will help determine how much BP and other operators might have to pay as a result of the April 20 blowout and spill at the Deepwater Horizon rig. One lawsuit has put potential damages — presuming the oil keeps spewing out until August, as BP has predicted — at $19 billion.
An accurate tally will also help those charged with the clean-up decide which weapons to deploy — and how many — to mop up, burn off, corral or collect the mess created by what is easily the worst oil spill in U.S. history.
So, given all that is at stake, how can the estimates of what's coming from that wellhead be so wildly divergent?
"That's easy to explain," said Steven Wereley, who literally wrote the book on how to make this kind of calculation. "Some of them are wrong."
Early estimates: 1,000 versus 95,000 BPD
Wereley, a professor of mechanical engineering at Purdue University in Indiana, is a kind of oil spill sleuth. He was one of the first independent experts to put a figure to what was really coming out of the Macondo wellhead, nearly a mile down on the sea floor.
His initial estimate, based on what he saw in a low-resolution 30-second video of the wellhead provided by BP on May 13, was 95,000 barrels per day, or bpd. That counted everything that was spewing from the well, not just oil.
Wereley made that first calculation in response to a reporter's query about whether it could be done just by looking at the wellhead. Even he reckoned that the figure was high, however, because he didn't know how much of what he saw bubbling out of the pipe was oil and how much was gas.
He and other scientists who made similar calculations took some heat from BP over their numbers.
"The rate of flow from the riser is determined in a number of ways and by a number of variables," BP said in a May 21 statement. The British oil giant noted that while the riser pipe's original interior diameter was 19.5 inches, the accident distorted it by about 30 percent, and a drill pipe trapped inside the riser reduced the flow area by another 10 percent.
"Thus, some third party estimates of flow, which assume a 19.5 inch diameter, are inaccurate. As well, there is natural gas in the riser," the company said. "Data on the hydrocarbons recovered to date suggests that the proportion of gas in the plume exiting the riser is, on average, approximately 50 percent."
BP spokesman Robert Wine noted the difficulty of early estimates: "Initially there was no way of assessing accurately since there are no meters to measure a leak, and the blowout preventer gauges weren't able to give any usable information." Wine said even the government's first figure of 5,000 bpd, made by calculating the surface area covered by the spreading slick, had a wide margin of uncertainty.
"Subsequent updates have been able to use more data from the blowout preventer and are using the collected flow rates," Wine said. "But they are still estimates."
When Wereley and others made their original estimates, however, BP had not yet released information about the oil-to-gas ratio or the dimensions of the misshapen pipe.
Once that data was public, Wereley and other engineers went to work. The oil-to-gas ratio turned out to be 29 percent oil to 71 percent gas; taking that into account, Wereley's early estimate for the broken well's oil flow rate was roughly 30,000 barrels a day.
Most of the flow was gas, largely methane, a potent climate-warming chemical that can create oxygen-free "dead zones" in a body of water like the Gulf of Mexico. But methane's effects are not instantly visible like oil's.
Among other reasons, the oil flow rate is important because of how the Clean Water Act allows damages to be calculated. If a company is found to have shown gross negligence or willful misconduct in polluting U.S. waters, it can be ordered to pay $4,300 for every barrel of oil spilled.
Coast Guard Admiral Thad Allen was blunt in mid-June: "That's the $100,000 question — we need a flow rate. And we're never going to know exactly what it is until we have a tight seal on that and we can actually measure production."
Globs, chunk and billows
It turns out that there is a way to calculate what's coming out of the well without putting a meter on the leak, and that is particle image velocimetry. Wereley and three colleagues wrote a book on this subject, "Particle Image Velocimetry: A Practical Guide," published in 2007.
To understand this method, think of some clouds floating across the sky. They don't change their shape constantly, so if you see something that looks like a lamb, you can track it for a while as it moves with the wind.
Now take a look at online video of the BP wellhead — some early, low-resolution video is available here on YouTube — and you can see some cloud-like billows coming out of the broken pipe.
Experts in fluid mechanics, people who study how liquids act, call these cloud-like formations turbulent structures.
Wereley said it took him two hours to look at the ones he saw on the May 13 BP video and calculate how much was coming from the well. He made it sound like a kindergarten class could do this using just their eyes and a ruler.
"It's not rocket science," Wereley said. "It's not that hard once you know what you're doing."
After all, he said, what you're doing is calculating a rate — the number of barrels of oil leaking each day — and rate equals distance over time.
Here's how he explained it:
"If you watch the videos in slow-motion ... you'll see globs of fluid ... some identifiable chunk or billow ... and you'll see they're carried downstream by the flow, away from the exit of the pipe.
"Measuring the speed of these things is pretty easy. Basically if you see one of these structures at some location in one image, and you see that it's moved in the next image ... then all I need to know is what is the time between these two images. And that's encoded in the movie, which plays back at a certain speed so many frames per second."
You put your ruler on the spot where the glob was in the first frame and then on the spot it moved to in the second frame, measure the difference between them and voila! You have the speed at which this glob of oil and gas moved. Except that it's in pixels per second, not in any real-world dimension.
For a real-world measurement, you'd need to be able to compare the globs and their movement to a stationary object that's also in the video, whose size you know for sure. That would be the broken riser pipe from which all the globs are spilling. That pipe is, for now, not going anywhere.
The outer diameter of the riser pipe is 21.5 inches. Wereley figured out how many pixels that was in the video, and from that was able to calculate the size of the turbulent structures and how fast they were moving in inches per second. He then used that figure to calculate how much was coming out, and how fast, producing a figure measured in barrels per day.
That figure, which Wereley arrived at using computer codes that make thousands of measurements, was 70,000.
But fluid mechanics can be a tricky business, especially with an opaque liquid like oil.
While Wereley and other experts could reasonably estimate the speed and amount of oil coming from the outside of the jet of oil spurting from the pipe, they didn't know for certain how fast the oil coming from the inside of the jet was going — because they couldn't see it. It was obscured by the dark oil at the outside.
Imagine it this way: you can see all of the water coming from a faucet, no matter what the diameter of the faucet is, because water is clear. But what if chocolate syrup suddenly started pouring out of the faucet? You'd be able to see the syrup on the outside of the stream coming from the tap, but you'd only be able to guess at what was on the inside, because chocolate syrup is opaque, like oil.
If you knew a bit about fluid mechanics, you'd probably assume that the center of the flow — the part you can't see -- is moving a bit faster than the chocolate syrup at the edges.
The middle moves faster
Why? Because the stuff in the middle is largely unaffected by things at the edges that work to slow liquid down. In the chocolate syrup example, the inside of the faucet and possibly the air in the room could act as a drag on the outside of the chocolate stream.
Similar forces apply to the oil coming out of the broken wellhead. The sea water around it acts as a brake on the oil on the outside of the stream, without having as much of an effect on the oil that's on the inside, Wereley said.
Mindful of BP's criticism of his initial estimate, Wereley wanted to be conservative when he was working on his updated calculation. So he based it on the assumption that the flow inside the jet of oil was moving at about the same speed as the flow at the outside of the jet, all but guaranteeing that the estimate would be on the low side.
Until mid-May, Wereley and other experts — including Timothy Crone of Columbia University's Lamont-Doherty Earth Observatory and Eugene Chiang at the University of California-Berkeley — were working on their own on this question.
Then Congress got involved, and things changed.
On May 19, Representative Ed Markey, the Massachusetts Democrat who chairs the House global warming subcommittee, asked BP to show the public live high-resolution video from the broken wellhead. (This video feed is available here.)
Wereley testified that day, along with Frank Muller-Karger, a University of South Florida professor of biological oceanography. Wereley couldn't fathom any realistic way BP's estimate of the flow rate at that time — 5,000 barrels per day — could be right.
Lamar McKay, BP America's president, said at the hearing that officials still couldn't say which estimates were correct. The higher estimates were "theoretically possible," he said, "but I don't think anyone who's been working on this thinks it's that high."
A hypothetical worst case
Soon after Wereley's testimony, he was chosen as a member of the government's Flow Rate Technical Group, a collection of academics whose job it is to determine the magic flow rate number.
"The government doesn't want to trust a couple of scientists working in their spare time, so they set up the Flow Rate Technical Group to come up with an official government-sanctioned number," he said.
The team studied the new high-resolution spill-cam video, and estimated the flow at 20,000 to 40,000 barrels a day, before the June 3 operation to cut the riser and cap it so oil could be collected and sent up to the surface. After that June 3 procedure, the flow was estimated at 35,000 to 60,000 bpd.
After that, Wereley considered the technical group's job largely complete, but that was before an underwater robot bumped into a containment cap on the wellhead on June 23, prompting BP to take it off to assess any damage. The result: a new surge of oil until the cap was reinstalled 10 hours later. Even an untrained eye could see the difference between the flow with the cap on and the increased flow with the cap removed.
Which brings up BP's worst-case-scenario estimate of 100,000 barrels per day, provided to Congress in early May and publicized the following month by Markey.
While 100,000 barrels per day is a high number, the company document that mentions it calls this a low probability scenario of what could happen if the blowout preventer — which didn't prevent a blowout but which is still keeping some percentage of the oil and gas from leaking — and the wellhead were removed.
Wereley did not hazard a guess about how likely this is, calling it hypothetical.
"But what it also tells you is, if you're throwing around numbers like 100,000 barrels per day, you know pretty well that it's not 1,000 barrels per day. It stands to reason that if you put the blowout preventer on there, it's not going to stop 99 percent of the flow. They should have expected a much larger flow than 1,000 barrels per day."