A federal judge was set to begin hearing three weeks of testimony Monday about how much oil made it into the ocean during the 2010 Gulf of Mexico oil spill.

Experts for BP and the federal government will provide U.S. District Judge Carl Barbier with very different estimates when the second phase of a trial resumes for litigation spawned by the spill.

The amount of oil that spewed into the Gulf is a key factor in determining how much more money BP and its contractors owe for their roles in the deadly disaster.

Justice Department attorneys will try to persuade Barbier that the best set of data on oil flow comes from a pressure gauge on the capping stack used to seal the blown-out well.

"The pressure data, collection rates, and geometry of the capping stack are by far the most accurate and reliable sources of information on flow rate, and were recognized as such by all parties at the time," they wrote in a pretrial filing.

BP, however, says the government's experts ignored other important data. Company lawyers say its experts used a "proven methodology" that doesn't require "simplistic and unverified assumptions about flow conditions."

"In contrast, the United States' experts employ unproven methods that require significant assumptions and extrapolations in lieu of, and even directly inconsistent with, the available data and other evidence," company attorneys wrote.

The Deepwater Horizon drilling rig was working at the site of BP's Macondo well off the Louisiana coast when the well blew out April 20, 2010. The explosion on the rig killed 11 workers and set off a massive fire. The rig sank less than two days later to the bottom, about a mile below the Gulf surface.

The Justice Department's experts estimate 4.2 million barrels, or 176 million gallons, spilled into the Gulf after the blowout. BP has urged Barbier to use an estimate of 2.45 million barrels, or nearly 103 million gallons, in calculating any Clean Water Act fines. Both sides agree that 810,000 barrels, or 34 million gallons, escaped the well but were captured before the crude could pollute the Gulf.

Under the Clean Water Act, a polluter can be forced to pay a maximum of either $1,100 or $4,300 per barrel of spilled oil. The higher maximum applies if the company is found grossly negligent, as the government argues BP should be. But penalties can be assessed at amounts lower than those caps.

Using the government's figures, a maximum penalty if the company is found grossly negligent could total $18 billion. Using the company's figures, that maximum penalty would be around $10.5 billion.

For the trial's first phase, Barbier heard eight weeks of testimony about the causes of the April 2010 well blowout.

Barbier divided the trial's second phase into two parts. For the first segment, he heard four days of testimony last week about BP's efforts to cap the well. He set aside 12 days of testimony for the second segment, which will consist almost exclusively of technical testimony by experts.

Government experts believe the oil was flowing from the well at a higher rate shortly after the blowout than it was when the well was sealed with the capping stack.

"Basic principles of oil production hold that reservoir pressure depletes and flow rates wane over time," Justice Department attorneys wrote.

BP's experts concluded that flow rates increased over time, due in part to the erosion of steel rams on the rig's blowout preventer. Martin Blunt, a BP expert who is a professor of petroleum engineering at Imperial College in London, also took other factors into consideration, including the "compressibility" of the rocks in the reservoir BP was drilling.

"In assessing the data, Dr. Blunt uses a conservative lens," BP attorneys wrote. "Dr. Blunt accounts for fundamental geological facts and principles of physics acknowledged by United States experts but omitted in their flow calculations."