Thank you for your answers. That helped me understand the use of gas. I guess i was thinking the 400k unit would burn less gas overall because it took less time, BUT it seems my theory was wrong because it will take more gas (even though it's a shorter amount of time) to warm the pool because the unit is bigger. Either way I decided to go with the 400k unit. I just thought it would be a better option to heat the pool quicker. I am not sure if I will every use the heater in Dec-Feb unless it happens to be a warmer day (that happens sometimes in coastal SC). I am hoping to extend the season from March to Nov.
For you, and for anyone else who reads through this thread in the future, here is how heaters work as far as your decision goes. If you do not like math, stop reading this post.
A BTU is the amount of energy needed to increase 1 pound of water by 1 degree. To make this more usable, it takes 8.33 BTUs to increase 1 gallon 1 degree.
Let me give you an example that is super simple, and leaves out lots of factors I will bring in later after the example.
Your pool is 10,000 gallons, and is 80 degrees. How many BTUs do you need to increase the pool to 85 degrees?
The math answer is (# of gallon in pool) x (8.33 BTUs per/gallon) x (Desired end temp - Starting Temp)
10,000 x 8.33 x 5 = 416,500 BTUs.
So in theory, it would take a 400K BTU heater 1.04 hours to raise the pool temp 5 degrees. But that is in theory and does not include lots of factors. Now in practice things change, and here is just a list of how this might happen.
The big factor is your pool losing temperature to the air and the ground. For this, I can only give you an example. Right now my pool gets up to about 80 during the day, and is dropping down to 76 at night, while the air temp is going from about 80 down to 60 over the same period. How does this effect your heater? Well going back to the example, I have this as an estimate.
10,000 x 8.33 x (76-80) = - 333,200.
Lets just say that this is linear (which truthfully it is not for lots of reasons that arent important now) but you are losing 333,200/12=27,767 per hour. So now lets look at the math example in a more complicated way
What happens in 1 hour of the heater being on?
-Generate 400K BTUs
-80% efficiency means you need 500K BTUs to create that amount of output going to the pool.
-On your gas bill, 1 therm = 100K BTUs
-500K BTUs is 5 therms.
-A therm of natural gas will be around $1 on average, so it will cost $5 per hour to run your 400K pool heater for 1 hour at full power.
But then how will this effect your pool?
Going back to your 10K gallon pool, you need 8.33 BTUs per gallon per degree, so that means to raise your pool 1 degree, you need 83,300 BTUs
In our example, you generated 400K BTUs, so simple division says that you generate enough heat to raise your pool 4.8 degrees. Now in my example (and yours will vary here) you will also lose about 28,000 BTUs of heat in that same hour, so now the math looks like this
(400,000-28,000)/83300= 4.4 degrees in 1 hour and it would cost you about $5 to achieve that
I think this math is right, though Im sure someone will point out a typo and then I will edit accordingly.
Sorry for the math.