BP's lawyers will fight attempts to fine the oil giant up to $18 billion (£11.1bn) over the 2010 Deepwater Horizon disaster, when a new trial opens in New Orleans on Monday.

The latest legal battle revolves around the company's efforts to cap its runaway well, and the amount of oil that entered the Gulf of Mexico during the 87-day spill.

The trial, expected to last a month, could add up to $18 billion in financial penalties to BP's bill for the disaster – five times the $3.5 billion originally set aside for fines. That is on top of the $42.4 billion the company has spent to date on cleanup, claims, and fines.

BP is also fighting a second battle to limit payouts to thousands of individuals and businesses in the Gulf who lost livelihoods because of the spill.

The company has already outspent the $7.8 billion it set aside for the uncapped settlement, and recently took out newspaper ads saying the system was being abused.

Monday's outcome hinges on what the court decides about whether BP did everything it could to cap the well. The court will then turn to the dispute over how much oil escaped into the Gulf.

The trial is the second of three phases being heard by US district judge Carl Barbier.

The first phase, which wound up in April, was to apportion blame for the events leading up to the fatal blowout of the well among BP and its partners, Transocean Ltd and Halliburton Co.

The blowout killed 11 men and polluted vast swathes of ocean and beach and devastated wildlife and industry in five Gulf states.

On Monday the government, joined now by BP's former partners on the well, will argue that the company deliberately underestimated the size of the spill, and wasted time trying to plug the well with debris, when the flow was too strong.

The argument will be critical to the final tally of BP's legal bills.

Under the Clean Water Act, BP could be fined $1,100 for each barrel of oil that escaped into the Gulf, rising to $4,300 a barrel if the company is found to be guilty of gross negligence.

"I think BP has an uphill battle establishing that their efforts to cap the well were successful because of the sheer length of time involved," said Blaine Lecesne, a law professor at Loyola University in New Orleans, who has been following the trial.

"We all recall those images of those futile efforts: one device after another everything from injecting debris into the well to the top hat to finally what actually worked which was this custom built device to cap the well."

However, BP lawyers can claim the company did its best given the complexity of the event – a blownout well on the ocean floor a mile below the surface, Lecesne said.

BP in pre-trial motions argued that the federal government reviewed and approved of its various plans to cap the well at every juncture, and that other oil companies also agreed with its strategy.

The court will then spend about three weeks hearing from technical experts about how much oil ultimately escaped into the Gulf.

The federal government estimates 4.2 million barrels of oil entered the Gulf in those 87 days. BP says it was 2.45 million, and that the government used untested methods to reach its figure. "United States experts employ unproven methods that require significant assumptions and extrapolations in lieu of … available data and other evidence," company lawyers said in a finding.

The judge is not expected to give his ruling until next year.

Even once those fines are set under the Clean Water Act, BP could still be hit with high bills for environmental restoration to the Gulf. Research published last week in the PloS scientific journal found that it could take months for the deep ocean near the well site to recover.

"There is a lot at stake," said David Yarnold, president of the Audubon Society conservation group. "There is enough at stake here to really begin rebuilding America's wetlands. There is enough at stake here to really offer the kind of reparations that the Gulf coast deserves."

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