Petrodollar recycling as it is being widely disseminated is a myth.
Michael Hudson’s Super Imperialism has the correct take on US monetary imperialism.
Petrodollar does exist though, but only in the sense that “you’re not allowed to use your dollar revenues (which we printed freely) to industrialize yourself and are only allowed to use them to purchase treasury bonds and American weapons”, not that “America requires the sales of petroleum in dollars to finance itself” that many bitcoin/gold enthusiasts would like you to believe.