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

Basis: 100 mol feed (75 mole CH₄ and 25 mole C₂H₆)

Reaction: CH₄+2O₂ CO₂+2H₂O and C₂H₆+ 7/2 O₂ 2CO₂+3H₂O

Number of moles of oxygen when 15% excess air is used is

Amount of gases leaving the furnance at 800⁰C is

O₂: 273.125-(75*2)-(25*3.5)= 35.625 mol O₂

N₂: 3.76*273.125= 1026.95 mol N₂

CO₂: 75+(25*2)= 125 mol CO₂

H₂O: (75*2)+(25*3)= 225 mol H₂O

Obtain the enthalpy from Specific Enthalpies of Selected Gases Table.

Specific enthalpies at 800⁰C is

_O2,800=25.35 kJ/mol

_N2,800=23.86 kJ/mol

_CO2,800=37.36 kJ/mol

_H2O,800=29.05 kJ/mol

For specific enthalpies at 450⁰C, interpolate the values between 400⁰C and 500⁰C

Specific enthalpy of O₂: At 400⁰C, it is 11.72 kJ/mol and at 500⁰C, it is 15.03 kJ/mol.

_O2,450=13.375 kJ/mol

Specific enthalpy of N₂: At 400⁰C, it is 11.15 kJ/mol and at 500⁰C, it is 14.24 kJ/mol.

_N2,450=12.695 kJ/mol

Specific enthalpy of CO₂: At 400⁰C, it is 16.35 kJ/mol and at 500⁰C, it is 21.34 kJ/mol.

_CO2,450=18.845 kJ/mol

Specific enthalpy of H₂O: At 400⁰C, it is 13.23 kJ/mol and at 500⁰C, it is 17.01 kJ/mol.

_H2O,450=15.12 kJ/mol

Energy balance is

Amount of heat transferred from the gas, Q is

where n is the Number of moles of each gas

Therefore, the magnitude of amount of heat that must be transferred to achieve the required cooling is Q=17.341 MJ