* US oil up around 12 pct in Q3, Brent up 20 pct
* But worries that demand may falter in Q4
* Higher prices could spark more U.S. shale production (Adds comment, graphic; updates prices)
TOKYO, Oct 3 (Reuters) - Oil prices fell on Tuesday, declining for a second day and sapping more strength from a third-quarter rally, amid signs that a global glut in crude may not be clearing as quickly as some had hoped.
U.S. crude was down 14 cents, or 0.3 percent, at $50.44 a barrel by 0149 GMT, after closing the previous session down $1.09, or 2.1 percent.
The U.S. benchmark posted a third quarter gain of around 12 percent, its strongest quarterly climb since the second quarter of 2016, but has now dropped nearly 5 percent from a six-month high reached on Thursday.
Brent crude, the global benchmark, was down 19 cents, or 0.3 percent, at $55.93 a barrel. The contract fell 67 cents, or 1.2 percent, in the last session.
Brent had notched up a third-quarter gain of about 20 percent, the biggest increase for that quarter since 2004 and traded as high as $59.49 last week. It is down about 6 percent from that level.
"The fourth quarter is not too kind to the price of oil, as we switch from summer demand to expectations of winter demand," said Jonathan Barratt, chief investment officer at Ayers Alliance in Sydney. "A lot of (refinery) maintenance occurs at this time so feeder demand is not there."
Iraq said on Monday that exports rose slightly in September from its southern oilfields, while an earlier Reuters survey indicated that the Organization of the Petroleum Exporting Countries (OPEC) overall boosted output.
Oil prices climbed last week on tension in Iraqi Kurdistan after the region's independence vote, with Turkey threatening to close a pipeline that brings oil from the region in northern Iraq to the Mediterranean.
Turkey has not carried out the threat, analysts said.
The recent rally had also been driven by signs that a three-year crude glut is easing, helped by a production cut deal among global producers led by OPEC.
However, Middle Eastern oil producers are concerned the price rise will stir U.S. shale producers into more drilling and push prices lower again. Key OPEC producers consider a price above $60 as encouraging too much shale output.
One bullish sign was a letter from Libya's National Oil Company on Monday that declared force majeure on deliveries from Sharara, the country's largest oilfield.
(Reporting by Aaron Sheldrick; Editing by Richard Pullin)