I’m an engineer…and I work in energy and chemicals…this what I do for a living 
knowing the answer will ruin your view of the imaginary world of manga…haha…
but since I can share some insight…
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first off…this post apocalyptic world is post war…first thing anyone will do is ration whatever stock piles they have for fuels (that’s everything)…think WWI/WWII (but apocalypse…so much worse)…
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then imagine these are strategic resources so they will be the first that are attacked to weaken both (or as many sides as are fighting)
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Whatever fuels are left that are fought over, etc…would be gone…or people would just burn them (if I can’t have it no one can…think back to the Iraq war…and all those wells that burned for months…huge environmental mess and such a waste of resources)
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Then assuming you still have fuel left…it’s not really stored “ready to use” in tankage for filling (like you might think)…sorry to burst the bubble…blending pumps are used at the refinery to blend online directly (small quantities) for immediate use to the truck/rail loading racks. This is partly due to the ethanol blending requirements. Ethanol is hydroscopic (absorbs water)…water in fuels is generally bad…so it’s not mixed until it is going to be used. Diesel and Jet is typically pumped through a dryer (depending on what’s available to the facility)…There are tanks for batches that are mixed, but it isn’t just sitting around for more than a day (generally). It’s made and shipped back out. Off spec blends (depending on the reason) are either adjusted for octane or if it’s a sulfur spec that’s off it might be shipped to a different part of the country (usually pipeline)…i.e…stuff that you can’t use in California you can use in other states…
So assuming that all of this somehow happens to be possible… and that by some miracle there is still an undamaged tank full of gasoline range or diesel range material that’s on spec and ready for your tank…if it sits around for a few months…this is what happens…
- First off the light ends vaporize…more of them are added to your winter fuels you need a high enough vapor pressure to start the engine (butanes and light c5s)… these leak continuously through flanges/floating roofs/etc…(it’s very slow but it does happen…post apocalyptic…unmaintained equipment…they will vent off quick)…it’s the reason you can’t just put straight run material into your engine …it won’t start or it will vapor lock (too heavy/too light). or you’ll get knocking (preignition/ damages the engine)…also w/o sulfur and nitrogen treating (hydrotreating)…your catalytic converter will die so fast…and olefins will gum up your injectors… on and on and on…Gasoline and cars now aren’t anything like they were in the early/mid 1900s. Fuels now (all of them) are much cleaner and much less “wild” …You can put in stabilizers to try to maintain fuel for longer term storage, but to last for a post apocalyptic event…forget it…
Sorry to bust the bubble…but apocalyptic events are just bad all around … personally I don’t have any desire to be a prepper…surviving a war is one thing…apocalypse, nothing really left…that’s a whole different thing…that’s truly the end of the world right?