Ronaldo Schemidt / Contributor

ExxonMobil $XOM 0.00% senior vice president Neil Chapman warned Thursday that global oil inventories are approaching record lows and that prices will spike sharply within weeks, according to CNBC.

Speaking at the Bernstein conference in New York, Chapman laid out a stark timeline. "We're approaching unheard of inventory levels," he said. "I mean really, really low levels. You can debate whether that's going to hit, those really low levels, in two weeks or three weeks. Once you get to that point, then you'll see price shoot up."

Once stockpiles reach historic lows, physical Brent could climb to between $150 and $160 a barrel, Chapman said. Prices at that level would erode consumption enough to pull them back down, he said. July Brent futures settled below $94 a barrel on Thursday.

Chevron $CVX +0.35% CEO Mike Wirth, also speaking at the Bernstein conference, offered a similar assessment, according to Oil & Gas Journal. "The buffers and the shock absorbers are being steadily drawn down," Wirth said, adding that he expected the squeeze to show up in physical prices over the coming weeks, with conditions tightening further as summer gets underway.