California oil refinery operators including Chevron Corp., Andeavor Inc., and Valero, could spend about $58 million during the next year to comply with the state’s new refinery safety rules, the state says.

The new safety rules, which were published by the state’s Office of Administrative Law Aug. 4 and take effect Oct. 1, require refinery operators to make changes to better anticipate and prevent major accidents such as the 2012 Chevron refinery fire in Richmond, Calif., that prompted the overhaul. The fire injured six workers and caused an estimated 15,000 residents to seek medical care as...