NEW ORLEANS » The amount of oil discharged into the Gulf of Mexico as a result of a 2010 rig explosion was more than BP estimated, but less than the government calculated, a federal judge determined Thursday in a ruling that could cost the London-based oil giant more than $13 billion.

U.S. District Judge Carl Barbier ruled that 3.19 barrels — or just under 134 million gallons — were discharged into the Gulf after the explosion at BP’s Macondo well. BP said it was 2.4 million barrels. The government had said the amount was 4.2 million, a number that could have resulted in nearly $18 billion in maximum penalties under the Clean Water Act.

Those penalties are to be determined in a trial set to open next Tuesday. In pre-trial briefs, the government has argued that the oil giant should pay as much as $4,300 per barrel spilled. The discharge figure Barbier settled on Thursday means maximum penalties could reach about $13.7 billion — but he has not yet decided how much per barrel BP must pay. BP has argued that the penalties should be lower than what the government is asking for, but has not offered a specific figure.

Barbier’s finding — a figure roughly midway between the government’s and BP’s estimates — came more than a year after a trial during which the judge found that BP acted with "gross negligence" in the 2010 explosion of the Deepwater Horizon offshore rig. BP is appealing.

"Both sides presented evidence to support their cumulative flow estimates, and each mounted effective attacks on the other’s calculations," Barbier wrote. "There is no way to know with precision how much oil discharged into the Gulf of Mexico. There was no meter counting off each barrel of oil as it exited the well. The experts used a variety of methods to estimate the cumulative discharge. None of these were perfect."

Lawyers for BP argue that the company already faces costs totaling $42 billion, including a $14 billion response and cleanup effort. They say a low-end penalty would accomplish the Clean Water Act purposes of deterring environmentally dangerous behavior and encouraging effective cleanup responses.

BP spokesman Geoff Morrell reiterated that stance in a statement Thursday evening.

In a 47-page ruling recapping BPs efforts to control the spill and the conflicting evidence of how much was lost, Barbier said about 168 million gallons of oil was released from the well’s reservoir but the figure was reduced to about 134 million gallons after recovery efforts.

The Deepwater Horizon rig exploded April 20, 2010, killing 11 workers and sending oil spewing into the Gulf for 87 days.