Boiler efficiency can be defined as the ratio of useful output to heat input in the fuel.
Depending on local usage, the latter can be either the Higher or the Lower Heating Value.
A proper calculation of efficiency requires a definition of the boiler boundary which separates the elements to be considered part of the boiler from those that are excluded. Equipment is generally considered outside the boundary when it requires an outside source of energy (heat or electricity) or when the heat exchanged is not returned to the boiler generating system. Of course, boiler efficiency is lower than combustion efficiency (see Sect.6.3), particularly because of additional heat losses from the exterior boiler surfaces through the insulation, generally called radiation losses.
A wider definition of boiler plant efficiency, instead of the single boiler, can take into account all kinds of energy consumption and recovery, which are not consid- ered for the efficiency of the boiler itself.
Two basic procedures to calculate efficiency are discussed here:
1. Input–output or direct method;
2. Heat-loss or indirect method.
Of course, the two methods would give the same results if all the data required can be measured without significant error.
Note that efficiency is generally defined according to national rules to which reference must be made,so particular attention must be paid to fuel heat input,taken as HHV(mainly in the USA)or LHV (mainly in Europe).
6.7.1 Input–Output Method
Efficiencyð Þ ¼% output input
100
¼ useful output or heat absorbed by the fluid heat input in the fuel
100 This method, also called the direct method, requires the direct measurement of both input energy, that is, fuel flow rate, and the useful output energy. In order to quantify the output energy, it is necessary to measure temperature, pressure, and flow rate of generated steam and boiler feedwater.
Difficulties in making these measurements, the lack of instrumentation at most industrial boiler plants, and the possibility of significant errors make large-scale use of this method impracticable.
It should be pointed out that the choice of heat input equal to either the Higher or the Lower Heating Value determines a great difference in the related efficiency values. If the ratio between the HHV and the LHV, which roughly equals 1.12 for natural gas and 1.065 for oil,is calledα and the boiler output power has the same value,the ratio between the two efficiency values is:
0.893 (for natural gas) Efficiency ( % HHV reference )
Efficiency ( % LHV reference ) =1
= LHV HHV=
0.939 (for oil) 6.7.2 Heat-Loss Method
Efficiencyð Þ ¼% 100 losses heat input in the fuel
100
These losses are mainly the combustion losses already discussed in Sect.6.3. They are listed below with some comments on their origin:
• Waste heat going up the stack. The greater part is the heat carried by dry flue gases (sensible heat). Another part of the stack loss is the moisture loss (latent heat), that is, the heat used to evaporate and superheat water vapor resulting from the combustion of hydrogen in the fuel (this must be considered only if Higher
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Heating Value is assumed as heat input in the fuel), the humidity of the combustion air, and the water contained in the fuel. Industrial boilers not equipped with waste heat recover equipment such as air preheaters or economizers have very large flue gas losses because of the high stack-gas temperature (473–573 K; 200–300C; 392–572F);
• Losses due to incomplete combustion. These consist mainly of combustible material in the flue gas such as carbon monoxide, hydrogen, and hydrocarbons.
Additionally, refuse may contain unburned solid fuels and other solid combustibles;
• Radiation losses through the exterior surfaces of the boiler. Approximate evalu- ation of these losses by charts developed by the ABMA (American Boiler Manufacturers Association) or similar ones is shown in Fig.6.6;
• Additional losses.
The indirect method is based on the determination of the above-mentioned losses, by first evaluating singly the heat losses per unit of fuel and then converting these values to a percentage loss by means of the heating (Higher or Lower) Heating Value.
The waste heat going up the stack is evaluated as the sum of three components:
1. Heat loss (sensible heat) due to dry gas is equal to the kilograms of dry gas per kilogram of fuel multiplied by the specific heat of the combustion gases (roughly 1 kJ/kgK or 0.24 Btu/lbF) multiplied by the temperature difference between the stack exit gas (ts) and the inlet air for combustion (ta) The stack exit temperaturetsis closely related to the recovery equipment temperature such as economizers and air preheaters;
Fig. 6.6 Example of radiation losses chart (each curve corresponds to a boiler rated power value)
2. Moisture loss due to the water contained in the fuel is equal to the kilograms of water per kilogram of fuel multiplied by the enthalpy difference between the water vapor mixture in the stack exit gas and water at ambient temperature;
3. Moisture loss due to the combustion of the hydrogen in the fuel equals the weight fraction of hydrogen in the fuel multiplied by 9 (as stated in Sect.6.1 where it is pointed out that the combustion of 1 kg of hydrogen produces 9 kg of liquid water) multiplied by the enthalpy difference between the water vapor mixture in the stack and liquid water at ambient temperature. This loss is considered only if the Higher Heating Value is assumed as heat input in the fuel.
The losses due to incomplete combustion are totally attributed to CO in stack gases and to the combustible in the refuse. In the latter case they are evaluated as the kilograms of dry refuse per kilogram of fuel multiplied by the heating value of the refuse determined by laboratory tests.
The radiation losses are estimated by reference to the above-mentioned ABMA charts or equivalent charts.
Additional losses, generally ranging between 0.5 and 1.5 %, are introduced to take into account losses neglected in the indirect method computation.
Graphic solutions were developed by using the above-mentioned or similar procedures in order to estimate stack gas losses (dry flue gas losses; all the moisture losses together) and losses due to incomplete combustion.
The heat-loss method requires the measurement of stack flue gas parameters (temperature; O2or CO2and CO concentrations as % by volume or as ppm) and of combustion air temperature.
The measurement of O2is generally preferred to that of CO2because simpler instrumentation achieves the same accuracy. Portable analyzers are available for both O2and CO2measurements.
Carbon monoxide is generally measured by means of handheld chemical absorb- ing analyzers (Orsat or similar analyzers) and length of stain detectors.
Stack opacity or smoke density is assumed as an index of the combustion conditions. It can be measured by means of hand pump filter paper or a similar tester where the color assumed by the paper is compared to a standard scale.
Generally, index 0 means no opacity. Optimum values range between 0 and 3 (Bacharach index).
The relationships between excess air and stack gas concentration of O2and CO2 for different fuels are shown in Fig.6.7.
Figure6.8shows a typical relationship between total stack gas losses and stack temperature for different values of stack excess O2and for a specific fuel (natural gas in this case). Notice that stack temperature increases with the excess of O2 because complete combustion is achieved. Similar curves are available for different fuels. Figure 6.9 shows the relationship between losses due to unburned combustibles and stack excess O2 for different values of CO emissions. Sets of values referring to both Lower and Higher Heating Values are reported.
Other methods, based on the evaluation of total stack losses and unburned losses through curves and standard coefficients are widely used:
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• Total stack gas losses%¼KsCOts2t%a whereKsis called Hassenstein coefficient (see Table6.5where only the Lower Heating Value is assumed as reference),ts
is the stack gas temperature andtais the ambient temperature (typical values of CO2% less than 10 %). This formula is acceptable if incombustibles are kept low;
• Losses for unburned combustible%¼KcCO2CO%þ%CO%whereKcequals 50.5 for fuel oil, 37.9 for natural gas, 59 for coal if the Lower Heating Value is assumed as reference (typical values of CO% less than 0.1 %).
Examples of evaluation are given in Sect.6.12.
In Fig.6.10the main combustion parameters are correlated by a set of curves called the Ostwald triangle. In particular, if CO2% and O2% are known, it is possible to check whether the combustion is complete, and if it is not, to determine the CO%. Otherwise, if only CO2% or O2% is known, by introducing CO%
(measured or estimated), it is possible to determine the other. Other sets of correlation curves also exist for use according to local practice.
Fig. 6.7 Typical relationship between stack gas concentrations of CO2(%) and O2(%) and excess air (%)
Depending on heat input as fuel,either Higher or Lower Heating Value, percentage losses are as follows:
total losses as % of Higher Heating Valueð Þ
¼total losses as % of Lower Heating Valueð Þ=αþ100ðα1Þ=α For natural gas,ratioα¼1.12;thus
total losses as % of Higher Heating Valueð Þ
¼total losses as % of Lower Heating Valueð Þ=1:12þ10:7 For fuel oil ratioα¼1.065;thus
total losses as % of Higher Heating Valueð Þ
¼total losses as % of Lower Heating Valueð Þ=1:065þ6:1 Fig. 6.8 Stack gas losses (natural gas)
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Fig. 6.9 Unburned CO losses versus O2concentration by volume for different values of CO emissions for natural gas (CO losses are here referred only to the Higher Heating Value; CO concentration equal to 100 ppm or 0.01 % in volume corresponds to 125 mg/Sm3)
Table 6.5 Hassenstein coefficient values for different combustibles (Kscoefficient referred to Lower Heating Values of input fuels and toC)
Hassenstein coefficient valuesa
CO2% by volume Gasoil Oil Natural gas Coal
4 0.523 0.543 0.418 0.683
5 0.530 0.550 0.427 0.684
6 0.536 0.556 0.437 0.685
7 0.543 0.563 0.447 0.686
8 0.550 0.570 0.457 0.687
9 0.557 0.576 0.466 0.688
10 0.564 0.583 0.476 0.689
11 0.571 0.590 0.486 0.690
12 0.578 0.596 0.691
13 0.585 0.603 0.692
14 0.592 0.610 0.693
15 0.694
aIfF is used, multiplyKsby 5/9
Fig. 6.10 Ostwald triangle for natural gase%¼VVthVth100; concentration by volume (dry)
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