The first equation can't be right. The heat released by fermentation comes from the reaction of sugar, so the heat to be removed comes to
change in sugar conc x amount of wort
The cooling rate would take the form:
kW of cooling = degrees Plato decrease per hour x Kg of wort x 560 kJ/kg extract / 3600 s/hr /100 (to convert deg P to a decimal fraction).
Coolong requirements are briefly discussed in Farber M, Barth R. 2019. Mastering Brewing Science: Quality and Production..p 286.(citation below).
Thermodynamics of fermentation are discussed in Williams LA. 1982. Am. J. Enol. Vitic. 33(3): 149-153.
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Roger Barth
Author (with M Farber) of Mastering Brewing Science ISBN 9781119456056
Retired
West Chester PA
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Original Message:
Sent: 10-19-2023 18:06
From: David Kyrejko
Subject: Utility Costs
Always a tricky one. You're trying to attempt a mass energy balance and I commend you for it.
You're off to a good start, as for the chiller, you're going to want to look at the name and see what it takes in COP (coefficient of performance). This will also (hopefully) have a whole chart giving you the amount of power consumed by the chiller to effect a given amount of cooling. Where it gets tricky is the temperature on the condenser (hot side) of the chiller has a lot to do with its efficiency. The lower the difference between the hot side and medium that's absorbing the heat (the air most likely) the worse it gets. Keep this especially in mind if you'll be operating in a hot area of the globe and make sure you de-rate your chiller accordingly (oversize the chiller to make up for poor environmental performance).
Not doing this kind of mass balance work is why that vast vast majority of chillers are undersized and summer is filled with instagram photos of brewers hosing down condenser coils...
If you're looking for a more in-depth series of calculations let me know.
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David Kyrejko
The Engine Room
Brooklyn NY
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