Total kWh = 14.3. So assuming $0.10/kWh we have $1.43.
(Pumps and other equipment not counted as they're negligible and are used on gas setups as well).
Takes about 1/2 of BBQ tank of propane to do the same thing from what people tell me, average price for refill is around $20 for me all taxes in.
(You mention 18 gallons but I don't know if that means pre-boil, post-boil, or what you want to get into the kegs).
So that's a 13.98:1 ratio.
10:1.43 != 13.98:1 (more like 7:1)
I think you used a full tank at $20, instead of 1/2 at $10 for you calc. Even using your $0.10/kWh which is a little low, and $20 for a fill which is a little high, it is ~7:1.
I was talking 18 gal, and actually a bit more, to the fermenter. That was with ~1/2 tank. Using those numbers would get it down below 5X. I will see how much I use tomorrow to get a more precise usage number. Also, using natural gas those numbers would be roughly cut in half to ~3X. Those numbers for LP and NG fit better with the theoretical numbers I came up with.
This is in line with what most electric brewers tell me too including those that have switched from gas to electric.
I wasn't questioning the electric usage numbers, except for this guy claiming $0.25. ~$2 sounds about right for a 10 gal batch. It was just the multiple didn't seem to be right because it would mean ~full tank of LP for a 5 gal batch. The electric usage is fairly easy to compute. LP usage is easy enough to measure, but I haven't found any precise numbers from somebody weighing tanks before/after (I will try to remember to get the bathroom scale out). NG would be more difficult, unless the only thing you run off NG is your rig.
As a sanity check, a gas water heater doesn't cost 15X as much as an electric water heater. Last I checked gas water heaters were cheaper to use or about the same. A gas water heater is more efficient than a gas fired brew kettle, but not 15X more efficient.
Not a relevant comparison.
That is why I said it was just a sanity check, and stated that a gas water heater is more efficient. It is relevant in that regard. Taking away the efficiency of the central flue, and adding in the extra inefficiency of the going to boil, it is still a stretch to get from a dead even playing field at 140F to 15X at boil.
As for the burner on a gas water heater, they are ~40K btu/hr for a 40gal, so it isn't that far off from the max BTUs I put through my burner.
Most gas brewers crank up the burner and 70-80% of the heat is lost to atmosphere. This is most certainly a large reason why the electric:gas price difference is about 10:1 (give or take).
The 70-80% heat loss agrees with my numbers, and gives (conservatively) 5X for LP and 3X for NG. The 10-15X requires 95-98% heat loss. Not that they can't get that high, especially if you overdrive the burner and get a bunch of unburned gas, along with flames up the sides of the pot, which I have done. But to say it is normal for gas brewers to do that would be like saying it is normal for e-brewers to boil a full HLT at max continously and add cold water to get strike and sparge water.
If there was a way to get 100% of the gas produced heat into the wort then the price would likely be much closer. The problem is there's no (easy) way to do that with gas.
Kal
If there was a way, NG would be 4X and LP would be 2X
cheaper than electricity. That is why the 15X number didn't make sense. I think 4-10X for LP and 2-5X for NG are more reasonable numbers.
Adding a heat shroud around the kettle could raise the efficiency a good bit, and is something I will be trying for the BK. Most brewers don't care about the cost enough to mess with increasing efficiency of their LP rigs, especially at the 5 gal size. I am dealing with 26 gal pots, so it starts to make some sense to try, especially to decrease the time to reach boil.
I am not ragging on E-Brewing, and want to make an E-HLT and E-HEX. E-brewing has enough advantages even without the cost savings- no filling tanks, no fumes, easier temp control, quicker boils, etc. I just haven't seen enough good info on what element to use that won't have the corrosion/rust issues. The latest I read is the black Incoloy elements are actually SS, and they have the non-rusting/corroding metal at the base as well.