Hey there! I'm happy to help!
The countries in the Middle East that export petroleum are Saudi Arabia, Iran, Iraq, United Arab Emirates, Kuwait, Qatar, Oman, and I think there are a few more but those are the main ones. Lots of Middle Eastern countries export it but these are the main ones. Places like Saudi Arabia and Iran have lots of oil fields available, so they would naturally export lots of petroleum.
Have a wonderful day! :D