Montgomery Burns is injecting Carbon Dioxide into the atmosphere on a cold winte

Question

1. Montgomery Burns is injecting Carbon Dioxide into the atmosphere on a cold winter day in an attempt to make the climate of Springfield sub-tropical. The CO2 enters the pipe at a pressure of 3MPa and 225 C and leaves the pipe at the same pressure but at 175 C. The mass flow rate of the gas is constant at 2 kg/s.

1. Determine the density of the gas and the volumetric flow rate at the INLET using bot the ideal gas relation AND the generalized compressibility chart Calculate the % error between the two values
2. Determine the volumetric flow rate at the OUTLET using both the ideal gas relation and the generalized compressibility chart.

Explanation / Answer

At the inlet :

P = 3MPA = 3*106 Pa

T = 225+273 = 498 K

Using the ideal gas equation : PV = (m/M)RT

PM = dRT , here M is molecular mass of CO2 = 44 g = 0.044 kg, d is density

Putting values we get : 3*106*0.044 = d*8.314*498

d = 31.88 kg/m3

Volumetric flow rate = mass flow rate/density = 2/31.88 = 0.0627 m3/s

Critical temperature Tc = 31.1'C = 304.1 K

Critical pressure Pc = 7.38 MPa = 7.38*106 Pa

Thus, Reduced temperature, Tr = T/Tc = 498/304.1 = 1.63 , Reduced pressure , Pr = P/Pc = 3/7.38 = 0.41

From the general compressibility chart we have : Z = 0.97 for these values of Tr and Pr

Now, using equation, PV = Z(m/M)RT , we have :

d' = 32.87 kg/m3

Thus, % error = (32.87-31.88)/31.88 * 100 = 0.097%

Volumetric flow rate = 2/32.87 = 0.0608 m3/s

Thus, % error = (0.0627-0.0608)/0.0627 * 100 = 3.03%

At the outlet :

P = 3MPA = 3*106 Pa

T = 175+273 = 448 K

Using the ideal gas equation : PV = (m/M)RT

Putting values we get : 3*106*0.044 = d*8.314*448

d = 35.43 kg/m3

Volumetric flow rate = mass flow rate/density = 2/35.43 = 0.0564 m3/s

Critical temperature Tc = 31.1'C = 304.1 K

Critical pressure Pc = 7.38 MPa = 7.38*106 Pa

Thus, Reduced temperature, Tr = T/Tc = 448/304.1 = 1.473 , Reduced pressure , Pr = P/Pc = 3/7.38 = 0.41

From the general compressibility chart we have : Z = 0.960 for these values of Tr and Pr

Now, using equation, PV = Z(m/M)RT , we have :

d' = 36.88 kg/m3

Thus, volumetric flow rate = 2/36.88 = 0.0542 m3/s

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