Question

Methane is flowing in a pipeline at a target rate of 20.7 m3/min at 30°C and 250 kPa. To check the flow rate, He is introduced at 25°C and 300 kPa. How many cubic centimeters per minute of He must be added if the minimum detectable concentration of He downstream of the injection point is 10 ppm?

I dont understand what "minimum detectable concentration of He downstream of the injection point" means?

Answer 1

moles of Methane entering = PV/RT

P= 250 Kpa= 2.467 atm V= 20.7 m3/hr =20.7*1000 L/ min=20700 L/min and T= 30 deg.c =30+273.15= 303.15K

R= 0.08206 L.atm/mole.K

n= 2.467*20.7*1000/(0.08206*303.15)=2052.82 moles/min

Mass of CH4= 2052.82*16 ( Moles*Molecular weight)=32845 gm/min

let the volumetric flow rate of helium = V L/min

300kpa= 300/101.3 atm= 2.96atm T= 25 deg.c= 25+273.15 K=298.15K

n1= moles of helium= 2.96*V/ (298.15*0.08206)=0.121V

Mass of helium = 4*0.121V= 0.482V

Mass of mixture= 32845+0.482V

Mass of heliu/mass of mixture = 0.482V/ (32845+0.482V) =10/10⁶ =10^-5

0.482V =10^-5*(32845+0.482V)

0.482V= 0.32845+10-5*0.482V

0.482*(1-10^-5)V= 0.32845

0.482V= 0.32845

V= 0.32845/0.482=0.68 L/min=0.68*1000cm3/min=680cm3/min