Oil also played an important role in the struggle after the war over the future of
the Ottoman province of Mosul, where a large oil field was eventually discovered
in 1927 at Baba Gargur near Kirkuk in the new, British-mandated Iraq. Oil was
next found in the Persian Gulf, beginning with Bahrain in 1931; there were
subsequent discoveries in Kuwait, Qatar, Saudi Arabia, the Trucial States (Abu
Dhabi and Dubai), and Oman. By 1960 the smaller Gulf states were producing 15
percent of the world’s oil, with another 10 percent or so coming from Iraq and
Iran.3 By 1970 this had risen to 30 percent.
http://www.brandeis.edu/crown/public.../meb/MEB24.pdf
This means in 1936, Middle East still produced very little oil.