If the Turks & Iranians got together to build a pipeline from Central Asia, they wouldn't bother to cut in the Armenians. They have a common border.
Once a pipeline was operating, it would supply Western countries, one way or another. Oil is fungible. One example of this is the way some Central Asian oil reaches the outside world: Iran imports oil (& I think gas) from Central Asia, & uses it in the north, e.g. Tehran. This substitutes for oil which would otherwise be transported from Iranian oilfields to Tehran. Instead, that oil is exported.
The exchanges above about pipelines remind me how much I wish more people here (not you) would look at maps. I know it's harder for those who don't carry an atlas around in their head
, but since they're on the web already, it only takes a minute to find one.