With the planet heating up and the Arctic sea ice turning to slush, energy companies are moving into the newly exposed polar waters to search for oil and gas. The Arctic Ocean is potentially ripe with fossil-fuel deposits, billions of dollars' worth. But drilling in the harsh terrain—with its large ocean swells and drifting icebergs—has proven extremely challenging so far.

Chukchi Sea (Fish and Wildlife Service)

Here's a perfect example of how tricky Arctic drilling can be: On Monday, Royal Dutch Shell announced that it was abandoning its plans to harvest oil from Alaska's Chukchi Sea this year, after the company sustained damage to a containment dome designed to cap any major spills.

"The time required to repair the dome, along with steps we have taken to protect local whaling operations and to ensure the safety of operations from ice floe movement, have led us to revise our plans," Shell said. "In order to lay a strong foundation for operations in 2013, we will forgo drilling into hydrocarbon zones this year.

Shell has spent $4.5 billion and nearly seven years obtaining leases to drill for oil in the Chukchi and Beaufort Seas off the Alaskan coast. The company has fended off dozens of lawsuits from environmental groups and Alaskan tribes who say that drilling could threaten sensitive wildlife habitats. And so, in late August, when the Interior Department at last granted Shell a permit for "limited" drilling in the Chukchi Sea, it looked as if oil production would finally commence.

But there was still the unruly Arctic to deal with. Shell managed to drill for about a day before encroaching sea ice forced the company to move its rig out of harm's way. And the damage to the containment dome during testing has forced the company to abandon its oil hopes this summer—the Interior Department's permit was contingent on Shell having a spill-containment system in place.

This latest setback for Shell comes after a number of snags throughout the year. Even though the Arctic sea ice melted to a record low this summer, the ice happened to be exceptionally thick this spring in several areas where Shell held leases. That forced the company to postpone its drilling plans by three weeks. Then, in July, the Coast Guard delayed Shell's oil-spill barge after questioning the ship's ability to operate in stormy weather. Later that month, Shell's Noble Discoverer drill ship escaped from its mooring off the Aleutian Islands and drifted to within 100 yards of shore. (The rig crew reported no damage.)

In the end, rather than completing five or six wells this year, as originally planned, Shell won't be able to finish any wells at all before the sea ice starts to grow again this fall. The company said that it would instead begin drilling a number of "top holes," the initial phase of drilling, in the Chukchi Sea to get a jump start on the 2013 season. Shell will also begin exploratory drilling in the Beaufort Sea.

There's an enormous amount of oil at stake in the region. Shell's geologists have said that their leases in the Chukchi Sea could one day yield 400,000 barrels of oil per day — about 7 percent of all current U.S. production — though it will take years before the company can bring that oil to market, due to a lack of infrastructure. A recent report from Nomura Holdings estimated that oil in the Chukchi and Beaufort seas could eventually yield $10 billion in value for Shell.

For now, critics are pouncing on Shell's failures. “Shell spent nearly $5 billion to exploit global warming for profit this summer, but the Arctic is proving to be the company’s Waterloo," said Greenpeace's deputy campaigns director, Dan Howells, in a statement. Greenpeace has charged that even safe drilling could disrupt the habitats of Arctic wildlife, including walruses and seals. And, of course, there remains the ever-present risk of an oil spill — which, amid the sea ice and high Arctic winds, could prove tricky to clean up. (The Obama administration, for its part, has largely supported Shell's endeavor, albeit under strict regulation.)

Other energy companies are watching Shell closely. Earlier this month, Norway's Statoil said it would delay plans to explore the Alaskan Arctic for oil and gas until 2015 at the least. "[I]n light of the significant uncertainty regarding Alaska offshore exploration," a Statoil spokesperson told the Anchorage Daily News, "we've decided to take what we believe is a prudent step of observing the outcome of Shell's efforts before finalizing our own exploration decision time frame."