Isnt southern Iraq where the oil infrastructure is with access to the Gulf ?
Freightening scenario if they seize that or all access to it.
There is oil in the Kurdish controlled areas as well.
All three sectarian areas of the country have oil fields, but Um Qasr, the port for Basra in the south has the the facilities for loading tanker ships.
They have been competing with the Kuwaitis in a race to upgrade their facilities/capacity for export from there.
Basra is also a major city in Iraq (I believe the third biggest). It was the jewel of the Gulf under the British, before the rise of Dubai. Majority Shia, and close enough to the Iranian border to pop artillery.