BP (NYSE:BP) is looking to put the Deepwater Horizon disaster in the rearview mirror, as U.S. District Court Judge Carl Barbier considers an agreement to settle economic and medical damages claims against the company by some 100,000 individual and corporate plaintiffs.

The settlement agreement, conditionally approved in May 2012, is currently undergoing review pursuant to a fairness hearing that Judge Barbier oversaw on Thursday. If the agreement passes muster, BP would pay $7.8 billion to the "class" of plaintiffs, to be divided up among them.

However, even if the settlement is approved, it would not put an end to BP's legal liability for the 2010 incident. Claims by the U.S. government and several states remain to be addressed. Additionally, some 13,000 members of the plaintiffs class have objected to the terms of the settlement, and may opt out from its terms. Finally, while the settlement estimates damages at $7.8 billion, it does not cap damages claims, which could rise over time.

In the event the judge does not approve the settlement, trial of the claims against BP is scheduled to commence Feb 25.

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