iraqi oil pipeline
© Getty ImagesAn Iraqi worker gauges gas emissions from an oil pipe at the Daura oil refiner
Compliance across OPEC is in question amid conflicting interests regarding oil production cuts and an abrupt withdrawal announcement from Qatar.

While the tiny Gulf kingdom's departure is largely symbolic and unlikely to lead to further exits, a top energy analyst believes that if any country were to break ranks next, it would be Iraq.

"I think in terms of all the OPEC countries, to me the one that stands out over the last six to eight months is Iraq," Michael Cohen, head of energy markets research at Barclays bank, told CNBC's "Squawk Box Europe" on Tuesday.

"Iraq has been out of line with its target frequently... so if restrictions to cut were too stringent, Iraq might feel it in its best interest to no longer be a member of the organization," Cohen added.

As the 15-member OPEC's second-largest oil producer and still suffering from swathes of debilitated infrastructure and poverty after years of war and sanctions, Iraq has an incentive to keep its taps turned on. According to the International Energy Agency, more than 90 percent of Iraq's government revenue comes from oil.

In pointing to Iraq, Cohen cited the visits of Saudi oil minister Khalid al-Falih to Baghdad over the last two months, although he admitted he did not know the content of officials' conversations, which were not all made public.

"We're not privy to the nature of those conversations, but clearly there is a lot of concern in terms of keeping Iraq to what it says," Cohen said.

According to media reports, Al-Falih met with his Iraqi counterparts and the country's Prime Minister Adel Abdul-Mahdi to discuss increasing cooperation in the energy and electricity fields. The U.S. has been encouraging Saudi investment in Iraqi reconstruction as a measure to push back against neighboring Iran's heavy clout in the country.

Iraq's oil sector underwent one of the most successful turnarounds of any sector after the U.S. invasion in 2003 that ousted Saddam Hussein. The country was pumping a record 4.76 million barrels per day (bpd) in October, according to its former oil minister. Its increased production, as well as multi-year output highs from Libya, contributed to 2018 peaks in global production this fall.

The Saudis have been working to rally support for oil production cuts amid a global supply glut that saw crude prices fall 25 percent from year-highs reached in early October. But the OPEC/Non-OPEC Joint Ministerial Monitoring Committee (JMMC) held mid-November in Abu Dhabi was unable to commit to a course of action.

"Libyan, Iraqi and Venezuelan output are surprising to the upside and the economic outlook has worsened," Barclays wrote in an oil market report earlier this month. "Saudi pressure to keep Iraqi output in line has only just begun with Minister Al-Falih's recent trip to Baghdad. So, OPEC is not yet able to answer how sustainable these trends are."

The leaders of the world's two largest oil exporters, Saudi Arabia and Russia, last weekend "agreed to extend" a deal to limit production and support oil prices, Russian President Vladimir Putin said. And expectations are high that OPEC and non-OPEC members will coordinate a supply cut when meeting in Vienna, Austria, later this week.

On the back of these expectations and tentative hopes for a thaw in U.S.-China trade relations, oil prices pared some of their more recent losses.

Iraqi officials estimate they need $100 billion in funding to rebuild homes and infrastructure in parts of the country decimated by the three-year campaign against the Islamic State, which ended late last year. And amid pockets of ongoing ISIS resistance and crippling government corruption, the imperative to diversify revenue sources still faces massive challenges. Oil will remain critical to the country's reconstruction funding.

Thamir Ghadhban, Iraq's recently-appointed oil minister, told media in late October that pumping more oil was a top priority for the country of 38 million. The goals are not just short term - Iraq's national Basra Oil Company plans to increase production from 3.2 million bpd to 5 million bpd in the next seven years.