Its giant Lake Charles refinery and its refineries in Texas and Illinois produce roughly 4 percent of the nation’s refined petroleum products. But Citgo is even more crucial to Venezuela. It imports 175,000 barrels of Venezuelan crude daily — nearly one of every five barrels the country exports worldwide, providing the leftist government with desperately needed dollars.

“Citgo is a hard-currency cash cow for Venezuela,” said Ramón Loureiro, global business development director for KBC Advanced Technologies, a consulting firm that works with Citgo.

Citgo also sends roughly 29,000 barrels a day of refined fuels like gasoline back to Venezuela.

For all of Citgo’s American roots, Venezuelan themes abound in its modern Houston headquarters. A Venezuelan flag flies out front, and a bronze statue of three Venezuelan workers adorns the lobby. A mural depicting Venezuela’s liberator, Simón Bolívar, decorates the hallway outside the executive suites inscribed with his motto: “God grants victory to perseverance.”

Perseverance is a theme repeated by Citgo’s executives. “It’s really business as usual,” said Rick A. Esser, a Citgo vice president and chief strategy officer. “We are focused on doing the day to day every day.”

Events are sorely testing that determination.

Several of Citgo’s most senior executives have been imprisoned in Venezuela since late last year, awaiting trial on corruption charges. Asdrúbal Chávez, Citgo’s chief executive and a cousin of former President Hugo Chávez, has had his American visa revoked, forcing him to direct operations by videoconference calls.

Then there is the existential threat posed by Pdvsa’s debt. This month Venezuela must pay more than $840 million to holders of Pdvsa’s 2020 bonds. A default would prompt a foreclosure on the bonds’ collateral, 50.1 percent of the company stock of Citgo Holdings, one of Citgo’s two holding companies. Lenders could then demand accelerated principal and interest payments.