Brent crude futures LCOc1 were trading up 25 cents or 0.5 percent at $51.05 per barrel at 0136 GMT.
US West Texas Intermediate (WTI) crude futures CLc1 were at $47.73 a barrel, up 18 cents, or 0.4 percent.
US crude inventories fell by 9.2 million barrels in the week to Aug. 11 to 469.2 million, industry group the American Petroleum Institute said on Tuesday.
That compared with analyst expectations for a decrease of 3.1 million barrels.
"The market took this as a mildly bullish report," said William O'Loughlin, investment analyst at Rivkin Securities.
However, gasoline stocks climbed by 301,000 barrels, compared with analyst expectations in a Reuters poll for a 1.1 million barrel decline.
Official Energy Information Administration (EIA) data will be published late on Wednesday.
More broadly, analysts said ample supplies were preventing prices from moving much higher.
"It is the ongoing fundamental issue of excessive supply that is continuing to weigh on oil prices ... Not a lot has changed despite the OPEC and Russia efforts recently. While these producers have tried to limit their oil output, US shale oil continues to rise," said Fawad Razaqzada, market analyst at futures brokerage Forex.com.
The Organisation of the Petroleum Exporting Countries together with non-OPEC producers like Russia has pledged to restrict output by 1.8 million barrels per day (bpd) between January this year and March 2018.
Offsetting much of that effort, however, US oil production has soared by almost 12 percent since mid-2016 to 9.42 million bpd. C-OUT-T-EIA
"OPEC and Russia still face an uphill battle in reducing the global supply surplus in the face of growth in output elsewhere (US shale oil, Libya, Nigeria) and less than compliant behaviour in their midst (Iraq, UAE)," French bank BNP Paribas said in a note.
"US crude oil inventories have been steadily declining this summer but it is not evident that inventories are declining in quite the same proportion in the rest of the world," it said.
On the demand side, analysts also see a gradual slowdown in consumption growth as gasoline demand peaks in the United States due to improving fuel efficiency and the rise of electric vehicles, while China's voracious oil thirst also starts to taper off.