Someone on a forum asked me what size heating elements I intended to use in my brewery. My answer was simple – but then I decided to try to do some math…
My batch size is going to be 10 gallons. I am planning on using a 4500 watt element for my HLT and a 5500 watt element for my BK. These numbers are based purely on random guesses. But… I’ve been wanting to know too. So let’s figure it out.
I just found this info on Wikipedia:
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A BTU is the energy required to raise one pound of water by one degree Fahrenheit. A U.S. gallon of water weighs 8.3 pounds. So, to raise a 40-gallon tank of 55 °F (13 °C) water up to 105 °F (41 °C) would require (40 × 8.3 × (105 − 55) / 100,000) BTU, or approximately 0.17 CCF, at 100% efficiency. A 40,000 BTU/h heater would take 25 minutes to do this, at 100% efficiency.
In comparison, a typical electric water heater has a 4500 watt heating element, which if 100% efficient results in a heating time of about 1.1 hours.
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Okay, so based on that info and the Wiki entry for BTU we find that the formula for calculating power required to heat water is: BTUs = (GALLONS * 8.3 * (FINISH_TEMP – START_TEMP))
And from http://www.mhi-inc.com/Converter/watt_calculator.htm we find out that 1000 watts is 3414 BTUs.
And based on random crap I found around the Internet we know that heating elements (and heat sources in general) are measured in BTUs per hour or Watt hours. i.e. how many BTUs they put out in an hour or how many watts they put out in an hour.
So now we just have to figure out the two formulas based on time.
So, using my case of a HERMS system let’s say I want to know how long it will take to raise 15 gallons of 55 degree water to my 170 strike temperature. That’s:
(15 * 8.3 * (170 – 55)) = 14317 BTUs
If I use a 4.5kW element I am creating (4.5 kW * 3414 BTUs per kW) = 15363 BTUs per hour
So my time to heat my water is 60 minutes / 15363 BTUs * 14317 BTUs = 55 minutes!
That was actually much less difficult than I expected 
Based on that info, I think that I will put a 5500 in my HLT and the 4500 in my BK. The big difference here is the temperature difference. To go from tap water to sparge water it’s a 115 degree difference but to go from mashed wort at 156 to boiling it’s only 56 degrees – so it will make more sense to have the bigger heater in the MLT. It will save me about 10 minutes in heating my mash and sparge water.
Now, getting back to your original question – RIMS seems more difficult to calculate because the water is moving past the heating element. I’d need to think about it more but maybe that doesn’t matter. If water is always in contact with the element and water is constantly being moved through the tube maybe that’s the same as being in contact with all the water at once. You end up applying more BTUs to less water, so maybe it averages out. Let’s assume it does.
If you wanted to ramp 20 gallons 1 degree in one minute it’s:
(20 * 8.3 * 1) = 166 BTU hours * 60 minutes = 9960 BTU minutes / 3414 BTUs per kW = 2.9 kW. So, it seems like with a 100% efficient system you could use a 3kW element to get your steps. I think the real problems will be trying to get 20 gallons of wort past the element in 1 minute. It looks like my March 809 pumps are a max of 6 gallons per minute, so you’d need at least 3.3 minutes to get all the wort past the element.
I guess another option would be to oversize the element to decrease the amount of wort that needs to flow past it. If it will take 3.3 minutes to move your wort past the element, what if instead you use 3x the heat? If you use 3x the heat you would only heat 1/3 of your kettle but the wort would come out of the RIMS much hotter and would increase the total temperature of the wort.
So, there’s my attempt I am sure someone who knew anything about thermodynamics would just read this, laugh and walk away, but it’s probably better than guessing!