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Three other members of the Organization of the Petroleum Exporting Countries - Qatar, Iraq and Libya - had also fielded candidates for the position, which is OPEC's second most senior after the secretary general.
Al-Qahtani works at the Saudi Ministry of Energy and is a member of the Saudi OPEC delegation. He has also worked for state oil company Aramco, where he was in charge of its global economic and energy outlooks and scenarios.
OPEC governors are meeting at the group's Vienna headquarters on Tuesday and the talks are continuing, sources said.