* IMF lifts growth outlook for 2018, 2019 to 3.9 percent
* Strong demand comes as OPEC, Russia withhold oil supplies
* Crumbling refinery profits could dent crude orders
* Coming Up: API data 4:30 p.m. EST (2130 GMT) (Updates throughout, changes quote, adds details, changes byline, dateline, previous LONDON)
NEW YORK, Jan 23 (Reuters) - Oil rose more than 1 percent on Tuesday with benchmark Brent crude above $70 a barrel for the first time in a week on Tuesday, boosted by healthy world economic growth prospects and expectations for continued production curbs by OPEC, Russia and their allies.
Brent crude futures were up $1.06 at $70.09 a barrel as of 11:02 a.m. EST (1602 GMT), not far off the three-year high of $70.37 reached on Jan. 15.
U.S. West Texas Intermediate (WTI) crude futures rose $1 to $64.59 a barrel. WTI reached its highest since December 2014 on Jan. 16 at $64.89.
The International Monetary Fund on Monday revised upward its forecast for world economic growth to 3.9 percent for 2018 and 2019, a 0.2 percentage point increase from its last update in October.
"The IMF's upward revision of its growth forecast is generating tailwind," Commerzbank analysts wrote. "This further improves the already fairly rosy demand prospects on the oil market."
The demand growth comes at a time of supply curbs by the Organization of the Petroleum Exporting Countries, Russia and other producers, which began in January 2017 and are due to run until the end of 2018.
Saudi Energy Minister Khalid al-Falih told CNBC on Tuesday that while he is "still anxious" about the fragility of the oil market, "we think we're on our way."
OPEC's main objective for the cuts is to eliminate a global surplus in oil stocks and rebalance the market. There is some expectation that OPEC will let the agreement expire at the end of 2018, but major producers have not yet suggested that this is in the offing.
In addition, the sharp plunge in Venezuelan production is offsetting increases from the United States, which is on the cusp of breaking its all-time production record of 10.04 million barrels per day.
U.S. Energy Department oil inventory figures will be released Wednesday morning; industry group the American Petroleum Institute will issue data on stocks Tuesday afternoon at 4:30 p.m. EST.
Venezuela's output fell to a meager 2 million bpd in 2017, far short of expectations for 2.5 million bpd, and the International Energy Agency said it could keep declining in 2018.
"Six months ago there was a lot of consternation about how fast (U.S.) production might grow but that's been offset by Venezuelan volatility," said Tony Scott, managing director of analytics at BTU Analytics in Denver.
He added that with Saudi and Iranian production likely to remain steady throughout the year, it was hard to see an increase in supply that would undermine the rally.
French bank BNP Paribas said it expects inventories to rise near the end of the year. The bank raised its 2018 oil price forecasts by $10 a barrel, expecting WTI to average $60 and Brent $65.
(Additional reporting by Henning Gloystein in Singapore; Editing by Marguerita Choy and Edmund Blair)