Question

A fuel gas containing methane and ethane is burned with air in a furnace, producing a stack gas at 300 ° C and 105 kPa (absolute). You analyze the stack gas and find that it contains no unburned hydrocarbons, oxygen, or carbon monoxide. You also determine the dew-point temperature.

(a) Estimate the range of possible dew-point temperatures by determining the dew points when the feed is either pure methane or pure ethane.

(b) Estimate the fraction of the feed that is methane if the measured dew-point temperature is 59.5 ° C.

(c) What range of measured dew point temperatures would lead to calculated methane mole fractions within 5% of the value determined in Part (b)?

Answer 1

Basis : 1 mole of mixture

let x= moles of methane,1-x =moles of ethane, a

Combustion reactions are CH4+2O2---->CO2 +2H2O

moles of H2O formed =   2x , moles of CO2 formed = x

for the combustiaon of ethane C2H6+7.5O2---->2CO2 + 3H2O

moles of CO2 formed = 2*(1-x) and moles of H2O formed = 3*(1-x)

Products Contain : CO2= x+2*(1-x)= 2-x, H2O= 2x+3*(1-x)= 3-x

total moles = 2-x+3-x= 5-2x

mole fractions : CO2= (2-x)/ (5-2x) H2O= (3-x)/ (5-2x)

partial pressures : H2O= 101.3*(3-x)/ (5-2x), mole fractions : CO2= (2-x)/ (5-2x)

Vapor pressure of H2O =partial pressure at dew point

x can have a value from a minimum of 0 to maximum of 1. The assumed moles are tabulated and based on that

mole fractions of water are calcualred and partial pressure is calculated.

The data is tabulated.

x( moles of CH4)	Mole fraction H2O	partial pressure of H2O (Kpa)	Partial presure (mmHg)
0	0.090361446	9.487951807	71.21846386
0.1	0.093754041	9.844174318	73.89234126
0.2	0.097683505	10.25676807	76.9893525
0.3	0.102288225	10.74026368	80.61856721
0.4	0.107758621	11.31465517	84.93006466
0.5	0.114364135	12.00823422	90.13620769
0.6	0.122498979	12.86239281	96.54769294
0.7	0.132763796	13.94019857	104.6379185
0.8	0.146121148	15.34272051	115.1655287
0.9	0.164216453	17.24272756	129.4273616
1	0.190114068	19.96197719	149.8385932

the vapor pressure data sugggested the temperature to be from 45 deg.c to 60 deg.c

59.5 deg.c correspond to 0.985 mole fraction CH4.

methane moe fraction = 0.985*0.95 =0.94

the range is 58 to 59.5 deg.c