BP will face a maximum fine of $13.7 billion under the US Clean Water Act for its 2010 spill of 3.19 million barrels of oil into the Gulf of Mexico - the worst in US history.

The fine is about $4 billion less than the UK-based company could have faced, as a judge found on Jan. 15 that the size of the spill was smaller than the US government originally calculated.

Penalties will be assigned after the third and final phase of the company's non-jury trial, which starts on Jan. 20 in New Orleans, Louisiana. BP lawyers are expected to argue for a small fine.

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

Even after the Clean Water Act fines are set, BP may face other bills from a lengthy Natural Resources Damage. This could require it to carry out or fund environmental restoration work in the Gulf.

BP has provided $3.5 billion for the Clean Water Act penalty in its accounts. The company has already pleaded guilty to misrepresenting the flow rate to the US Congress, as part of its $4 billion settlement of criminal charges with the Department of Justice in 2013.