How to calculate cooling capacity from a piping diagram

1. How to calculate the required cooling capacity

Required cooling capacity refers to the amount of heat required to cool an object. Therefore, a heat calculation formula is used for calculation, and the units are "W" or "kW." Required cooling capacity can be calculated using the formula below.

[Calculation formula for required cooling capacity (calculation formula for heat amount)]
Q[kW]=①Vs×②Cs×③γs×④ΔT÷⑤t

Q: Heat capacity (load capacity) [kW]
① Vs: Volume of the object [m³]
② Cs: Specific heat of the object [kJ/kg・℃]
③ γs: Density of the object [kg/m³]
④ ΔT: Temperature difference of the object [℃]
⑤ t: Cooling time of the object [sec]

In actual calculations, in addition to the formula above, safety factor is added to take into account factors such as heat entering from outside (in this article, a 20% factor is used).

2. Situations where required cooling capacity is required and calculation examples

The main purposes of calculating the required cooling capacity based on a piping diagram can be divided into three parts:

• 1. Updating existing equipment ⇒ Check the existing cooling equipment
• 2. Changes in production volume/review of excess capacity ⇒ Calculate from calorific value and raw material supply amount
• 3. Increase in production volume, change in environment, addition of cooling equipment ⇒ Calculate cooling capacity shortage

There are a variety of situations where you may be faced with the need to calculate cooling capacity for plumbing fixtures, such as using regulated refrigerant equipment, aging or missing cooling capacity. Keep in mind how to do the cooling capacity calculation so that you can do it when you need it.

■ 1. Check the existing cooling system

Even if the cooling capacity is sufficient, if the equipment uses the discontinued refrigerant R22 (HCFC) or is aging, it is important to update the equipment as soon as possible, taking future maintenance into consideration.

When updating equipment that does not have a capacity problem, no special calculation formula is required. Check model specification and cooling capacity from the piping diagram and nameplate of the existing cooling equipment, and update to a cooling device with equivalent or higher specifications.

Updating equipment is a good opportunity to review its functions, so choose equipment from a wide range of perspectives, including not only cooling capacity but also energy-saving capacity and suitability for the usage environment.

■ 2. Calculate from the calorific value and the amount of raw material supplied

If your production volume has dropped significantly and you want to review over-specified equipment to promote energy conservation, you can calculate the "required cooling capacity" from the amount of heat generated and the amount of raw material supplied.

[Calculation example]
Calculation method for cooling capacity required when ethylene glycol raw material is kept at a temperature of 20°C or less in the raw material tank

<Piping diagram and heat source>

In cases where there are two paths with different temperatures, as shown in the figure, the heat quantity of each path, A and B, is calculated and then the total is added together to determine the required cooling capacity.

<Calculation formula for [Route A]>
Premise: Ethylene glycol raw material at 30℃ (room temperature) in a storage tank is cooled to 20℃ at 10L/min and supplied to the raw material tank.

Q[kW]=①Vs×②Cs×③γs×④ΔT÷⑤t

① Volume of ethylene glycol: 0.01m³ *
② Specific heat of ethylene glycol: 2.38 kJ/kg・℃
③ Density of ethylene glycol: 1120 kg/m³ (at 20°C)
④ Temperature difference between inside the storage tank and after cooling: 30℃ - 20℃ = 10℃
⑤ Cooling time of raw materials: 60 seconds *
*The raw material flow rate of 10 L/min is broken down into 0.01 m³/60 seconds, and calculations are made assuming ① as 0.01 m³ and ⑤ as 60 seconds.

Calculating ① to ④,
0.01 x 2.38 x 1120 x 10 = 266.56

To this, safety factor of 20% (x 1.2) is added to account for factors such as heat entering from outside.
266.56×1.2＝319.87

Finally, ⑤ divide by the cooling time.
319.87÷60＝5.3kW

The heat output of [Route A] is 5.3 kW.

<Calculation formula for [Route B]>
Premise: The ethylene glycol raw material, whose temperature is controlled in the raw material tank, is not supplied to the mixing tank but returns to the raw material tank, and the raw material, which was 20°C, rises to 25°C and returns at 5L/min.

Q[kW]=①Vs×②Cs×③γs×④ΔT÷⑤t

① Volume of ethylene glycol: 0.005m³ *
② Specific heat of ethylene glycol: 2.38 kJ/kg・℃
③ Density of ethylene glycol: 1120 kg/m³ (at 20°C)
④ Temperature difference between inside the tank and when it returns: 25℃ - 20℃ = 5℃
⑤ Cooling time of raw materials: 60 seconds *
*The raw material flow rate of 5 L/min is broken down into 0.005 m³/60 seconds, and calculations are based on ① being 0.005 m³ and ⑤ being 60 seconds.

Calculating ① to ④,
0.005 x 2.38 x 1120 x 5 = 66.6

To this, safety factor of 20% (x 1.2) is added to account for factors such as heat entering from outside.
66.6×1.2＝79.9

Finally, ⑤ divide by the cooling time.
79.9 ÷ 60 = 1.3 kW

The heat output of [Path B] is 1.3 kW.

<Total required cooling capacity >
The total required cooling capacity is the sum of the heat amounts from paths A and B.

[Heat amount of route A] 5.3 kW + [Heat amount of route B] 1.3 kW = 6.6 kW

We can see that the cooling capacity required for this piping system is 6.6 kW. Remember to add the safety rate when calculating the heat rate equation.

■ 3. Calculate cooling capacity shortage

If you are dissatisfied with your cooling equipment due to increased production volume or changes in environment temperature, or if you want to have some leeway in anticipation of aging equipment, calculate cooling capacity shortfall.

To determine cooling capacity deficiency, check how many degrees Celsius the temperature rises in how many minutes, and consider the "heat amount of the temperature rise = cooling deficiency."

[Calculation example]
Premise: In a reaction process for mixed raw materials as shown in the piping diagram below, cooling capacity of the existing chiller is insufficient, causing the temperature of the mixed raw materials to rise. Calculate the cooling deficiency (heat amount of the temperature rise).

If you want to keep 500L of mixed raw material at 30°C, but the temperature rises by 12°C in 30 minutes, the calculation formula is as follows.

Q[kW]=①Vs×②Cs×③γs×④ΔT÷⑤t

① Volume of mixed raw materials: 0.5m³ *Convert 500L to m³
② Specific heat of mixed raw materials: 2.1 kJ/kg・℃
③ Density of mixed raw materials: 950 kg/m³ (at 30°C)
④ Temperature difference between inside the storage tank and after cooling: 12℃
⑤ Cooling time of mixed materials: 1800 seconds *Convert 30 minutes to seconds

Calculating ① to ④,
0.5 x 2.1 x 950 x 12 = 11,970

To this, safety factor of 20% (x 1.2) is added to account for factors such as heat entering from outside.
11970 x 1.2 = 14364

Finally, ⑤ divide by the cooling time.
14364÷1800＝8.0kW

The heat generated by the temperature rise is 8.0 kW, so to keep 500 L of mixed raw material at 30°C, an additional 8.0 kW of cooling capacity is required.

If the cooling equipment is not capacity, the problem can be solved by updating to cooling equipment with specifications that can cover the overall required cooling capacity, or by adding a chiller unit or heat exchanger to make up for the shortfall.