Well lets see...
The al Hassa basin in Saudi Arabia has produced oil since it was discovered there in 1938, at Dhahran.
About 15 years ago a comprehensive exploratory study was done on the Rhub al Khali (empty quarter) of Saudi Arabia, and the proven plus estimated reserves located there were found to be approximately eight times the production thus far in the al Hassa basin, and this without secondary recovery (water or gas injection).
In addition, oil in rather vast quantities has been recently discovered in Mauritania, among other places.
Oil running out?
Not any time soon.