Question

A fuel gas containing 75.0 mole% methane and the balance ethane is burned completely with 15.0 % excess air.

The stack gas leaves the furnace at 800.0 °C and is cooled to 450.0 °C in a waste-heat boiler, a heat exchanger in which heat lost by cooling gases is used to produce steam from liquid water for heating, power generation, or process applications.

Taking as a basis of calculation 100.0 mol of the fuel gas fed to the furnace, calculate the amount (magnitude) of heat (MJ) that must be transferred from the gas in the waste heat boiler to accomplish the indicated cooling. Provide your answer to 3 significant figures.

Answer 1

according to question we have 100 moles of fuel gas

75 moles methane & 25 moles of ethane

combustion reaction for methane

CH4+2O2 =>CO2+2H2O

& for ethane it is

C2H6+7/2 O2 ---> 2CO2+3H2O

for 1 mole of methane 2 moles of oxygen is required

so for 75 moles of methane 150 moles of oxyegn is required

& as 1 mole of ethane need 3.5 mole of oxygen

therefore 25 moles of ethane will need 87.5 moles of oxyegen

so total oxygen needed = 150 +87.5= 237.5 moles

so required air = 237.5*100/21 = 1130.952 moles

as we use 15 % excess air

supplied air = 1.15 *1130.952 = 1300.595 moles

therefore composition of stake gas will be

N2 = 0.79*1300.595 =1027.470 (N2 act as inert & mole % of N2 in air is 79%)

O2 =0.15*237.5 = 53.625 (as 15% excess O2 will remain unreacted )

H2O = 2*75+3*25 = 225 moles

(as 1 mole methane produce 2 mol water & for each mole of ethane 3 moles of water )

CO2 = 75+2*25 = 125 moles

(as 1 mole methane produce 1 mol CO2 & for each mole of ethane 2 moles of CO2 )

so from this we can find

Cp mix data as we know mole data we can find mole fractions ,Cp values from reference books & can find heat transfer as

Q = mR (Cp/R)dT

where xi is mole fraction of species i

so mole fraction calculation

for CO2 =mole of CO2/Total moles =125/(125+225+53.625+1027.470) = 125/1431.095 =0.087

for O2 = 53.625/1431.095 = 0.037

for H2O = 225/1431.095 = 0.157

for N2 = 1027.470/1431.095 =0.718