* U.S. crude inventories fall for third week
* Refined product stocks remain high in United States, Asia
* Many traders see $50-60 a barrel oil price as fair value
* Brent forward curve below $60 until 2021 (Updates prices)
By Ahmad Ghaddar
LONDON, June 9 (Reuters) - Oil prices fell on Thursday as traders took profits after three sessions of gains and after reaching 2016 highs thanks to a fall in U.S. crude inventories and supply disruptions.
Brent crude oil futures LCOc1 were down 90 cents a barrel at $51.61 a barrel at 1316 GMT, after setting a 2016 high of $52.86.
U.S. crude CLc1 was down by 91 cents at $50.32 after hitting a 2016 high at $51.67.
A rebounding U.S. dollar also weighed on prices.
"If you look at the week behind us ... there was support for commodities from the currency side, the equity side, and the emerging markets side," said Bjarne Schieldrop, chief commodity analyst at SEB.
"We see some reverse of that now," he added.
A fall in the dollar against a basket of currencies .DXY to a five-week low on Wednesday boosted oil prices, but the index recovered on Thursday, standing up 0.47 percent at 1315 GMT.
A weaker dollar makes oil cheaper for holders of other currencies.
Oil prices also gained ground after data on Wednesday from the U.S. Energy Information Administration (EIA) showed U.S. crude stocks last week fell by 3.23 million barrels, while inventories of gasoline and middle distillates rose. EIA/S
Supply outages in Nigeria and Canada have also supported oil prices.
Consultancy Energy Aspects estimates fire-hit Canadian output losses will total 29 million barrels across May and June "after adjusting for turnaround work that was underway before the wildfires broke out, and assuming a pre-wildfire utilisation rate of 85 percent of (the 2015 average)".
Nigeria's Niger Delta Avengers militant group on Wednesday rejected an offer of talks with the government to end its attacks on oil facilities and said it had blown up a Chevron (NYSE:CVX) CVX.N pipeline site. some analysts said there are signs that downward pressure on prices is mounting.
ANZ bank said price rises were "tempered by an increase in (U.S.) crude production of 10,000 barrels per day to 8.75 million barrels per day and the number of active rigs increasing by 9 to 325".
Traders also said refined product stocks were building up in the United States and Asia. traders and analysts say a price of $50-60 per barrel may be fair value. This is reflected in Brent's forward curve, which stays within that range until early 2021. CHART-Brent crude oil forward curve
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