HOUSTON — With billions of dollars in penalties at stake, the civil trial of the British oil company BP begins its second phase on Monday, which will set the amount of oil that spilled into the Gulf of Mexico from the 2010 Deepwater Horizon rig explosion that killed 11 workers and soiled hundreds of miles of beaches.

The government will argue that a total 4.2 million barrels of oil was discharged into the sea over 87 days, the equivalent of nearly one-quarter of all the oil that is consumed in the United States in a day. BP will counter that the number was closer to 2.45 million barrels. This phase of the trial will also determine if BP prepared adequately for a blowout and if it responded properly once the oil started flowing.

Both sides will present their case in Federal District Court in New Orleans using competing technical calculations over the next four weeks. Hanging in the balance are Clean Water Act fines that range from a maximum of $1,100 for every barrel spilled through simple negligence to as much as $4,300 a barrel if a company is found to have been grossly negligent.

“This will be largely a battle of experts,” Blaine G. LeCesne, a law professor at Loyola University New Orleans.