When the ship tried to head back north, protesters tried to block the vessel with kayaks and then suspended themselves from a bridge over the Willamette River, obstructing safe passage. A court then threatened Greenpeace with fines of $2,500 an hour if the protesters did not clear the way.

The Obama administration has set strict limits on how Shell can operate. It prohibited the company from simultaneously drilling two wells, as planned. The United States Fish and Wildlife Service ruled that marine wildlife protections required a 15-mile buffer zone between simultaneous drillings, while the company had planned for a nine-mile buffer. Workers on Shell’s ships also have to keep watch and avoid crossing the migratory paths of whales and other marine mammals.

“Most of the natives up here in the north are concerned with the marine mammals,” said James Pakotak, a resident of Barrow, Alaska, where the airport serves as a hub for many of Shell’s workers. The storms that battered Shell’s flotilla also hammered the town. “What if there’s an oil spill? What then?” Mr. Pakotak said.

To be sure, there are those who still believe in the Arctic’s potential. They cite efforts to drill there in the 1970s and 1980s, as well as a study by the United States Geological Survey in 2008 that estimated that 13 percent of the world’s untapped oil and 30 percent of its natural gas lay in the Arctic.

The National Petroleum Council, in a report commissioned by the Department of Energy and released this year, said the technology and expertise already existed to extract oil and natural gas safely in icy conditions, replacing declining supplies on Alaska’s North Slope.

Ben van Beurden, Shell’s chief executive, said in a conference call last month that the company’s stake could ultimately be “multiple times” more bountiful than in the vast Gulf of Mexico.

“Alaska is a long-term play,” he said. “That is the way you have to look at it. We can’t be driven by today’s, tomorrow’s, or next year’s, or last year’s oil price.”