Question

A fuel gas produced by gasifying coal is to be burned with 20% excess air. The gas contains 50.0 mole % nitrogen and the balance carbon monoxide and hydrogen. A sample of the gas is passed through an infrared spectrometer, which registers a signal R that depends on the mole fraction of carbon monoxide in the sample, and a reading R 38:3 is recorded.  Analyzer calibration data are as follows:

x (mol CO/mol)	0.05	0.10	0.40	0.80	1.00
R	10.0	17.0	49.4	73.6	99.7

A power law (x = aRb ) should be suitable for fitting the calibration data. Derive the equation relating x and R (use a graphical method), and then calculate the molar flow rate of air required for a fuel feed rate of 175 kmol/h, assuming that CO and H2 are oxidized but N2 is not.

Answer 1

the plot is drawn and shown below. Best fit is straight line

x=0.011R-0.094

for R= 38.3

x= 0.011*38.3-0.094=0.3273

tihs is the mole fraction of CO.

mole fraction of CO =0.3273

Mole fraction N2= 0.5, mole fraction H2= 1-0.3273-0.50=0.1727

Fuel flow rate =175 kmol/hr, Feed components flow rates H2= 0.1727*175=30.22 kmol/hr, CO= 0.3273*175=57.28 kmol/hr, N2= 0.5*175= 87.5 kmol/hr

Combustion reactions are

CO+1/2O2--->CO2, moles of oxygen required = 57.28/2 =28.64 Kmol/hr H2+0.5O2---> H2O, moles of O2 required= 30.22/2= 15.11 kmol/hr

total oxygen to be supplied= 28.64+15.11 =43.75 kmol/hr

Air contains 21%O2 and 79%N2. Air to be supplied = 43.75/0.21=208.33 kmol/hr

Air is suplied 20%excess, air flow rate = 208.33*1.2 =250 kmol/hr

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