At least 11 very large crude carriers (VLCCs) have been reported as booked with storage options, rising from around five vessels at the end of last week. Each VLCC can hold 2 million barrels.
Separately, the Ti Oceania - one of the world's biggest oil ships, known as an ultra-large crude carrier, with a 3 million barrel capacity - has been booked by trader Vitol to store oil, the data and market sources say.
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That means at least 25 million barrels are currently estimated as being earmarked for floating storage. Some of the tankers could nonetheless still be used for conventional oil transportation.
Shell, Trafigura, Vitol and Gunvor all declined to comment. Koch could not be immediately reached for comment.
The strategy works because oil prices for delivery in the future are trading at a premium to those in the spot market - a market structure known in the industry as contango - with investors expecting prices to eventually recover from the near 60 percent slide in oil in the last seven months.
International benchmark Brent crude has fallen to just above $45 a barrel, near a six-year low, having averaged $110 between 2011 and 2013. Contracts for delivery in December are above $56.
"Should this widening contango trend continue, we expect more charterer interest for hiring VLCCs as floating storage," said analyst Omar Nokta of Clarkson Capital Markets.
But despite the attraction, the costs involved prohibit all but the biggest players.
Taking into account vessel hire and other expenses including bunker fuel and insurance, overall monthly costs are estimated anywhere in the region of $1.5 million per tanker.
Tanker market upside
After years in the doldrums, due to a glut of ships and soft demand, tanker rates have been strengthening in recent months helped by firmer bookings and slower fleet growth.