Apparently written in 2008, the Wiki article says that the line ceased operation in 1990 and "Today, the entire line is unfit for oil transport."
But things may have moved on since then. There is another line to note, the Kirkuk-Banias Pipeline:
This too has been out of service for some time, but in 2010 Iraq and Syria "agreed to build two new Kirkuk–Baniyas pipelines" for heavy and light oil." It has been said that President Assad saw this as part of a "Four Seas" strategy to become a key link between the East and the Mediterranean.
Martin Armstrong says that Assad has been blocking the Nabucco gas pipeline, the West's counter to Gazprom's tendrils in Europe:
But there's also the question of not putting all your eggs in one basket. The proposed Nabucco pipeline route in the above 2009 Economist Magazine map runs from Kurdish areas via a semicircle though Erzerum and on to Ankara and Europe, giving Turkey control of additional vital energy supplies.
It's possible that the West has seen Syria not so much a threat, or obstacle, as an opportunity to diversify supply lines.
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