Fluid Dynamics Tackles the Oil Spill
In a perverse way, fluid dynamics has taken center stage as oil continues to spill into the Gulf of Mexico. Physicists and engineers from across the country who specialize in fluid flows have weighed in on how much oil has been flowing out of the damaged pipe a mile beneath the ocean’s surface.
Admiral Thad Allen, the National Incident Commander for the Gulf oil spill, formed the Flow Rate Technical Group (FRTG) on May 20th to determine exactly how much oil is spewing into the Gulf. The team brings together scientists and experts from multiple government agencies and universities to analyze video of the gushing pipe, and the surface slick.
The full official estimate now states that for the first month and a half of the spill roughly 26,500 barrels a day flowed into the Gulf of Mexico with a standard deviation of about 6,250 barrels. This estimate only covers the time up to June 3rd before the top of the leaking pipe was cut, affecting the flow. Group members are continuing to work to estimate how much oil is leaking after the riser pipe was cut. After cutting the pipe, BP placed a capture device on top and is capable of diverting about 15,000 barrels per day of leaked oil. As APS News goes to press, the situation is fluid and continues to evolve.
Steven Wereley, an associate professor of mechanical engineering at Purdue University and a member of the team, used a common technique to estimate the flow of oil coming out of the broken pipe. Particle image velocimetry (PIV) records how fast a jet of fluid is shooting into a liquid. Once the liquid’s speed is determined, it’s a simple algorithm to calculate the pressure and flow rate of a jet of fluid.
“It’s basically just feature tracking,” Wereley said, “There are thousands of people in the US that do this technique, you can call almost any university and they’ll have someone who could estimate the leak.”
Wereley appeared before the Subcommittee on Energy and Environment of the House Energy and Commerce Committee, saying that using PIV on the short videos of the gushing pipe, he first pegged the flow at somewhere between 70,000 to 100,000 barrels per day. After more video and information about the oil to gas ratio became available, he revised his estimate down to a base of 12,000 to 25,000 barrels per day.
The FRTG used PIV together with two other methods to come to their final numbers. NOAA had airplanes fly over the spill with an Airborne Visible/InfraRed Imaging Spectrometer (AVIRIS) which can measure the area and the depth of the oil spill. Researchers combined the volume of oil on the surface with estimates of how much has evaporated, been burned off, or dispersed to get a total amount of oil that leaked.
For their initial estimate, researchers were able to check their numbers against readings from the Riser Insertion Tube Tool. Stuck into the end of the leaking pipe on May 16th, the RITT pumped about 3,000 barrels of oil a day to a tanker on the surface before it was replaced with the current capture device. Researchers took the pressure and flow readings from the RITT and extrapolated how much oil was leaking out the end of the pipe and other holes.
Scientists outside of the technical group have also used PIV and other common fluid physics techniques to estimate the flow of oil. Many of these estimates have been picked up in the media.
“This was a homework problem that was too good to resist,” said Eugene Chiang of the University of California, Berkeley who teaches a course on estimating orders of magnitude. His first estimate used PIV and was carried on PBS NewsHour. It pegged the flow at somewhere between 25,000 and 100,000 barrels of oil a day, “It’s a really simple calculation, almost embarrassingly so.”
Pirouz Kavehpour at UCLA came up with a more conservative figure using a slightly different technique. He looked at the shape that the gushing oil made as it flowed into the seawater to estimate its critical Reynolds number, which he then fed into an equation that gave a total volumetric flow rate.
Using this calculation, Kavehpour estimates that at bare minimum at least 5,000 barrels per day is pouring into the Gulf. This base line is closer to BP and NOAA’s initial figures; however he didn’t put any upper limit on the amount, saying that there wasn’t enough available data to say what the upper limit might be. He said also that he was concerned about the accuracy of some of the other estimates seen in the media.
“None of these estimates are peer reviewed,” Kavehpour said, “Which is really bad I think.”
The wide range of estimates also highlights how far away from an ideal lab setting the situation actually is. Accurate flow rates have been devilishly hard to calculate because of limited available information. Typically in a lab, PIV uses reflective particles that are easily tracked by high speed, high definition cameras.
Nearly a mile under water, uncertainties abound. There are no reflective particles or high definition cameras to track the flow. Researchers using PIV have had to rely on tracking eddies suspended in the water using the grainy video available.
Mirko Gamba, a post-doc at Stanford University, used a method similar to Chiang’s and came up with a range of 30,000 to 90,000 barrels per day.
“If we had good quality images and knew what we are looking at and had a sense of scale, seeing it from all sides, we could do a much better job to pinpoint this number,” Gamba said.
The biggest uncertainty is that the ratio of oil to methane gas gushing out of the broken pipe is constantly changing. Even within the original 30-second video, it is clear that the proportion of methane gas to oil can change dramatically over just a few seconds. Without a consistent flow, or a way to easily find its average, large error bars surround nearly all estimates.
Other factors, such as the poor quality of the released video, difficulty gauging sizes and proportions, limited viewing angles, and the opaqueness of the oil itself have likewise limited the precision of estimates.
“It’s really only meant to give an order of magnitude,” Chiang said of his estimate, “I can’t even claim to know the first significant figure, but I can claim to know the exponent.” He revised his estimate lower later after it was learned that the inner pipe which carried the oil was half the diameter of the outer protective pipe seen in the video.
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