Heres some info onnNat Gas Heating for comparison:
To give you an idea of the energy volume it takes to quickly heat 35,000 gallons, which is no small feat:
1. Multiply the total gallons of water in the pool by 8.3 (pounds per gallon)
This will give you the total weight of the water
(35,000 gal x 8.3 = 290,500 lb)
2. So an 80% efficient 400k BTU heater would get you 320,000 btu of energy an hour (divided by your volume), a.k.a. 1.1 degree increase per hour - in ideal conditions with reasonably warm air temps...otherwise there are additional calculations
3. If your natural gas rate per CCF (close to a therm) in VA is like mine in Michigan, your hourly cost of NG for heat up on a 400 btu gas heater that's 80% efficient would be about $2.46/hr (if your rate is .77 per therm).
So, IMHO, even if you DO get the right size heater (eg a 400k btu ng heater) you are probably better running it up once then retaining/preserving heat, eg just Thermostatting to desired temp and keeping a good cover on at night, in day if you want cover off, using an evaporation barrier like Cover Free to reduce evaporation (which is 70% of heatloss) OR keeping a solar cover on during day also to get sun effect heating, etc. eg. Heat, then preserve heat at all costs
Sometimes its cheaper to maintain heat 24/7 - especially in summer - than to constantly just "run up" when you want to use it.
For example, our gas costs on a 24,000 gallon pool were pretty much the same once we started Thermostatting at 88 degrees instead of running it up just before use...and the bonus was the pool was always the temp we wanted. Until this year we never covered it at all, but did use an evaporation barrier (Cover Free) that made a big difference.
On my 266 btu heater with 24k gallons, if I wanted a 5 degree increase daily, my daily cost would be about $7.50 or $225/ mo in ideal summer conditions. Thermostatting to constant 88 cost me under that in July and August, and about $100 more in June and September (and about $200 more - eg $420 in cold April/early May and October with lots of nights freezing.) With that said, Thermostatting doesn't always make sense....eg I now operate throughout winter in a done, using a cover, on 3 scheduled daily heat runs preserving temp at 95 degrees for physiotherapy exercises every morning.
Which is how I've come across the calculations and observations on energy use