It's a path-dependent calculation, not a state-dependent calculation, so the numbers are all over the map. Take two cases:
(1) Alberta tar sands production, which relies on imports of natural gas to melt and process the tar sand into a crude oil equivalent, called syncrude. If the syncrude is shipped to San Francisco Bay for refining at Chevron's Richmond Refinery, then you have to tag on the shipping fuel used, the gas used in the refinery, and finally the tanker fuel used to move the fuel to a gas station in San Francisco. Finding all these numbers is not easy, it's often proprietary, but you can find that a lot of natural gas is used at refineries (bulk numbers):
(2) Sweet light crude from a pressurized reservoir that's refined a few miles away from the oil field and used in a nearby city.
The end-product, refined gasoline, has the same state property (energy density) regardless of how it was manufactured, but that's irrelevant for getting the energy that it cost to make it. I imagine the spread can be pretty wide indeed, as the above examples show.
My understanding is that a lot of natural gas is used at refineries because, for so long, it was effectively "free" - there was a limited market for it and it was a byproduct of refining the stuff you wanted (light and heavy oils).
(1) Alberta tar sands production, which relies on imports of natural gas to melt and process the tar sand into a crude oil equivalent, called syncrude. If the syncrude is shipped to San Francisco Bay for refining at Chevron's Richmond Refinery, then you have to tag on the shipping fuel used, the gas used in the refinery, and finally the tanker fuel used to move the fuel to a gas station in San Francisco. Finding all these numbers is not easy, it's often proprietary, but you can find that a lot of natural gas is used at refineries (bulk numbers):
https://www.eia.gov/dnav/pet/pet_pnp_capfuel_dcu_nus_a.htm
(2) Sweet light crude from a pressurized reservoir that's refined a few miles away from the oil field and used in a nearby city.
The end-product, refined gasoline, has the same state property (energy density) regardless of how it was manufactured, but that's irrelevant for getting the energy that it cost to make it. I imagine the spread can be pretty wide indeed, as the above examples show.