The world could run out of oil reserves in just three months, according to an industry consultant.
IHS Markit, a market-research firm, says current supply rates mean inventories will rise by 1.8bn barrels in the first half of the year.
With an estimated 1.6 billion barrels of storage capacity left, producers will be forced to cut production because there will be nowhere to put the extra oil by June.
The oil market has been hit hard by the drop in demand caused by the outbreak, with Saudi Arabia vowing to pump crude at a steep discount after talks with Russia over a cut in output broke down.
Pakistan on Thursday banned imports of crude oil and fuel because its storage sites were full.
Vitol and Gunvor, two of the world's top traders, say they have a strong interest in stockpiling oil and that several traders have booked supertankers to stock up on oil at sea.
Supply is likely to exceed demand by 12.4m b/d in the second quarter, IHS said, with other traders, Banks and consultants also forecasting large surpluses.
Vitol said on Wednesday that demand was down as much as 20 million barrels from last year.
Jim Burkhard, director of oil markets at IHS, said production would have to be reduced or even shut down.
Current prices are already showing signs of a potential shortage of storage space.
In the us, so-called WTI cash volumes fell to their lowest level since December 2008, and us futures delivery points are expected to see a surge in inventories in the coming weeks and months.
Brent is trading deep into a contango, where the spot price is lower than the futures price for months to come.
As markets try to create the necessary financial incentives to stockpile oil by putting pressure on short-term prices, spot prices discount those prices for months to come.
Because the market is trying to create the necessary financial incentives to store by putting pressure on short-term prices.
A measure of actual barrels of oil on the spot market also points to global weakness.
Of the world's top three oil producers, Russia has the least storage space, about eight days' worth, IHS said.
Saudi Arabia has 18 days and the us has 30.
These figures are based on the amount of output that can be stored if exports are reduced.
Nigeria, Africa's largest producer, has the least storage space in the region measured by IHS.
IHS said production, estimated at 1.9m b/d in the first quarter of this year, would fill available local storage space in half to two days.
Energy Aspects Ltd., a consultancy, also expects tanks to be filled in the coming months.
The company said inventories would quickly spiral out of control as Opec pushes production to record highs.
We will run out of oil storage space in the third quarter of this year, and we will implement production containment earlier.