Wed Jul 04, 2012 10:19 pm
You can estimate the volume of water needed to cool boiling wort by looking at the energy balance before and after cooling.
This method is a "best case, perfect world" estimate, so it calculates the minimum amount of water necessary, never really attainable, but it bounds the problem.
It doesn't care how the energy was transfered (your specific equipment and process), just how much heat needs to transfer.
It will answer the question: "Can I cool it with this much ice water?", as long as "no" or "maybe" are good enough answers.
Ideal Energy Balance:
The heat energy transfered by cooling 5 gallons of boiling wort to 70°F is equivalent to the energy required to increase the temperature of some minimum volume of ice water to 70°F.
Assuming the specific heat and density of water and wort are about equal (they're not, but close enough for this calc):
5 gal * (212-70)°F = x gal * (70-32)°F
solving for x, x = 18.7 gal of water a 32°F
This ignores all other heat losses or additions during the process and doesn't consider the rate of cooling (and resulting efficiency).
It also ignores the fact that ice needs to change phase into water (absorbing more energy that accounted for here), ambient heating of the ice water that is not perfectly insulated and any heat added by a pump and motor (submersible pumps dissipate heat direcly into the water they are moving.
The other big stored energy source ignored in this calculation is the mass of your kettle/burner at 200+°F! Lots of stored energy in all that stainless steel.
In practice, the flow rate required to maximize the heat exchanger efficiency is painfully slow, and for most cases, not worth the time.
I use 3 gallons if ice added to about 2 gallons of water recirculating thru my immersion chiller to drop the wort from 90°F to about 60°F. This is after I've cooled with tap water.
I divert the inital hot water into my picnic cooler, add some PBW and use it for clean-up. The rest of the water is diverted into a clean plastic trash can for rinsing equipment.