Oil traded near zero, after plunging below that level for the first time in history amid rapidly filling American storage tanks, as the U.S. benchmark’s May contract entered its final trading session.

Futures in New York fluctuated between positive and negative territory, after plunging to as low as –$40.32 on Monday. The June contract, where the majority of trading is now taking place, fell below $20, as did Brent futures for the same month.  The spread between the two reflects the growing fear that those who take physical delivery of crude in the near future may not find any outlet or storage for those barrels as refineries curb operations. The world’s biggest independent storage company said Tuesday almost all of its space is sold.

With the coronavirus pandemic bringing the U.S. and much of the global economy to a standstill, processors are using far less crude, leaving so much unused oil that American energy companies are running out of room to store it. And if there’s no place to put the oil, nobody wants a crude contract that is about to come due.