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My 1/2 hp well pump draws approx this power:
3.6 Amps X 220 Volts = 792 Watts 'Run'
7.2 Amps X 220 Volts = 1,584 Watts 'Startup'
Will two 12V 100AH 1280 Watt batteries put in series to make a 24V be enough?
Depends how long you plan to run it. (And if it's a synchronous AC motor, I will expect a significantly higher surge startup load than just double.)
I would expect a PJ inverter to run closer to 80% efficiency, so 800W * 1.2 = 960W / 24v = approx 40A continuous run load on the batteries.
The battery chemistry will contribute, and even the life span of the battery too.
lifepo4 cells are typically rated somewhere around 2000 cycles (after which they are at 80% of original capacity so may well do the job for quite a while longer) if they are run from fully charged to flat and back again.
A typical AGM lead acid battery will get somewhere around 300 cycles if they are run from fully charged down to 20% charge. Peukert's effect raises its head here too. 792 watts at 24V is at least 33A (ie not including system efficiency). A lot of AGM batteries are rated at 20 hour discharge rates, discharge them at a higher rate and you get less AH out of them. At 33 amps we are close to the 3 hour rate, so the AGM battery is going to fall short of its rated 100AH capacity. Decent manufacturers will state the expected AH vs discharge rate for their batteries, if not find a generic battery manufacturer that does provide the information and assume this is what any 100AH 20 hour rated battery will do, they are roughly the same in most cases.