Why wasn’t Iraq War funded by oil profits?

Am I wrong in remembering something about the cost of the war in Iraq eventually being paid off with Iraqi oil proceeds? I’ve read that the cost of this war for the United States is in the trillions. I’ve read that Iraq is awash in oil profits. What don’t I understand here? Did all the money spent on this war and all of the oil profits end up with Halliburton?

Charles Chimera