Combustion Calculations for air and Turbine Exhaust Gas

SIMPLIFIED COMBUSTION CALCULATIONS for Air or Gas Turbine Exhaust: V.Ganapathy

This article reviews a simple approach namely the MM Btu method to evaluate combustion air needs in steam generators and the oxygen consumption in gas turbine HRSGs. The advantage is that no deatiled calculations are required.

MM Btu method of combustion
It can be shown that each fuel such as oil,gas or coal requires approximately a fixed amount of air for complete combustion on a Million Btu(HHV)basis.This quantity does not change much with fuel analysis for practical purposes. From fundementals,for solid fuels and oil,the dry stochiometric air wa required for combustion can be shown to be:
wa=11.53C+34.34(H₂-O₂/8)+4.29S where C,H₂,S,O₂ are carbon,hydrogen,sulfur and oxygen in the fuel,fraction by weight. For gaseos fuels,where the analysis is on weight fractions,wa is given by:
wa=2.47CO+34.34H₂+17.265CH₄+13.3C₂H₂+14.81C₂H₄+16.12C₂H₆-4.32O₂
We can show for a wide variety of fuels with different analysis,the air required on a MM Btu basis falls closely within a small range.This value,C,is shown in Table below,which also shows how C was obtained.

Example 1
Let us calculate the amount of air per Mm Btu fired for fuel oil. Let C=87.5,H=.125 and deg API=28,a typical # 2 fuel oil.
HHV is obtained from the formula: HHV=17887+57.5xdeg API-102.2S,where S=%sulfur.
HHV=17887+57.5x28-102.2x0=19497 Btu/lb
Amount of theoretical dry air in lb/lb fuel from above is:
wa=11.53x0.875+34.34x0.125=14.38 lb/lb fuel.
1 MM Btu fuel fired requires (1x10⁶/19497)=51.28 lb fuel
Hence air required for 1 MM Btu fuel=51.28x14.38=737 lb
Example 2
Take the case of natural gas with a volumetric fuel analysis:CH₄=83.4,C₂H₆=15.8,N₂=0.8
Converting to weight basis:% CH₄=83.4x16/(83.4x16+15.8x30+.8x28)=72.89
similarly,C₂H₆=25.89 and N₂=1.22.
Using the above formula,wa=17.265x0.7289+16.12x0.2589=16.75 lb/lb fuel
HHV =0.7289x23876+0.2589x22320=23,181 Btu/lb. Combustion constants 23,876 and 22,320 were taken from tables available in books.
The amount of fuel equivalent to 1 Mm Btu fired=1x106/23181=43.1 lb and air required for this amount=43.1x16.75=722 lb.
Example 3
Take the case of 100% propane. 1 lb fuel requires 15.7 lb air from fundementals. 1 MM Btu fired has 1x106/21661=46.17 lb of propane. hence 1 MM Btu fired requires =46.17x15.7=725 lb air.

Table of combustion constants C
Blast furnace gas         575
Bagasse                      650
CO gas                        670
Refinery and oil gas      720
Natural gas                  730
Furnace oil and lignite   745-750
Bituminous coals          760
Anthracite                    780
Coke                            800

C is air required in lb/MM Btu(HHV)

Gas Turbine Exhaust combustion
Let Wg=gas turbine exhaust flow,lb/h containing O% volume of oxygen.Let Q=amount of fuel fired in MM Btu/h on LHV basis to raise the exhaust gas temperature.If A is the amount of air required to do this,the equivalent amount of air in the exhaust gas is from fundementals:
A=Wgx100xOx32/(23x100x29.5) where 32 ,29.5 are the molecular weights of oxygen and exhaust gas.The amount of fuel that can be fired using A lb of air from MM Btu method is:
Wf=Ax10⁶/(CxHHV) lb/h
The fuel input Q =WfxLHV Btu/h=Ax10⁶/(CxHHV)xLHV
Substituting for A from above,we have Q=Wgx100xOx32x106xLHV/(23x100x29.5xCxHHV).The ratio LHV/(CxHHV)=0.00124 for both natural gas and fuel oils. Hence,simplifying,we have:
Q=58.4WgO
This is a very important equation relating gas turbine exhaust gas oxygen and fuel input on LHV basis. For example,to raise 150,000 lb/h of exhaust gas from 900 F to 1400 F requires Q=150,000x0.3x500=22.5 MM Btu/h approximately. To estimate the amount of oxygen consumed in this process,use above equation. Q=58.4x150,000xO or O=2.6 %voume. That is,only 2.6 % volume of oxygen is consumed. Typical exhaust gases contain 14-15 % oxygen by volume. Hence a large amount of fuel can be fired raising the gas temperature to as high as 2500-3000 F. For some fuels,some amount of augmenting air may be required.Check with the burner supplier.
More accurate combustion calculations in steam generators and gas turbine Hrsgs may be performed using the programs described at the web page below.

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