Question

300% excess air having a dry bulb temperature of 25 degree celsius and relative humidity of 60% is used to fully combust 1 kg/hr of methane in a boiler and the heat of reaction is used to generate steam. Hot water enters the boiler as a saturated liquid at 102 degree celsius and leaves as superheated at 40 bar and 400 degree celsius.

The combusted gases leave the boiler at 450 degree celsius and are then cooled to 25 degree celsius causing some of the water in the gas to condense.

Assuptions:

The combustion reaction takes place at 450 degree celsius.

The combusted gases can be assumed to have the properties of air.

The heat capacity of air can be assumed constant at an average temperature of 225 degree celsius.

so, what is the moisture content of the incoming air on a dry basis? and how much energy is transferred during the cooling of the combusted gases?

Answer 1

1. Let Mw be the moisture content of incomming air on wet basis which is essentially the Relative Humidity (60%) ; Mw =60%

Moisture content of incomming air on dry basis (Md) = Mw * 100 / (100 - Mw) = 150%

2. Basis : 1 kg/hr of Methane entering the boiler. The reaction for complete combustion is

CH4 + 2O2 = CO2 + 2 H2O.

OR

16 kg/hr CH4 + 64 kg/hr O2 = 44 kg/hr CO2 + 36 kg/hr H2O

Now CH4 entering the boiler is 1 kg/hr and hence the mass balance of each reaction and product shall be

1 kg/hr CH4 + 4 kg/hr O2 = 2.75 kg/hr CO2 + 2.25 kg/hr H2O.

Therefore Theoritical O2 required for burning 1kg/hr of CH4 = 4 kg/hr

Mass fraction of O2 in air = 0.23

Theoritical Air required for complete combustion of 1kg/hr of CH4 = 4/0.23 = 17.4 kg/hr

Nitrogen present in Theoritical air = N= 17.4* 0.77 kg/hr = 13.4 kg/hr

Actual air supplied = % excess air * Theoritical air required for complete combustion/100 = 300*17.4/100 = 52.2 kg/hr

Excess air supplied =E= (Actual - Theoritical ) = 52.2-17.4 = 34.8 kg/hr

Mass flow of products (CO2 + H2O) for 1 kg/hr of CH4 = M= 5 kg/hr ( as per above stochiometry)

Total mass flow of the combustion gases at the outlet of boiler = m = (excess air + Mass flow of products for 1 kg/hr of CH4 burnt) + Inert Nitrogen in theoritical air (N) = E+M+N = 53.2 kg/hr.

Assumption: The Cp of air is assumed to be 1.03 kJ/kg K at an average temperature of 225 deg C. (From Perry handbook)

Inlet temperature of Hot gas = T1 = 450 deg C

Inlet temperature of Hot gas = T2 = 25 deg C

Energy transfer during cooling of combustion gas = m Cp (T1-T2) = 23277 kJ/hr