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The distillation of crude in crude units are basically the same everywhere.
Differences come about with different crudes that are on fringes of what we
normally use.  This part of the process is the same for Shell, Valero and
all the others.

After the Diesel side cuts comes off the Atmospheric Column and the Vacuum
Column in the Crude Unit, it goes off to the Diesel Hydrotreater to get
cleaned up, treated further and sent off to storage.  Additives are blended
into the fuel prior to the trucks picking it up at the loading rack.  (for
those refiners that supply multiple brands, additives are blended to match
the brand. Think of it as a paint supplier.  They supply basic white paint
and additives to blend into the end product "color" the customer wants.) It
is this portion of the process (DHT and additives) that introduces the
differences between the refiners.

Then you have the potential differences in condition of the underground
tanks and lines at the stations and whatever contaminates might have entered
the tanks.

So, yeah, fuel from different brands and different stations can be
different.  Personnally, I wouldn't put Shell into any of my vehicles.  I
didn't like their gasoline and don't like their diesel.  YMMV

FMB