Sources also said that ADNOC's supply cuts will mostly hit Asia, although refiners there said that the cuts fell within contractual allowances under which ADNOC can alter agreed monthly supply volumes.
Oil prices, which had been gradually slipping back a year ago after strong gains following the announcement of the OPEC deal have surged again today and by shortly after midday in London brent crude futures had risen by $2.28 to hit $56.61 a barrel.
And Saudi Arabia may be prepared to go further, too.
January crude oil contracts were at US$53.63 per barrel as North American stock markets opened-up $2.13 from late Friday. Oil prices could slip back below $40/bbl under that scenario.
Meanwhile, China's November crude output fell 9 per cent on a year earlier to 3.915 million barrels per day, data showed on Tuesday, but recovered from October's 3.78 million bpd, which was the lowest in more than seven years.
European oil companies jumped more than 2 percent on the oil surge and helped the pan-regional STOXX50 index add 0.2 percent, having just had its best week in exactly five years.
In another sign of the reflation trade, breakeven rates - the gap between yields of five-year USA debt and a matching tenor in inflation-protected securities was at two-month highs, indicating markets are expecting inflation to accelerate.
But they added that oil markets were still broadly supported by the deal to crimp output.
But even with its new-found friends, there is still a lot of extra global production sloshing around, and some may try and take advantage of a new gap in the market.
If the agreed cuts are seen to be met in their entirety before production is ramped up elsewhere, most likely by US shale producers, oil prices could reach $61 a barrel next year, according to Goldman Sachs, who have a 2017 price target of $55.
But this had all changed by September this year, when the oil cartel initially chose to make the cut.
In the process, Saudi negotiators wrong-footed many hedge fund managers, who had established large short positions in futures and options last month expecting there would be no deal or only a very weak one.
Khalid Al-Falih, Saudi Arabia's energy minister, said the country will "cut substantially to be below" the target agreed last month with members of OPEC.
"Make no mistake about it - this historic agreement is a game-changer".
"And OPEC accounts for only about 40% of world crude production, so yes, there's a day-one impact, but I think it's at the edges here".
"Admittedly, after a big gap we may see a retracement of some sort in prices now but ultimately the fundamentals still point to higher levels going forward".
A further deal over the weekend brought in producers outside OPEC - including Russian Federation - who agreed to cut output by 558,000 barrels per day.
"Saudi Arabia was the main driver for this deal to come through", Hamoudi said. The value of an investment may fall.
Nigeria, Libya, and Iran have been allowed to continue increasing their output, and while Nigeria and Libya have internal problems that might interfere with immediate production growth plans, Iran is already welcoming Western companies back into its energy industry - something that a lot of analysts believed was unlikely to happen because of mutual mistrust.