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BP's (BP -0.67%) former CEO Tony Hayward agrees with OPEC that its strategy of maintaining the oil glut and thereby helping to drive down prices will quickly crush the US shale boom and that oil prices will rally sooner than many people expect.

Hayward, one of 42 speakers at the Financial Times' Global Summit in Lausanne, Switzerland, on April 20-22, said the average global price of a barrel of crude will soon be around $80, up from the current price of about $60, demonstrating that OPEC is "the most successful cartel in history."

The key, Hayward said, was deciding at its meeting in November to maintain overall production levels at 30 million barrels a day in an effort to undersell U.S. shale producers, whose use of hydraulic fracturing, or fracking, is more expensive than conventional drilling and isn't profitable when the price drops to around $60.

"The peak of U.S. shale supply has arrived – earlier than anticipated," said Hayward, who now runs Iraqi Kurdistan-focused Genel Energy. "The supply chain in the U.S. has been decimated ... . It will take several years to take activity back."

He pointed to the steep drop in the number of drilling rigs now in use in the United States. "The supply base is shrinking, [OPEC is] maintaining their market share," Hayward said. "It seems like [the cartel's strategy has] been a big success. ... It's having exactly the consequences they envisaged." As a result, he said he believes that American output soon would slow down or even begin to fall.

These points could have been taken directly from OPEC's Monthly Market Report, released April 16, which forecast U.S. oil output will first rise this year to about 13.65 million barrels per day in the second quarter of 2015, but then flatten briefly and finally begin to drop for the rest of the year. It said this also applies to Canadian production.

"US [shale] oil and Canadian oil sands output are expected to see lower growth following the recent strong declines in rig counts," the report said.

In his speech, Hayward said OPEC's strategy wasn't the only reason for his optimism about oil prices.

He also gave credit to independent oil companies for sharply reducing their capital expenditures and work forces, which he said also "are laying the seeds for the next bull market." He said the industry did the same during 1990s, eventually generating a price rally that lasted from 2003 to 2007.

OPEC isn't Hayward's only ally in expecting oil prices to rise. Paul Horsnell, director of commodities at the British financial services firm Standard Chartered, says what many call a glut is merely a slight edge in supply over demand, and virtually any shift in demand could reverse the price trend.

"There was never a glut," Horsnell told The Wall Street Journal. "The global surplus in the first part of the year was 1 percent. It will be gone by July and the market will be in deficit as we move into September."

And of course, there are those who disagree with Hayward's view, arguing that production will exceed demand for a long time at a rate of between 1 million and 2 million barrels of oil per day, then going into storage when it can't be sold. Because of this, they argue, global output can't fall fast enough to match demand.

One is Michael Coleman, the chief operating officer at the futures and commodities trader RCMA Asset Management in Singapore. He says many larger oil companies still have much of the money they earned when oil was selling at over $110 per barrel, so they can afford to keep producing even during the current price slump.

"From our perspective, we don't think enough damage has been done yet to current production," Coleman said. "Until demand starts to significantly chew into the big inventories that have been built up, I think ... we'll be in the school of [$]40-60 for [West Texas Intermediate crude] for some period of time."