Petrochemical companies are making multibillion-dollar bets to profit from the abundant cheap natural gas pouring out of shale-rock formations across the U.S. Making sure those plans pay off will be a focus of this week’s IHS World Petrochemical conference in Houston. Natural-gas prices have plummeted in recent years as a new wave of supply has been unlocked from Texas to Pennsylvania through technological advances, including horizontal drilling and hydraulic fracturing. The low prices have been tough on some oil and gas companies’ bottom lines. But the trend has given chemical and plastics producers a reason to expand in the U.S., creating jobs and reviving a sector of the economy that many people had written off. The manufacturing renaissance sweeping across the U.S. today is a shift from the turn of this century, when it seemed unlikely that new petrochemical plants would be built in places such as the coastal region near the Gulf of Mexico, according to Dave Witte, general manager of IHS Chemical, an energy consulting group. The assumption was that new petrochemical plants and associated investments in plastics, rubber resins and metals manufacturing would be focused in Asia and countries rich in natural gas, such as Iran. “There’s a lot more interest in what’s happening, and people are coming here to figure that out,”