* EIA says U.S. crude stocks fall 5.6 million barrels
* Refinery runs up 3 pct as maintenance season ends
* OPEC keeps 30 mln bpd output cap for 2014 first half
* Keystone XL pipeline may relieve Cushing bottleneck
(Updates prices to settlement)
NEW YORK, Dec 4 (Reuters) - U.S. crude oil futures rose more than $1 on Wednesday, a fourth straight day of gains as government data showed an unexpected fall in U.S. stockpiles in the world's largest oil consumer.
The U.S. government's Energy Information Administration (EIA) report showed domestic crude stocks fell 5.6 million barrels in the week ended Nov. 29, snapping 10 straight weeks of builds. A Reuters poll had forecast a build of 300,000 barrels.
"We know it's the end of the year and (oil companies) like to draw down supply, but that's more than what even the most bullish analysts were looking for," said Phil Flynn, an energy analyst at the Price Future Group in Chicago, Illinois.
Brent crude oil futures slipped after the 12-member Organization of the Petroleum Exporting Countries agreed on Wednesday to renew for the first half of 2014 a collective oil production cap of 30 million barrels a day.
Brent crude for January delivery fell by 74 cents to settle at $111.88 after reaching a session low of $111.46. U.S. crude rose $1.16 to settle at $97.20 a barrel, having earlier touched a five-week high of $97.58 and posting its largest 4-day percentage gain since early July.
Brent's premium over U.S. crude, or West Texas Intermediate (WTI) <CL-LCO1=R>, narrowed to $14.68 a barrel, shedding almost $2 from Tuesday's close of $16.58.
It earlier touched a low of $14.47, shaving nearly $5 from the $19.41 gap set on Nov. 27 and notching the largest four-day decline in the spread since Oct. 2012.
Traders said market participants were liquidating Brent-WTI positions, particularly once it narrowed past $16.
The EIA data echoed figures from the American Petroleum Institute (API) on Tuesday that showed a drop of 12.4 million barrels in domestic inventories. The EIA's 5.6 million barrel draw cut around one-sixth of the 36 million barrels that had built up over the previous 10 weeks.
Much of that oil went to crude-hungry refiners, which registered a 3 percent uptick in utilization rates over the week to reach 92.4 percent.
"The refiners are acting like we're going into the Fourth of July (holiday)," said Flynn, a time when demand for refined products is usually strong. "Do they know what holiday it is?"
The gains in U.S. crude followed Tuesday's $2 rise on TransCanada Corp's announcement on Monday that it would begin operating its Keystone XL pipeline on Jan. 3, allowing stockpiles of crude at the Cushing, Oklahoma hub to move to the U.S. Gulf Coast, where a large share of the country's refining capacity is concentrated.
The OPEC agreement came despite two of its members, Iraq and Iran, having set high output targets for the year ahead.
Libya hopes to reopen on Dec. 10 all oil ports blocked by protests over political and financial demands, and resume full production about a week later, Oil Minister Abdelbari al-Arusi said on Wednesday.
Many oil analysts were sceptical.
"I don't know if anyone in their right mind would trade on that (statement)," said Andy Lebow, vice president at Jefferies Bache in New York.
(Additional reporting by Joshua Franklin in London, Jacob Gronholt-Pedersen in Singapore; Editing by Jason Neely, David Goodman, Bob Burgdorfer, Krista Hughes and Andre Grenon)