The next step for some U.S. refineries that have already cut way back may be a full stop. Marathon Petroleum Corp. plans to idle its Gallup, New Mexico, refinery next week, according to a person familiar with the matter. It’s the first U.S. facility to shut as the coronavirus pandemic empties skies of passenger planes and the roads of cars.

It’s not likely to be the last. Major U.S. refiners, including Marathon, Valero Energy Corp. and Phillips 66, have lowered rates at their facilities to be at or near minimum levels as storage tanks fill up with fuel they can’t sell. While that “minimum” level differs from company to company, and in fact from plant to plant, it’s seen typically somewhere around 60% to 65% of capacity. Below that, many facilities need to be idled.

“If after cutting rates to a minimum, refiners are still unable to move their products, they are faced with the prospect of completely shutting down,” said Andy Lipow, president of Lipow Oil Associates LLC in Houston.

Slowing down a refinery isn’t like turning down the fire on a gas range when the water threatens to boil over. A refinery is a complex web of interconnected units, so once the amount of crude being processed in the distillation unit falls too low, secondary units don’t have enough feedstock to keep running. Since many units operate under high pressure as well as high temperature, it becomes more difficult to maintain the proper conditions for operation.

“It’s complicated to keep the refinery in balance,” said Stephen Wolfe, head of crude oil at consultant Energy Aspects Ltd. “The rule of thumb for me was always 65% of the CDU. Below that, things get complicated. As you reduce rates, all the downstream operations have to be properly supplied, there are hydraulics limitations to how low you can go.”

Refiners have been forced to take drastic measures to reduce fuel supply with gasoline demand plunging by almost half and storage tanks filling up. Measures to slow the spread of Covid-19 have hit gasoline and jet fuel especially hard, sending wholesale prices in some markets below 20 cents a gallon and crushing profit margins.

U.S. refiners are processing the least crude and other feedstocks since 2011, down some 3.5 million barrels a day from year-end, according to government data. But with overall fuel demand down more than 7 million barrels a day since early March, the reductions haven’t been enough to stem the growing glut.