HOUSTON, April 26 (Reuters) - A tanker carrying Guyana's first share of oil from a recently inaugurated floating production facility has set sail for Rotterdam, tanker monitoring data showed on Tuesday.

South America's newest crude producer, which has secured billions of dollars in investment from an Exxon Mobil, Hess Corp and China CNOOC consortium, earlier this month fetched $106 million from the sale of 1 million barrels of Unity Gold light sweet crude to Exxon.

Exxon won the purchase through a competitive bidding process following the expiration of a previous deal with a unit of Saudi Aramco for marketing the government's share of crude.

The Bahamas-flagged Suezmax vessel Dimitrios is expected to deliver its cargo on May 10, according to Refinitiv Eikon data.

The Guyanese government, which will receive a larger volume of crude produced off the country's coast this year, has not revealed how it will manage future oil sales.

But Vice President Bharrat Jagdeo in February said Guyana was exploring cutting out the "middleman" and directly selling its share of crude from the country's two floating production, storage and offloading facilities in a move to save on marketing fees.

Exxon did not reply to a request for comment on the final customer or destination of the cargo.

Guyana's government has engaged in previous talks with India to directly sell crude to the Asian nation's refineries, but the parties have failed to reach an agreement over prices.

Exxon earlier on Tuesday said it found oil in three new wells drilled off Guyana's coast, raising recoverable oil and gas potential from its discoveries to nearly 11 billion barrels.

(Reporting by Marianna Parraga Editing by Chris Reese)