Question

unit operation, introduction to material balance

3) A fuel gas containing 60 mole% methane and the balance ethane is burned completely with 35% excess air. The stack gas leaves the furnace at 700°C and is cooled to 250°C in 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 mol/s of the fuel gas fed to the furnace, calculate the amount of heat (kJ/s) that must be transferred from the gas in the waste heat boiler to accomplish the indicated cooling,

Answer 1

ANSWER :-

GIVEN DATA

Methane gas content in fuel gas = 60%

Ethane gas content in fuel gas = 40%

Percentage of excess air = 35% for ethane

Temperature at inlet = 700' C

Temperature at outlet = 250' C

Basis -100 mol/sec of fuel gas

Reactions taking place

CH, +3.50 - 200 + 3H2O

$CH_{4}+2 O_{2}\rightarrow CO_{2}+2H_{2}O$

Mole of oxygen
02),162 = (60 + 2) + 40+ 3.5)1.3

12 = 302

Mole of nitrogen
-N2 = (1.2)

$n_{N2}=\frac{79}{21} (302)$

$n_{N2}=1139.095$

$n_{CH4}=60$

$n_{C_{2}H_{4}}=40$

In the product gas :-

"Ho = 2(nCHA +3(CHA)

олно = 2(60) + 3(40) = 240

$2n_{_{O_{_{2}}}}=$ -$-2n_{C_{O2}}$$-nH_{2O}$

$n_{o2}=42$

Now,refrence gases at 25' C and 1 atm,CH4 and C2H6 at 25'C and 1 atm

Substance	$n_{in}$	$H_{in}$	$n_{out}$	$H_{out}$
CHH4	60	0	0	0
C2H6	40	0	0	0
O2	302	5.31	42	28.89
N2	1139.095	5.13	1139.095	27.19
H2O	-	0	240	33.32
C02	-	0	140	42.94

$Heat processed Q = \sum [n_{in}H_{in} - n_{out}H_{out}]$

Heat processed = [(42*28.89) +(1139.095*27.19) + (240*33.32)+(140*42.94) - (302*5.31) - (1139.095*5.13)] kJ

Heat processed Q = [(1213.38) +(30971.9930)+(7996.8)+(6011.6) - (1603.62)-(5843.55735)] kJ

Heat processed Q = [(46193.7703) - (7447.17735)] kJ

Heat processed Q = 38746.59295 kJ

For product gases

Substance	$n_{in}$	$H_{in}$	$n_{out}$	$H_{out}$
O2	42	28.89	42	13.375
N2	1139.095	27.19	1139.095	12.695
H2O	240	33.32	240	15.12
CO2	140	42.94	140	18.845

$Heat processed Q = \sum [n_{in}H_{in} - n_{out}H_{out}]$

Heat processed Q = [(42*13.375) +(1139.095*12.695) + (240*15.12)+(140*18.845) - (42*28.89) - (1139.095*27.19) - (240*18.845) - (140*42.94)] kJ

Heat processed Q = [(561.75) +(14460.81102) + (3628.8)+(2638.3) - (1213.38) - (30971.9930) - (4522.8) - (6011.6)] kJ

Heat processed Q = [(21289.6610)-(42719.773) KJ

Heat processed Q = 21430.1120 KJ