Nearly three years after the explosion and sinking of an oil rig in the Gulf of Mexico that killed 11 workers and spilled 5 million barrels of oil, a federal judge in New Orleans is scheduled to hear opening arguments today in a civil trial that will determine how much more BP PLC (NYSE: BP) will have to pay in fines and penalties. The company has coughed up more than $24 billion so far and figures it may end up with another $18 billion or so before the case is closed.

Now $42 billion is not chump change, even for BP. But plaintiffs in the case want much more from the firm. The big issue is whether BP acted with gross negligence. If the judge decides that the company did, BP is liable for up to triple damages.

Claims against both rig owner and operator Transocean Ltd. (NYSE: RIG) and cement contractor Halliburton Co. (NYSE: HAL) are not yet resolved, but are not at issue in the trial that begins today.

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