(Reuters) — BP P.L.C. will try to whittle away at $13.7 billion in potential fines under the Clean Water Act as the penalty phase in its trial over the 2010 Gulf of Mexico oil spill starts Tuesday.

Several billion dollars in potential fines were avoided Thursday when U.S. District Court Judge Carl Barbier put the size of the spill at 3.19 million barrels. That was well below the government's estimate of 4.09 million barrels, which could have led to $17.6 billion in fines for the worst offshore disaster in U.S. history.

The Clean Water Act penalties would come on top of more than $42 billion the oil major has set aside for cleanup, compensation and fines. About 810,000 barrels were collected during cleanup.

Clean Water Act rules say when assigning penalties the court must take into account BP's ability to pay, history of past violations, and steps it took to clean up the spill.

The U.S. government named as the defendant in the case BP's exploration and production unit, known as BPXP, which could conceivably limit the size of the fine.

"We believe that ... BPXP should be subject to a Clean Water Act penalty at the lower end of the statutory range," Andrew Langan, a lawyer for BP, said in a statement.

Environmental groups say it could take decades for the Gulf ecosystem to recover. They disagree with BP's assertions that the Gulf has recovered better than expected.

"The court has the opportunity and responsibility ... to hold BP fully accountable for the damage done to the Gulf and to assign the maximum penalty," the National Wildlife Federation said in a joint statement with other groups.

The first two phases of the trial, over the degree of negligence and the spill's size, have concluded.

Under a "gross negligence" ruling Judge Barbier issued in September, BP could be fined a statutory limit of $4,300 for each barrel spilled, though he has authority to set lower penalties.

BP has also filed motions saying the maximum fine per barrel is in fact just $3,000 because Congress never passed laws to adjust it for inflation.

A simple "negligence" ruling, which BP sought, caps the maximum fine at $1,100 per barrel.

After the Clean Water Act fines are set, BP may face other bills from a Natural Resources Damage Assessment — which could require BP to fund environmental restoration work — and other claims.