Back in the fuel crisis of the 1970's, and with the opening up of the Alaska North Slope oil fields, Congress passed a law forbidding the export of US oil. What with everyone sitting in lines at the gas station just to fill the family car, it seemed like a quick short cut to making more oil and gasoline available to US consumers.
Now, 40 years later, the industry has managed to radically increase domestic oil production. They want to sell some this new oil production abroad.
Let 'em. The oil companies are far better equipped to figure out the best way of turning oil into cash than any set of inside the beltway bureaucrats.
The price of oil is set by international markets, the domestic price will be the same whether we sell abroad or not. If anything, American oil sales will depress the international price of oil. Which will reduce the domestic price, since the domestic price is the international price.