Your boss asks you to calculate the flow through a natural gas pipeline. Since i

Question

Your boss asks you to calculate the flow through a natural gas pipeline. Since it is 26 inches inner diameter, it is impossible to run the gas through any kind of meter or measuring device. You decide to add 100 lb of CO2 per minute to the gas through a small ½ in. piece of pipe, collect samples of the gas downstream, and analyze them for CO2. Several consecutive samples after 1 hour are:

1hr, 0 min: 2.0 % CO2

1hr, 10 min: 2.2 % CO2

1 hr 20 min: 1.9 % CO2

1 hr 30 min: 2.1 % CO2

1 hr 40 min: 2.0 % CO2

a)      Calculate the flow of gas in pounds per minute at the point of injection if the gas upstream of the point of injection is 100% CH4.

b)      Unfortunately for you, the gas upstream of the point of injection of CO2 already contained 1.0 % CO2. How much was your original flow estimate in error (in percent).

Explanation / Answer

Calculate the flow of gas in pounds per minute at the point of injection. (thenatural gas is all methane, CH4)

Solution

Assume

yUCO2 = with yUCH4 1.00

basis 1 min

C in kgmol/min

C=100lb/min= 100 kg/2.2046 min *1 kgmol/44kg

=1.031 kgmol Co2/ min

Average yDCO2=0.020

C-D yDCO2 =0

D= C/ yDCO2 =1.031 /0.0204 =50.53 kgmol/min

Overall balance to get U

U+C=D

U=D-C= 50.53 -1.03 = 49.50 kgmol/min

U= 49.50 kgmol/min *16.04 49.50 kg /Kgmol *2.204 6lb/1 kg =

= 1751 lb/min----answer

================================

Unfortunately for you, the gas upstream of the point of injection of CO2 alreadycontained 1.0 percent CO2. How much was your original flow estimate in error(in percent)?

Solution

Correction

Yuco2 =0.01

And

yUCH4=0.99

yDCO2=0.0204

yDCH4=0.9796

Balance on co2

UYuco2 + DYuco2 =0

Balance on ch4

UyUCH4 - DyDCH4=0

BY PLUGGING VALYE

U=C/ (UyUCH4 / DyDCH4 (UYuco2 - DYuco2)

=1.039 Kgmol /0.99/0.997%(0.0204-0.01)

=97.10 kgmol/min

U=3434 lb/im

% error=(3434-1751) /3434 =49%-answer

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