A fuel gas containing 95 mole% methane and the balance ethane is burned complete

Question

A fuel gas containing 95 mole% methane and the balance ethane is burned completely with 25% excess air. The stack gas leaves the furnace at 900 degree C and is cooled to 450 degree 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. (a) Taking a basis of calculation of 100 mol of the fuel gas fed to the furnace, calculate the amount of heat (kJ) that must be transferred from the gas in the waste heat boiler to accomplish the indicated cooling. NB/You need to first determine the composition of the stack gas using your material balance skills. (b) How much saturated steam at 50 bar can be produced from boiler feedwater at 40 degree degree for the same basis of calculation? (NB/assume all heat transferred from the gas goes into the steam production). (c) At what rate (in kmol/s) must fuel gas be burned to produce 1280 kg steam/hr in the waste heat boiler? What is the volumetric flow rate (m^3/s) of the gas leaving the boiler? Assume ideal gas. (d) Briefly explain how the waste-heat boiler contributes to the plant profitability (think about what would be required in its absence).

Explanation / Answer

CP/R data ; CO2= 5.457+1.045*10-3T, N2= 3.280+0.593*10-3T, O2= 3.639+0.506*10-3T

H2O= 3.470+1.450*10-3T, R= 8.314 J/mole.K

n= no of moles of gas and CP= speciif heat of gas

CP/R data ; CO2= 5.457+1.045*10-3T, N2= 3.280+0.593*10-3T, O2= 3.639+0.506*10-3T

H2O= 3.470+1.450*10-3T, R= 8.314 J/mole.K

Enthalpy change of CO2= 105*8.314{5.457*(723-1173) + 1.045*10-3*(7232-11732)/2}

=105*8.314*(-2901) =-95661 joules

Enthalpy change of N2= 976*8.314*(3.280*(723-1173) +0.593*10-3*(7232-11732)/2}=-14029696 joules

Enthalpy change of O2= 42.5*8.314*(3.639*(723-1173) +0.506*10-3*(7232-11732)2}=-654893 joules

Enthalpy change of =205*8.314*(3.470*(723-1173)+1.450*10-3(7232-11732)/2}=-3715456 joules

Heat is removed and hence enthalpy change is –ve.

Total enthalpy change= -95661-1402996-654893-3715456 =-5869196 joules=-5869 Kj

Heat than can be extracted during the cooling proces of gas= 5869 Kj

This is the heat produced per 100mols of fuel= 5869/100= 5.869 Kj/mole

Enthalpy of water at 40 deg.c= 167.452 Kj/kg ( from steam table)

Enthalpy of saturated steam at 40 bar =2800 Kj/kg ( from steam table)

Enthalpy difference= 2800-167.452= 2632 Kj/kg

Hence steam that can be prodced= 5689/2632 =2.16 Kg

c) steam to be produced= 1280 kg/hr. Enthalpy required= 1280 Kg/hr*2632 Kj/kg=3368960 Kj/hr=935 Kj/sec

moles/s of fuel required= 935 Kj/sec/ 5.869KJ/mole= 159 moles/sec of fuel.

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