How to calculate a ton of refrigeration (TR) for the chilling system?

A ton of refrigeration (TR) is a unit of heat extraction capacity of the refrigeration or cooling equipment. Generally, TR is defined as the amount of heat transferred to freeze or melt 1 short ton of ice at 0 deg. C in 24 hours. 

1 TR is approximately equal to 12000 BTU or 3024 Kcal/hr of energy/heat load. 

The heat of fusion of water is about 335 KJ/kg or 80.01 kCal/kg. 1 short ton is equal to 2000 lb or 907 kg. 

Example: 1000 kg/hr of air is to be cooled from 45 deg. C to 10 Deg. C in the heat exchanger with chilled water for some process requirement then what will be chiller capacity required. Temp. the difference across the chiller is assumed to be 5 deg. C. The chilling water is pumped through heat exchanger using a centrifugal pump. Chiling circuit is as below,

Ans:

TR is the amount of heat to be extracted from the system or process.

Assumption :

1.    Air is 100 % dry at inlet temp.

2.    The system is well insulated and Heat gain from the atmosphere is negligible.

Here cooling duty of the heat exchanger is the amount of heat to be extracted and heat added by a chilling water recirculation pump.

Let's calculate Chilling duty (Qa) of the heat exchanger.

Qa    = Air Flow rate x Cp of Air x ( Air in temp – Air out Temp)

         = 1000 x 0.24 x ( 45-10 )

         = 8400 Kcal/hr

Qa = 8400/3024 = 2.78 TR ------------------ I

Let's calculate the chilling water flow rate (Mw) for Qa

Chilling water flow rate (Mw)  = Qa /( Cp x ( Chiller temp. Diff.)

Mw = 8400 /(1*5) =

Mw = 1.7 m3/hr ------------------------ II

Pumping power (Shaft power) with about 30-meter liquid head and 30 % pump efficiency is about 0.44 kWh. Assuming worse case that all pumping power  (Qp) will be added to liquid which is about 0.44 kWh i.e. 378 kCal/hr ( 1 kWh = 860 Kcal).

Total heat load on chiller is,

 Qc   = Qa+Qp

         = 8400 + 378

         = 8778 Kcal/ Hr ------------------------------ III

Chiller Capacity =  8778 Kcal/hr i.e. 2.9 TR.

Note:

1.    If air or gas is saturated or has moisture then the heat of condensation will be added to cooling duty to calculate actual chiller capacity.