This GAO document is from 1998 but it helps explain the difference betwen conventional and nuclear propulsion for carriers. It estimates that nuclears carriers have life-cycle costs of $22,2 billion while conventional carriers have $14,1 billion. Also, conventional carriers spend less time on extended maintenance and have more flexibility on this. It found little difference in the operational effectiveness betwen them. It mentions that nuclear carriers can acelerate faster than conventional ones
The other key point I see here is
Conventional carriers replenished aviation fuel about every 2.7 to 3.1 days and the nuclear carrier every 3.3 days--after only a fraction of their fuel and supplies were exhausted.
If you have to replenish aviation fuel, you might as well replenish propulsion fuel at the same time.
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If a similar $8100 Million difference in lifecycle cost applies between Chinese nuclear versus conventional carriers, then it is clear that conventional carriers are vastly superior. Particularly since China doesn't already have a mature nuclear carrier design and replenishment ships are cheap.
The Royal Navy Tiger-class replenishment ships are only $180 Million to buy, and my guesstimate is that they have a lifecycle cost of about $540M.
So adding an additional replenishment ship is a far cheaper and more effective option, than in going for a nuclear-powered carrier.
And that logic is even stronger when operating within the 2nd Island Chain, which means Chinese CSGs don't have far to travel and are close to resupply ports.
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If you use the aviation fuel figures in the report, you end up with
JFK: 5days of aviation operations. Based on 1.8M gallons of aviation fuel @ 10000 litres per aircraft x 160 sorties per day
Nimitz: 10days of aviation operations. Based on 3.5M gallons of aviation fuel @ 10000 litres per aircraft x 160 sorties per day
So refueling every 3days is not an issue.