So instead of a fuel truck you have a battery swapper.
You'll have to ship the batteries somewhere they can charge/reprocess, but you also need to ship fuel, so it's a 1-to-1 tradeoff (you can ship the batteries by land).
Not that much more (theoretically) - Al-air batteries could reach up to ~8kWh/kg, which is in the same range as jet fuel's 12ish. Aluminum is also denser than jet fuel, so per unit volume it could be even closer.