LPG is not a by product!!!
Offshore you either have your gas platforms or the oil platforms, gas= LPG and many others, the oil platforms pull up the crude oil from the bed and from that when its distilled you get all of your paraffins, kerosine, petrol and deisel, bitumen etc, deisel is slightly dearer to make as it requires more effort/cost to remove it from the column as it is "heavier" than petrol and most others.
You get a minor amount of lpg/other gasses when extracting the black gold but nowadays because (some) of the wells do not have the pressure for the oil to flow naturally they force the gas back down to pressurise the well, this is called natural gas lift.
On a brighter note i shut down a shell (gas) platform 2 years ago for a week @ £30 million a day
they were not happy chappies