The first chapter in a saga of litigation and claims for damages following the BP 2010 Gulf oil spill is just days away from being finished.

In a hearing Wednesday, U.S. District Judge Carl Barbier in New Orleans said he is likely to preliminarily approve BP's estimated $7.8 billion settlement with hundreds of thousands of third party claimants, despite requests from some parties for a delay in the settlement's approval.

The settlement provides $2.3 billion for the Gulf seafood industry, $105 million to cover medical costs and $57 million to fund a tourism advertising campaign for the Gulf region, reported the Wall Street Journal.

BP and the plaintiffs steering committee reached a final agreement on April 18, after the settlement was negotiated the month before.

There is no cap to the settlement amount, but BP estimated this first round will cost the company $7.8 billion.

Final approval could come by year's end, and would include $600 million in legal fees, the WSJ reported.

The American Shrimp Processors Association on Tuesday objected to the $2.3 billion payment for losses sustained by shrimpers and other seafood harvesters, saying the money excludes processors, distributors and packagers who were also affected by the spill.

Halliburton Co., an oil field service company that helped build the ill-fated Macondo well and is also being sued by BP, said it did not have enough time to review the settlement package and thus objects to its approval. The company is joined by the state of Florida, which contends the settlement focuses too much on the state's Panhandle rather than other parts that also face the Gulf, the WSJ said.

If Barbier approves the settlement, the next step will be to determine how liable BP is for its role in the oil spill. Under the Clean Water Act, the company could face $1,100 in fines for negligence and as much as $4,300 in fines for every barrel of oil spilled in the Gulf if found grossly negligent.

This week, the Department of Justice levied the first charges and made the first arrest in its investigation into the Gulf incident, accusing a former BP engineer of obstructing justice.

On April 20, 2010, an explosion on the Deepwater Horizon oil production platform killed 11 workers and caused the platform to sink, setting off the worst environmental disaster in U.S. history.

Roughly 5 million barrels of oil spilled into the Gulf.