Exxon and Chevron executives warn at Bernstein conference that near-record-low oil inventories will push Brent prices to $150-$160 within weeks.

The price of physical Brent oil cargoes will spike to $150 to $160 per barrel once inventories hit all-time lows, Exxon executive Neil Chapman said.

"We're approaching unheard of inventory levels. I mean, really, really low levels. Once you get to that point, then you'll see price shoot up. Once you get to that really low…