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Boiler Efficiency Calculations SimplifiedBY V.Ganapathy
Plant engineers  often look for simplified procedures to estimate boiler Efficiency using field data. Boiler efficiency is mainly impacted by the following variables:
 
Excess air 
Exit gas temperature 
Ambient or reference temperature 
Fuel type and analysis

The heat loss method disussed in ASME PTC 4.1 may be used for evaluating the efficiency of steam generators. For quick estimates of oil and natural gas fired steam generators,however,the following equations may be used.These equations were arrived at by the author after performing several calculations.
 
Natural gas 
Efficiency,% HHV=89.4-(0.001123+0.0195xEA)(Tg-Ta) 
  
           %LHV=99.0-(0.001244+0.0216xEA)(Tg-Ta)  

Oil fuels-# 2 and #6 
Efficiency,%HHV=92.9-(0.001298+0.0195xEA)(Tg-Ta) 
  
           %LHV=99.0-(0.001383+0.0203xEA)(Tg-Ta) 

Tg,Ta=exit gas and reference air temperatures,F 
EA=excess air factor-12 % excess air means EA=1.12 
In the above formule,1 % casing plus unaccounted losses was assumed. 

Efficiency on HHV and LHV basis can be related using the formula: 

HHVxEfficiency on HHV basis=LHVxEfficiency on LHV basis 

Example:A natural gas fired boiler with 15 % excess air has an exit gas temperature of 280 F,ambient=80 F. Determine efficiency on HHV and LHV basis. 

Efficiency-%HHV=89.4-(0.001123+0.0195x1.15)x(280-80)=84.64 % 
              -%LHV=99.0-(0.001244+0.0216x1.15)X(280-80)=93.78% 
 

 
Excess air from field data 
If % oxygen on dry basis is known from field data,the excess air can be estimated as: 
EA=Kx21/(21-%O2) 
K=0.98 for natural gas and 1 for oil 
Example:If  % oxygen dry in an oil fired boiler is 3,the excess air EA=21/(21-18)=1.17 or 17%.The same value of oxygen in a gas fired boiler would translate to about 0.98x1.17=1.15 or 15% excess air. 
Another formula that is used is:
EA=100xO2/[.264N2-(O2-CO/2)]
where O2,CO,N2 are from Orsat's analysis on dry basis.
Casing Heat Losses
This ranges from 0.3 to 1 % depending on the boiler size. The larger the boiler,lesser the loss. If say the hot face temperature is 366 F,wind velocity=100 fpm and ambient temperature=70 F:
The casing temperature has to be arrived at based on a trial and error procedure;however here let us assume that it is 86 F if a 3 in mineral fiber insulation is used.Heat loss from casing :
q=0.173x0.9x[5.464-5.34]+0.296x(86-70)1.25x(169/69)0.5=30.5 Btu/ft2h (0.9=casing emissivity-see my books for details)
Loss through insulation=0.316x(366-86)/3=29.5 Btu/ft2h,where 0.316 Btu in/ft2hF is the average K value of the insulation
If total surface area of the boiler is say 1000 ft2,then total loss=30,000 Btu/h.In a boiler generating 20,000 lb/h,the duty is about 20 MM Btu/h. Hence the loss=(0.03/20)x100=0.15 %.One may add a margin to this value. 
 

 In the above expressions it is assumed that there is no large amount of loss due to CO formation or incomplete combustion and the total casing,unaccounted loss=1 %. Loss due to CO is:
L=10160xCxCO/(CO+CO2)/HHV,where C=% carbon in fuel,CO,CO2,% volume of the gases. If CO=1000 ppm,CO2=12,C=87%,HHV=19000 Btu/lb, then L=(0.1/12.1)x10160x87/19000=0.38%.Typically CO is is the range of 100-200 ppm in well maintained boilers.Hence the CO loss is very low and generally not computed and is included in the margin.
One could also use the program discussed in  Books,Software on Boilers,HRSGS,Steam Plant Calculations to perform these calculations more accurately.A thumb rule is that a 40 F change in exit gas temperature is equivalent to about 1 % change in efficiency.
ECONOMIZER VS AIR HEATER
Plant engineers should always consider the use of economizers to improve boiler efficiency. As an example,if the stack gas temperature is 550 F in a 100,000 lb/h boiler without an economizer and say 300 F with the economizer,the approximate change in efficiency=(550-300)/40=6.25 % or about 7.5 Mm Btu/h energy savings or about $ 18.75/h based on 2.5 $/MM Btu fuel cost. Even if the economizer costs $ 50,000,the payback is less than 2700 hours! Unfortunately initial cost alone is often considered while making decisions on energy equipment.
Note that air heaters have a few negative aspects compared to economizers as heat recovery equipment: They increase the combustion temperature,which increases NOx formation(not desirable) and the gas/air side pressure drops are significantly higher compared to the economizer,resulting in higher fan power consumption and larger fan size; air-heaters could be more expensive and also occupy more space.Hence the present trend is to use economizers in packaged oil,gas fired steam generators. Air heaters widely were used in designs developed  about 20-50 years ago.They may be required in solid fuel fired boilers to improve the combustion process.

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