Valero Energy Corp. and PBF Energy Inc. refineries in the Los Angeles area could face stricter safety requirements when using hydrofluoric acid or be forced to eliminate its use altogether under a new rule local regulators are weighing.

The South Coast Air Quality Management District is still weeks away from releasing a draft rule, but the latest iteration backs off banning the chemical outright as suggested in April 2017.

A final rule could be adopted as...