# Boiler Efficiency Calculation: a complete guide

Boiler efficiency is a quantity that indicates the relationship between input energy entering the boiler with output energy produced by the boiler. However, the boiler efficiency calculation can be defined in three ways:

1. Combustion Efficiency
2. Thermal Efficiency
3. Fuel-to-Steam Efficiency

Boiler Combustion Efficiency

Combustion boiler efficiency generally describes the ability of a burner to burn the entire fuel into the boiler combustion chamber (furnace). The efficiency of this type is calculated from the amount of fuel that does not burn along with the amount of air combustion air (air excess). Burning boiler can be said to be efficient if there is no remaining fuel in the end outlet of boiler combustion chamber, so does the number of residual air.

To obtain high combustion efficiency, burner and boiler combustion chamber must be designed as optimal as possible. On the other hand differences in the use of fuels also affect the efficiency of combustion. It is known that liquid fuel and gas (LNG and HSD) produce higher combustion efficiency than solid fuels such as coal.

Calculating the combustion efficiency of the boiler is not difficult, we just need to reduce the total amount of heat energy released by thermal energy burning that passes out through the stack (chimney) divided by the total heat energy.

$\eta_{combustion}=\dfrac {Q_{in}-Q_{losses}}{Q_{in}}\times100\%$

Where:

$\eta_{combustion}$ : boiler combustion efficiency (%)

$Q_{in}$ : The total heat of combustion energy (calories; Joule)

$Q_{losses}$ : Heat energy passing out through the chimney (calories; Joule)

The only difficult thing in calculating the combustion efficiency is how to pursuit the optimal number. Combustion efficiency is characterized by the overall fuel burning in the combustion chamber. While the control parameters are used to ensure the overall fuel burning, is the amount of air combustion (air excess) coming out through the stack. The more the amount of air excess coming out through the chimney, then the more likely the amount of unburned fuel can pass through the chimney. But you should remember that the more the amount of excess water passing through the chimney, the amount of heat energy escaping the rest of airborne is also growing. Therefore there is an optimum number of excess amounts of air, so that the boiler combustion efficiency can obtain the most optimal number.

Appears in the graph illustration above that the higher the amount of air (oxygen) passing through the stack, the smaller amount of fuel including carbon monoxide burned imperfectly. But as we have discussed above, the higher the amount of air excess, so the combustion efficiency chart is going to go back down, since the heat energy was coming away with the rest of the air. Then certainly there is an optimum value of the air excess to obtain the best combustion efficiency. As an illustration, the optimum value of air excess to the combustion of natural gas is 5 to 10%, liquid fuel at the rate of 5 to 20%, and 15 to 60% for coal combustion.

Boiler Thermal Efficiency

Boiler thermal efficiency shows how the performance in terms of its function as a heat exchanger. The efficiency calculation will show how effective the transfer of heat energy from the combustion process of fuel into the air. However, the efficiency calculation is not very accurate, because it does not account for the loss of heat radiation and convection that are not absorbed by water. In addition, the calculation of the thermal efficiency of the boiler cannot be used for economic analysis, because these calculation doesn’t take notice carefully the amount of fuel consumed. On this basis we will not discuss more about the calculation of the thermal efficiency of the boiler.

One that is considered the most effective way to determine the performance of broiler more closely is to count Efficiency of Fuel-to-Steam (commonly referred to as Fuel Efficiency). In addition to considering the effectiveness of the boiler as a heat exchanger (thermal efficiency), the calculation of boiler’s fuel efficiency also notices losses due to radiation heat transfer and convection. The calculation of boiler’s fuel efficiency boiler should consider the consumption amount of fuel used, so it is very appropriate to be used as a point of boiler economic analysis.

Direct Method

There are two popular methods for calculating the fuel efficiency of the boiler; the direct method and the indirect one. The direct method, known as method of input-output, is done by comparing directly the heat energy absorbed by the water so that the change phase into a vapor (output energy) with the thermal energy generated by burning fuel in the boiler’s combustion chamber (input energy). Simple formulation of calculation using the direct method can be described as follows:

$\eta_{fuel}=\dfrac {Q_{steam}}{Q_{fuel}}\times 100\%$
$=\dfrac {Q\times \left( h_{g}-h_{f}\right) }{q\times GCV}\times 100\%$

Where:

$\eta_{fuel}$ : Boiler Fuel Efficiency (%)

$Q_{steam}$ : Total heat energy absorbed by water vapor (calories; Joule)

$Q$ ​: Discharge of water vapor out of boiler (kg / h)

$h_{g}$ ​: Steam enthalpy out of boiler (kcal/kg)

$h_{g}$ ​: Water enthalpy entering boiler (kcal/kg)

$Q_{fuel}$ ​: The heat energy produced by fuel burning (calories; Joule)

$q$ : Debit of fuel requirement (kg/h)

$GCV$ ​: Gross Calorific Value (kcal/kg)

In the direct method, there are some parameters that should be measured with precision in order to get an accurate calculation results. These parameters include:

1. Water discharge (feedwater) into the boiler
2. Water discharge desuperheater
3. Overall secondary flow rate as boiler blowdown, auxiliary steam, and so forth.
4. Pressure and temperature of the entire flow of a working fluid such as water entry, exiting steam superheater, entering and exiting reheater steam, auxiliary steam, and others.
5. Debit fuel needs
6. Calorific value (heating value) fuels
7. Other incoming energy

The following table shows the advantages and disadvantages of the methods of direct and indirect in the calculation of Boiler Fuel Efficiency.

 Advantages Disadvantages Direct Method The primary parameters of the definition of Boiler Fuel Efficiency (input-output) are calculated directly. Debit and fuel heating value, as well as debit and steam water properties, should be calculated as accurately as possible to minimize inaccuracies. Only requires a little calculation. Not able to demonstrate the potential causes of inefficiency. Does not require the value assumption of immeasurable loss. Must use indirect methods to assess the accuracy of the calculation. Indirect Method The primary calculations such as flue gas analyzer and exhaust gas temperature can be done very accurately. Requiring more calculations than the direct method. Calculations correction can be done to pursue the existing standards or to the fulfillment of the warranty. Not able to provide the data capacity and output automatically. Has a low level of uncertainty, because the calculation of the loss reflects only a small fraction of the total available energy conversion. Some loss points can’t be measured so that its value should be assumed. Biggest loss source can be known. Error calculation rate is relatively low.

Indirect Method

What is meant by the indirect calculation of Boiler Fuel Efficiency is a calculation that does not directly involve the formulation of the main components of the input and output boiler efficiency energy, but by calculating the losses that exist. Let us consider the following formula:

$\eta_{fuel}=\dfrac {output}{input}\times 100\%$

And if:

$input + credits = output + losses$

And then:

$\eta_{fuel}=\left[ \dfrac {input-losses+credit}{input}\right] \times 100\%$
$=\left[ 1-\dfrac {\left( losses-credit\right) }{input}\right] \times 100\%$

The definitions of inputs, credit, outputs, as well as the losses are in accordance with the following illustration which we have quoted from the standard book of ASME.

In accordance with the formula above, the calculation of the efficiency of indirect done by reverse the focus to the parameters of losses and credit energy. What meant by credit energy is secondary energies entering the boiler in addition to the primary energy of the fuel. While losses are parameters of wasted energy that are not converted into heat energy in the steam. Calculation instruction and measurement of these parameters are elaborated clearly through standardization issued by the American Society of Mechanical Engineers (ASME).

The indirect method is done with great detail on each measured parameter, so that the level of accuracy is considered much better than the direct method. But of course the indirect method requires a greater cost because it requires special equipment. For this reason many experts consider the indirect method is more suitable for use in large-scale boilers and certainly not very suitable used to calculate the efficiency of small boilers.

One parameter that should be taken into account in the both methods (direct and indirect) is the input energy from the fuel. In the indirect method, the input energy symbolized by the QrF is formulated as follows:

$QrF = MrF \times HVF$

Where:

$MrF$ = The flow rate of input fuel (kg/s)

$HVF$ = The heating value of fuel (J/kg)

The above formula looks identical to the formulation of the input energy in the calculation of the direct method’s efficiency. One important component coming into the formula above is the heating value of fuel. As we discussed in another article about the heating value, that there are two types of heating value, namely the higher heating value (HHV) and the lower heating value (LHV). Both are equally reflect the calorific value contained in the fuel, but both have a distinct difference in value. In most of the fuel, the HHV value tends to be bigger than the LHV. So if it is associated with the calculation of the efficiency of the boiler, the boiler efficiency value using HHV as a reference would be relatively small compared with the calculation of Boiler Fuel Efficiency using LHV as a reference.

References:

*Original article: Cara Menghitung Efisiensi Boiler
*Translated by: Todi