Gulf Oil Spill Velocimetry-Based Flow Rate Estimate

1. A method of measuring motion within a fluid body comprising the steps of: (a) injecting a plurality of solid particles into the fluid body in dispersed relation to move therewith; (b) applying a short pulse of light through an objective lens to the fluid body so as to broadly illuminate the fluid body, and then repeating the application of the light pulse after a known time delay; (c) after each pulse of the applied light, observing through the same objective lens the light scattered from the individual solid particles; (d) wherein only light from the solid particles lying within the depth of field of the objective lens will produce well-focused discrete images of discrete particles, thereby determining a two-dimensional measurement plane in the flowing fluid; and (e) comparing discrete images of discrete particles successively observed in the measurement plane as a function of time to determine the motion of the fluid body.

Particle Image Velocimetry (PIV) measures whole velocity fields by taking two images shortly after each other and calculating the distance individual particles travelled within this time. From the known time difference and the measured displacement the velocity is calculated. Since the flow can be quite fast one has to avoid blurred images and that‘s one reason to use laser pulses. They are only 6-10 ns long and freeze any motion. The other reason is that only laser light can be focused into a thin enough light sheet so that only particles in that plane are imaged. Otherwise the scattered light from particles in other planes would make this measurement impossible. A special camera is utilized so that it can store the first image (frame) fast enough to be ready for the second exposure. The "dead" time between the frames when the camera is "blind" is very short down to 100 ns.

Here is the Wereley's 1998 patent on the subject:
Here is Wereley's 2006 patent on the subject:

(b) applying a short pulse of light through an objective lens to the fluid body so as to broadly illuminate the fluid body, and then repeating the application of the light pulse after a known time delay;

BP has said repeatedly that there is no reliable way to measure the oil spill in the Gulf of Mexico by looking at the oil gushing out of the pipe. But scientists say there are actually many proven techniques for doing just that.

Steven Wereley, an associate professor of mechanical engineering at Purdue University, analyzed videotape of the seafloor gusher using a technique called particle image velocimetry.

A computer program simply tracks particles and calculates how fast they are moving. Wereley put the BP video of the gusher into his computer. He made a few simple calculations and came up with an astonishing value for the rate of the oil spill: 70,000 barrels a day -- much higher than the official estimate of 5,000 barrels a day.

The method is accurate to a degree of plus or minus 20 percent.


Given that uncertainty, the amount of material spewing from the pipe could range from 56,000 barrels to 84,000 barrels a day. It is important to note that it's not all oil. The short video BP released starts out with a shot of methane, but at the end it seems to be mostly oil.


"There's potentially some fluctuation back and forth between methane and oil," Wereley said.

But assuming that the lion's share of the material coming out of the pipe is oil, Wereley's calculations show that the official estimates are too low.

"We're talking more than a factor-of-10 difference between what I calculate and the number that's being thrown around," he said.

At least two other calculations support him.

Timothy Crone, an associate research scientist at the Lamont-Doherty Earth Observatory, used another well-accepted method to calculate fluid flows. Crone arrived at a similar figure, but he said he'd like better video from BP before drawing a firm conclusion.

Eugene Chiang, a professor of astrophysics at the University of California, Berkeley, also got a similar answer, using just pencil and paper.

Without even having a sense of scale from the BP video, he correctly deduced that the diameter of the pipe was about 20 inches. And though his calculation is less precise than Wereley's, it is in the same ballpark.


"I would peg it at around 20,000 to 100,000 barrels per day," he said.

Chiang called the current estimate of 5,000 barrels a day "almost certainly incorrect."

Given this flow rate, it seems this is a spill of unprecedented proportions in U.S. waters.

"It would just take a few days, at most a week, for it to exceed the Exxon Valdez's record," Chiang said.

BP disputed these figures.

"We've said all along that there's no way to estimate the flow coming out of the pipe accurately," said Bill Salvin, a BP spokesman.

Instead, BP prefers to rely on measurements of oil on the sea surface made by the Coast Guard and the National Oceanic and Atmospheric Administration. Those are also contentious. Salvin also says these analyses should not assume that the oil is spewing from the 21-inch pipe, called a riser, shown in the video.

"The drill pipe, from which the oil is rising, is actually a 9-inch pipe that rests within the riser," Slavin said.


But Wereley says that fact doesn't skew his calculation. And though scientists say they hope BP will eventually release more video and information so they can refine their estimates, what they have now is good enough.


"It's possible to get a pretty decent number by looking at the video," Wereley said.

Displacement can typically be accurate down to 10% of one pixel on the image plane.

According to news media sources the vast majority of the oil is either slowly settling to the bottom, billowing around at various depths, or slowly surfacing. Nobody seems to know.
I've been thinking that the potential impact of the leak would depend on the answer.
I've been wondering how much the density of the crude is affected by the pressures at that depth. These long chain hydrocarbons are subject to compressibility so density should increase. But, enough to keep the stuff down there?

Hi gwangi,

Interesting question. Petroleum is of course, a mixture of various hydrocarbons, and I have no idea what hydrocarbons are being released but I suspect it is fair to say they are relatively heavy with carbon chains in the neighborhood of 15 to 25 carbons. Let's assume the carbon chains follow the general rule C_nH_2n+2 and look at a couple of different hydrocarbons at 2500 psia and 40 F. There are reports of tar balls washing ashore, so I'll include an even heavier hydrocarbon. Here's what the density looks like:
C16H34: 34 lb/ft3
C24H50: 50 lb/ft3
C30H62: 52 lb/ft3

From this, it looks like these hydrocarbons are less dense than seawater, so they should come to the surface. Why is there a layer of these hydrocarbons reported deep under the surface? I don't know...

Hi gwangi,

Interesting question. Petroleum is of course, a mixture of various hydrocarbons, and I have no idea what hydrocarbons are being released but I suspect it is fair to say they are relatively heavy with carbon chains in the neighborhood of 15 to 25 carbons. Let's assume the carbon chains follow the general rule C_nH_2n+2 ...

Perhaps you could see he would be willing to address these concerns here? You never know, and his info is available at the Purdue U site https://engineering.purdue.edu/Engr/...ource_id=11641 . Divining what his methodology is from, a 12 and 4 year old patent respectively seems to be more amusing than scientific.

On the technical side, mheslep is simply wrong, in that the method requires this laser pulse. It is PREFERABLE, and necessary to achieve the desired sub-pixel accuracy.

Clearly this was not achieved in the absence of markers added, or a controlled pulse or binocular setup. That reduces accuracy, but does not necessarily invalidate the estimate as offered, nor the conclusion that surface estimates are grossly misleading by comparison.

From my post in the politics forum, here are the differences I see between the measurement methods he's patented and what is available to him with the gulf spill:

1. Low-speed photography, using a standard camera.
2. Poor light source (no laser or strobe light).
3. Opaque fluid.
4. No pre-selected, suspended particles.
5. No specialized depth-of-field focusing.
6. Uncertain opening size (even if he got the size right, breaking-off a pipe can change the geometry of the outlet).
7. Unstable flow.
8. Uncertain and inconsistent mixture of liquid and gas.
9. Uncertain camera angle.

Your reasons certainly explain why a method that usually has significant sub-pixel resolution yielded a result with more leeway than accuracy, but it does not invalidate the method.

The presentation by the media has been flawed....

What method? I've found no reference anywhere to a method existing to do what is being suggested Wereley did. Do you have one? What method? Flawed how? Can you explain exactly what he's doing and if there is any precedent for the method?