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The fire has been extinguished, Black Elk spokeswoman Leslie Hoffman said. She said an emergency response is under way, but declined further comment, saying the company will issue a statement later.
The US Coast Guard said 11 people were airlifted to hospitals while nine others were evacuated to other nearby energy facilities. Search and rescue helicopters were scouring the area, located around 17 miles south of Grand Isle, Louisiana.
No fatalities have been confirmed but two workers are missing. The 11 hurt included four who suffered burns and were in critical condition at Louisiana's West Jefferson Medical Centre, a hospital spokeswoman said.
When it caught fire, 22 workers were aboard the shallow-water platform, which was not actively drilling or producing oil and gas, the Coast Guard said.
An oil sheen is being monitored in waters nearby. The Coast Guard said there appeared to be little risk of a major oil spill because production was shut off before the fire, and Black Elk told authorities that any spill could be as little as 28 gallons.
The latest potentially deadly offshore incident comes a day after oil giant BP Plc reached an agreement to pay record penalties of $4.5 billion for its role in the 2010 Deepwater Horizon disaster, which spewed 4.9 million barrels of oil into the Gulf of Mexico and killed 11 workers.
The Black Elk platform sits in 20m of water and its production apparatus was shut off before the fire. In contrast, the BP disaster happened during a drilling operation in waters 1500m.
Federal data and SEC filings show that Black Elk, a minor producer in the Gulf, has a recent history of close calls, platform incidents and fines, including a $300,000 federal penalty it paid in September.
Today's incident could reignite a national debate over safety standards for offshore drilling. After the Horizon spill, the government overhauled offshore drilling regulations and imposed a ban on drilling that lasted for several months.
"BP and the government may have settled criminal matters yesterday, but today's incident shows that increasing safety of offshore drilling and for hard-working men and women is still not a settled matter," said Massachusetts congressman Ed Markey, the ranking Democrat on the House National Resources Committee, in a statement.
"This incident raises a number of questions about the nature and adequacy of safety measures on this offshore rig," Markey added.
The federal Bureau of Safety and Environmental Enforcement (BSEE) said it was sending safety inspectors to the Black Elk platform.
"They were not actively drilling," said Coast Guard spokesman Glenn Sanchez. "They were cutting a pipe or doing some type of maintenance that may have resulted in the explosion and fire."