The efficiency of a boiler is calculated as the ratio between the sum of the energy exiting the boiler (Q-OUT) and the sum of the energy entering the boiler (Q-IN):

Q-OUT / Q-IN = Efficiency

The difference between the two is the energy lost during the process:

Q-IN / Q-OUT = Energy Lost

A boiler is a heat exchanger and the efficiency of a boiler is the efficiency of the heat exchange process.

An efficient boiler takes greater advantage of the energy introduced to it and more efficiently converts that energy into water or steam, consuming less fuel.

##### Q-IN Calculation

Every fuel, upon being burned, liberates a quantity of energy that can be calculated if the fuel´s exact chemical composition is known. This energy is known as the gross calorific value (Hs).

Once produced, this energy is partially reabsorbed by the moisture content, of which all fuels contain a percentage, and while it does not form a part of the combustion process, it does come into contact with the energy produced. All the moisture then evaporates and reabsorbs some energy in doing so. The energy remaining after this reabsorption is known as the net calorific value (Hi) and is always less than the gross calorific value.

Taking into account this information, the energy entering a boiler can easily be calculated by measuring the quantity of fuel entering the boiler (FUELIN), and then multiplying this flow by the calorific value of said fuel (HS or HI):

Q-IN = FUEL-IN x Hs or Hl

When doing this calculation, the following parameters are normally assumed:

• Exact chemical composition of the fuel
• Moisture content of the fuel
• Measurement of the flow of fuel entering the boiler

All of these, assumed constant for calculation purposes, are in reality variable with a certain margin of error (the chemical composition of the fuel varies per lot and place of origin; the moisture content of the fuel varies depending on the fuel supplier or its place of origin; and the measurement of the flow meter has its own margin of error) which means that the calculation of the energy entering the boiler will have a margin of error as well.

##### Q-OUT Calculation

The sum of the energies exiting a boiler is comprised of steam or hot water produced (QV), blowdowns or leaks (QB), and losses due to radiation and convection (QHT):

Q-OUT = QV + QE + QHT

The energy from the steam or hot water produced (QV) can be calculated by obtaining from the Steam Tables the enthalpy of the water or steam at the pressure and temperature when exiting the boiler (hOUT) and the enthalpy of the water at the pressure and temperature when entering the boiler (hIN), and then measuring the flow of water or steam leaving the boiler (MOUT):

QV = M-OUT(h-OUT - h-IN)

The energy from the blowdowns or leaks (QB) can be calculated by obtaining from the Steam Tables the enthalpy of the water or steam at the pressure and temperature when exiting the boiler (hOUT) and the enthalpy of the water at the pressure and temperature when entering the boiler (hIN), and then by measuring the flow of blowdowns or leaks leaving the boiler (MB):

QE = ME (h-OUT - h-IN)

Due to the fact that the losses from blowdowns or leaks are normally quite small in magnitude, they usually are not taken into account when calculating boiler efficiency.

The energy lost through radiation and convection (QHT) is almost impossible to measure or calculate, therefore it is common practice that it be estimated according to the following table:

Boiler Type
Dry-Back Boilers with operating pressures from 0 to 135 PSI

Losses through Radiation and Convection (QHT)
≤3%

Boiler Type
Wet-Back Boilers with operating pressures from 0 to 135 PSI

Losses through Radiation and Convection (QHT)
≤0.5%

Once again, certain parameters, such as the flow of steam that exits the boiler, are assumed fixed for calculation purposes. In reality, however, these elements are variable with a certain margin of error, which means that the calculation of the energy exiting the boiler will have a margin of error as well.