Question

Methane (CH4) gas flows into a combustion chamber at a rate of 200 L/min at 1.50 atm and ambient temperature. Air is added to the chamber at 1.00 atm and the same temperature, and the gases are ignited.

a. To ensure complete combustion of CH4 to CO2(g) and H2O(g), three times as much oxygen as is necessary is reacted. Assuming air is 21 mole percent O2 and 79 mole percent N2, calculate the flow rate of air necessary to deliver the required amount of oxygen.

b. Under the conditions in part a, combustion of methane was not complete as a mixture of CO2(g) and CO(g) was produced. It was determined that 95.0% of the carbon in the exhaust gas was present in CO2. The remained was present as carbon in CO. Calculate the composition of the exhaust gas in terms of mole fraction of CO, CO2, O2, N2 and H2O. Assume CH4 is completely reacted and N2 is unreacted.

Answer 1

a. The reaction for combustion of methane is

CH4 + 2O2 -----> CO2 + 2H2O

1 mol of methane require 2 mol of O2 for combustion

Flow rate of methane is 200L/min at 1.50 atm and requires O2 flow of 600.L/min at 1.00 atm to fully react.

So, three times of O2 is required, which will be 3*600= 1800 L/min

but air has only 21% O2, so required air flow will be= 1800*21/100= 8.57 KL/min

b. one portion of CH4 require 2 part of O2

So, for one portion of CH4, we added in 6 portions of O2, and portion of N2= 6*79/21 = 22.571 portions of N2.

However, as it is given, only 95.0% of the carbon in the exhaust gas was present in CO2. Hence 95% portion of CH4 react with 1.9 portions of O2 to form 95% portion of CO2 and 1.9 portions of H2O. The remaining 5% portion of CH4 will now react with 7.5% portion of O2 to form 5% portion of CO, and 10% portion of H2O.

he resulting gas mixture would contain:
0% portion of CH4
95% portion of CO2
5% portion of CO
(1.9+10%) = 2 portions of H2O
(6-1.9-7.5%) = 4.025 portions of O2
and 22.571 portions of N2

Since there are a total of:
95%+5%+2+4.025+22.571 = 29.596 (portions),

Mole fraction of the components present in the gas are:

CO2: 95%/29.596 = 3.21%
CO: 5%/29.596 = 0.17%
H2O: 200%/29.596 = 6.76%
O2: 4.025/29.596 = 13.60%
N2: 22.571/29.596 = 76.26%