A fuel consists of carbon hydrogen sulphur oxygen and noncom

A fuel consists of carbon, hydrogen, sulphur, oxygen and non-combustibles is burnt under excess air conditions. A bomb calorimeter tests shows that the energy content of the fuel is 38.5 MJ/kg and after combustion the mass of ash is 5% of the original mass of the fuel burnt. The exhaust gas yields 14.2% CO_2, 15% H_2 O, 69.5% N_2, 0.3% SO_2 and 1% O_2. Determine; Air-fuel ratio The percentage composition of the fuel The Stoichiometric air-fuel ratio The mass of fuel required per hour for a continuous energy input of 1 MW Mass of ash produced per hour

Solution

Basis : 100 moles of exhaust gas. It contains 14.2moles CO2, 15 moles H2O, 69,5 moles N2, 0.3 moles SO2 and 1%O2

The source of nitrogen is Air and hence moles of air supplied= 69.5/0.79=87.97

Oxygen supplied = 21% of air = 0.21*87.97=18.47 moles

oxygen in the exhaust= 1 mole , total oxygen =18,47+1=19.47 moles

CO2 comes from C of the fuel and the reaction is

C+O2--->CO2

14.2 mole correspond to 14.2 mole of C and14.2 moles of oxygen

Fuel contains 14.2 moles of Carbon that is 14.2*12gm of Carbon = 170.4 gms

there are 15 moles of water and this comes from the reaction H2+1/2O2--->H2O

So moles of oxygen used = 15/2= 7.5 mass of hydrogen in the fuel = 7.5*2=15 gms

there is 0.3 moles of SO2 and this comes from S+O2---> SO2

moles of S in the fuel = 0.3 and mass of Sulfure in the fuel = 0.3*32=9.6 gms

Oxygen consumed for the reaction= 0.3 moles

Total oxygen= 19.47 moles

oxygen used=0.3(SO2)+7.5(H2O)+14.2 =22 moles

theoretical air to be supplied = 22/0.21=104.76 moles= 104.76*29=3038.04 gm

So excess of oxygen= 22-19.47= 2.53 moles

Fuel contains : C= 170.4gm, H= 15gms, S= 9.6gm, O2=2.53*4*16=80.96gm

Total mass of fuel = 170.4+15+9.6+80.96=275.96 gms

composition : C= 100*170.4/275.96 =61.75%, H= 15*100/275.96=5.44%, S= 9.6*100/275.96=3.5%, O2= 100*80.96/275.96=29.33 Ash= 5%

There is 5% ash which correspond to 5%. Hence 95% of fuel = 275.96 gm

100% = 275.96/0.95=290.48gm

air to fuel ratio = 87.97*29/290.48=8.78

theoretical air to fuel ratio = 3038.04/290.48=10.46

1kg of fuel produces 38.5 MJ=38.5*10⁶ joules, 1 Mj= 106 joules/sec

so fuel required= 1Kg/sec= 3600 kg/hr

there is 5% ash in the fuel so 3600kg/hr produces 3600*5/100= 180 kg/hr of ash