Calculating steam requirements – m cp ΔT.

A process needs heat at

• the correct temperature and
• the correct rate of heat transfer

Heat is being generated in the boiler in the form of steam. This heat is being distributed by steam lines to the process. Steam pressure determines the temperature at which heat is supplied, as saturated steam temperature is directly proportional to pressure. We need a ΔT of minimum 15-30°C to have efficient heat transfer (rate of heat transfer).

Consider a heat exchange process. The primary side is the steam space, and the secondary side is the process. Steam is condensing on the primary side into water. It is changing phase into liquid and giving off its latent heat to the process. This is Primary Heat (Q).

Primary Q = m x hfg

Where,
Primary Q = Quantity of heat energy released (in kcals)
m = Mass of steam releasing the heat (in kgs)
hfg = Specific enthalpy of evaporation of steam (in kcals/kg)

On the secondary side, this heat is being used for two things:

• 'heating up' heat - to increase the product temperature to the degree desired
• 'maintainance' heat - to maintain the product temperature as heat is lost by radiation, etc

Where,
Secondary Q = Quantity of heat energy absorbed (in kcals)
m = Mass of the substance absorbing the heat (in kgs)
cp = Specific heat capacity of the substance (in kcals / kg °C )
ΔT = Temperature rise of the substance (in °C)

This equation is also modified and used to establish the amount of heat required to raise the temperature of a substance, for a range of different heat transfer processes.
The above equations are very important. As Heat energy is being transferred from the primary to the secondary side, in an ideal condition,

Primary Q = Secondary Q

And this is the equation to calculate the theoretical heat balance of the entire system.

Example 1. Calculate steam flow rate for an autoclave which is heating 10,000 bottles of 1 litre each to a temperature of 120°C in 30 minutes. Steam supply is at 3 kg/cm2g.

Solution. What we are asking for is - what is the mass of steam that is supplied to the autoclave to heat these 10 bottles. This is 'm' on the primary side. First we will calculate the heat absorbed by the bottles (process), ie, secondary Q.

The formula

Secondary Q = m x cp x ΔT

Where,
Secondary Q = Quantity of heat absorbed by the bottles (in kcals)
m = Mass of water in the bottles which is absorbing the heat (in kgs)
= 10,000 bottles X 1lt = 10,000 lt = 10,000 kg
cp = Specific heat capacity of water (in kJ/kg °C ) = 1 kcal/kg °C
ΔT = Temperature rise of water (°C) assuming ambient is 30°C
= 120°C – 30°C = 90°C
Gives,
Secondary Q = 10,000 kg x 1 kcal/kg °C x 90°C = 9,00,000 kcal

So, 9,00,000 kcal is the heat energy absorbed by this autoclave on the secondary (process) side in 30 minutes. Steam at 3 kg/cm2g has 510 kcal/kg latent heat hfg (from steam tables).

As Sec Q = Pri Q,
9,00,000 kcal = m x 510 Kcal/kg
m = 9,00,000 / 510 = 1765 kgs

1765 kgs is the steam required in 30 mins. So, steam flowrate is 1765 X 60/30 = 3530 kgs/hr for this autoclave.

Suppose steam is supplied to a heat exchanger at 3 kg/cm2g - hg 630 kcal/kg. Condensate is coming out of the traps at 3 kg/cm2g hfg 130 kcal/kg. Ideally, the product should absorb 511 kcal/kg. But, it doesnt. Heat gets absorbed by the heat transfer barriers and is also lost via radiation. So, the actual heat absorbed is less than 511 kcal/kg.