Old Math Casts Doubt on Accuracy of Oil Reserve Estimates
Jan Arps is the most influential oilman you’ve never heard of.
In 1945, Arps, then a 33-year-old petroleum engineer for British-American Oil Producing Co., published a formula to predict how much crude a well will produce and when it will run dry. The Arps method has become one of the most widely used measures in the industry. Companies rely on it to predict the profitability of drilling, secure loans and report reserves to regulators. When Representative Ed Royce, a California Republican, said at a March 26 hearing in Washington that the U.S. should start exporting its oil to undermine Russian influence, his forecast of “increasing U.S. energy production” can be traced back to Arps.
The problem is the Arps equation has been twisted to apply to shale technology, which didn’t exist when Arps died in 1976. John Lee, a University of Houston engineering professor and an authority on estimating reserves, said billions of barrels of untapped shale oil in the U.S. are counted by companies relying on limited drilling history and tweaks to Arps’s formula that exaggerate future production. That casts doubt on how close the U.S. will get to energy independence, a goal that’s nearer than at any time since 1985, according to data from the U.S. Energy Information Administration.
“Things could turn out more pessimistic than people project,” said Lee. “The long-term production of some of those oil-rich wells may be overstated.”
Lee’s criticisms have opened a rift in the industry about how to measure the stores of crude trapped within rock formations thousands of feet below the earth’s surface. In a newsletter published this year by Houston-based Ryder Scott Co., which helps drillers calculate reserves, Lee called for an industry conference to address what he said are inconsistent approaches. The Arps method is particularly open to abuse, he said.
U.S. oil production has increased 40 percent since the end of 2011 as drillers target layers of oil-bearing rock such as the Bakken shale in North Dakota, the Eagle Ford in Texas, and the Mississippi Lime in Kansas and Oklahoma, according to the EIA. The U.S. is on track to become the world’s largest oil producer by next year, according to the Paris-based International Energy Agency. A report from London-based consultants Wood Mackenzie said that by 2020 the Bakken’s output alone will be 1.7 million barrels a day, from 1.1 million now.
U.S. crude benchmark West Texas Intermediate fell 41 cents to $99.21 a barrel at 10:10 a.m London time in electronic trading on the New York Mercantile Exchange. It has risen 0.8 percent this year.
Predicting the future is an inherently uncertain business, and Arps’s method works as well as any other, said Scott Wilson, a senior vice president in Ryder Scott’s Denver office.
“No one method does it right every time,” Wilson said. “Arps is just a tool. If you blame Arps because a forecast turns out to be wrong, that’s like blaming the gun for shooting somebody. As far as Arps being old, the wheel was invented a long time ago too but it still comes in handy.”
Rising reserve estimates gives the U.S. a false sense of security, said Tad Patzek, chairman of the Department of Petroleum and Geosystems Engineering at the University of Texas at Austin.
“We have deceived ourselves into thinking that since we have an infinite resource, we don’t need to worry,” Patzek said. “We are stumbling like blind people into a future which is not as pretty as we think.”
The Arps formula is only as good as the assumptions a company puts into it, Patzek said. Estimates can be inflated when Arps is based on limited drilling history for data or on a few high-performing wells to predict performance across a wide swath of acreage. Forecasts can also be skewed higher by assuming slower production declines than Arps observed.
In November 2012, SandRidge Energy Inc. cut its reserve predictions to the equivalent of 422,000 barrels per well from 456,000. Five months later, the estimate was cut again, to 369,000 barrels, company records show. Oklahoma City-based SandRidge has since made an adjustment upward to 380,000 barrels per well.
The early, more optimistic forecasts were based on a small number of high-performing wells, which led the company to overestimate performance for its other acreage, said Duane Grubert, SandRidge’s executive vice president for investor relations and strategy. The company now has more than 1,100 wells and has improved its drilling. It is confident that current estimates are reliable, Grubert said.
“Nobody knew that until we actually ground-truthed the field by drilling it,” Grubert said. “What we came up was, hmm, that initial estimate was a little high.”
SM Energy Co., a Denver-based producer, suffered a similar setback this year when its wells in the Eagle Ford shale in Texas fell short of forecasts. The company on Feb. 18 cut its prediction in one area to the equivalent of 475,000 barrels per well from 602,000. Estimating future production from early data is a challenge for the industry, said Brent Collins, a spokesman for SM Energy.
“This is especially true when you are trying to estimate an average from a limited number of wells,” Collins said.
Both SandRidge and SM Energy use variations of the Arps method, company records show.
Tapping shale formations differs from the drilling in Arps’ day, said Dean Rietz, an executive vice president in charge of reservoir simulation at Ryder Scott. The first commercial shale well was drilled in 2004, 59 years after Arps published his method.
In 1945, oil production meant drilling straight down to hit pockets of oil and gas that had become trapped after migrating upward from deep layers of rock. Today’s drilling targets those deep layers, boring through thousands of feet of the earth’s crust, then turning sideways to chew for a mile or more through layers that are harder and less porous than a granite countertop. The rock is shattered by a high-pressure jet of water, sand, and chemicals to create a network of small cracks to allow the oil and gas to escape. The largest fissures are narrower than the width of a paper clip. The smallest are thousands of times thinner than a human hair.
On a graph, these fractured wells appear to follow a different trajectory of decline than the conventional wells Arps studied, said Lee.
To replace the Arps calculation, researchers are testing new formulas with names worthy of indie bands: Stretched Exponential, which Lee helped develop; the Duong Method, devised by Anh Duong, principal reservoir engineer for ConocoPhillips; and Simple Scaling Theory, which the University of Texas’s Patzek worked on.
Rietz has made a well simulation model to predict production.
“Come back to me in 10 years, and I’ll tell you how reliable it was,” he said.
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