This time around, barring a WMD attack on Kuwait, their production will probably be increased, at the behest of the Americans. Production of the emirates will also be increased. That leaves Saudi Arabia. They need the money, it is doubtful that they can afford to drop their production.
The USAF and the USN will be tasked with keeping the Gulf open to shipping, a job they did ten years ago with fewer bases and worse logistics. The strategic reserve will be around to pick up the slack in case a tanker or two is caught in the crossfire. Don't bet on an oil shortage.
However, I would bet upon a panicked surge in prices for a while. The market price of oil would rise due to traders' fears of a supply interruption.
Give them a few weeks, and prices will come back down to "normal." (I'm still waiting to see gasoline for 99.9 cents per gallon like it was when I was younger...)
The USN will keep the tankers safe. There is no doubt of that.
Since we're planning ahead, there shouldn't be a major supply problem.
But there could be a shape spike in the price of gasoline for a few weeks.