How do I calculate/convert a ton-hour of chilled water to its kWh or Btu value?
The basic information you need in order to do this calculation is that the definition of a Btu is the amount of energy it takes to raise (or lower) the temperature of one pound of water 1 degree F.
Other definitions that will be useful:
- 1 kWh = 3412 Btu
- 1 gal water = 8.3 lbs.
- 1 Ton of cooling capacity = 12,000 Btu/hr
The strict answer to your question, then, is that one ton-hour of cooling is 12,000 Btu, or 3.516 kWh. In practice, what you will probably really want to know is how many kilowatt-hours it takes to run a particular chiller for an hour, or to cool a particular flow of water by a certain amount for an hour. I will address both of those problems.
Chillers are usually rated in kW per ton, in EER, or in SEER, which are actually comparable ratings. EER is simply the Btus of cooling provided divided by the watt-hours supplied, including fan energy, under prescribed test conditions. SEER is also Btus of cooling provided divided by the watt-hours supplied, including fan energy, but averaged over a typical cooling season. Thus, a rating of EER 12.0 is roughly equivalent to 1 kW per ton, although the actual test conditions for creating these ratings make these numbers not exactly equivalent. Because of the adjustment for seasonal weather conditions, SEER is more commonly used than EER, and is a more realistic rating to use for estimating actual energy usage. Most commercial units are rated in kW per ton.
A few examples will illustrate how to make the calculations.
Example 1. You have a 5-ton heat pump rated at SEER 12.0. How many kilowatt-hours does it take to run it for a typical hour?
5 ton x (12,000 Btu/ton)/(12 Btu/watt) x (kilowatt/1000 watt) x 1 hour = 5 kWh = 17,060 Btu
Example 2. You have a 10-ton chiller rated at 0.8 kW/ton. How many kilowatt-hours does it take to run it for a typical hour?
10 ton x 0.8 kW/ton = 8 kWh = 27,296 Btu
Example 3. You have a flow of chilled water at 10 gpm. The return chilled water is 55 deg. F. (entering the chiller), and the supply (exiting the chiller) is 45 deg. F. The chiller is rated at 0.8 kW/ton. How many kilowatt-hours does it take to run it for a typical hour?
Btus required for one hour of flow:
"delta-T" = 55-45 deg. F. = 10 deg. F.
(10 deg. F.) x 10 gpm x (8.3 lb.water/1 gal water) x (60min./1 hr.) = 49,800 Btu
49,800 Btu x 0.8 kW/ton x (1 ton/12,000 Btu) = 3.32 kWh