The predicament of the National Iranian Tanker Company (NITC) shows the impact of a series of measures, including a European Union oil embargo due to come into effect from 1 July, on the central pillar of Iran's economy.
Instead of transporting oil to customers around the world, 19 of the NITC's 34 ships are thought to be stationary, used only for "floating storage" the Daily Telegraph has been told. In all, the giant tankers now lying dead in the water have a capacity of 33 million barrels of crude, worth about £2.3 billion at today's prices.
The fact that Iran appears unable to sell this oil shows how much economic pressure the country faces on the eve of negotiations on its nuclear ambitions. Next week, Tehran's representatives will meet the world's leading powers in Baghdad with the aim of restoring confidence in the supposedly peaceful nature of their nuclear programme. Iran has sent conciliatory signals, with Ali Akbar Salehi, the foreign minister, telling a French delegation that he was "ready to take forward steps". Last year, by contrast, Iran declined to discuss the nuclear issue unless sanctions were lifted. The condition of the oil industry could partly explain its new flexibility.
Of the NITC's 25 supertankers, each able to carry 2 million barrels, 14 are believed to be stationary, according to Whale Rock Legal, a law firm specialising in sanctions compliance. Iran also has nine smaller Suezmax tankers, each with a capacity of 1 million barrels. Of these, Whale Rock believes that five are lying idle.
The fact that Iran is using valuable tankers for storage suggests that onshore holding facilities at Kharg Island, believed to have a capacity of 23 million barrels, must also be full.
"The leadership in Tehran is not stupid and they must realise that the whole exercise is costing them a very great deal and the question is: 'is it worth it'?" said Prof Paul Stevens, senior research fellow on energy at Chatham House. "This will have an effect on their bargaining position."
Last year, Iran sold almost 600,000 barrels of oil per day to the EU. Those exports will end by 1 July, forcing the country to seek alternative buyers. China, India and South Korea - now Iran's biggest customers - are also under pressure from America, which will exclude them from the US financial system unless they buy less oil from Tehran.
In addition, US and EU financial sanctions make it harder for Iran to sell its crude. Simply arranging payment through the global banking system can prove impossible.
China is importing an extra 450,000 barrels of crude per day for a new strategic reserve. The country could pay Iran in goods - not cash - in order to get around financial sanctions.
With Iran hunting for customers, however, China is in a position to drive a hard bargain, which could help to explain the number of tankers now lying idle, added Prof Stevens. "The Chinese are going to hang on until the last minute in order to beat the best price out of them," he said.
Iran's tankers routinely conceal their movements by turning off their "transponders", the devices which allow them to be tracked. But their locations can still be discovered by satellites. If its storage capacity - whether using tankers or onshore sites - hits physical limit, Iran would have to cut production simply because there would be nowhere to place its oil.
Copyright 2012 Telegraph Media Group Limited. All Rights Reserved.
(Originally published May 15, 2012, on telegraph.co.uk.)