Question

A process stream flowing at 35 kmol/h contains 15 mole% H2 and the remainder 1-butene. The stream pressure is 10.0 atm absolute, the temperature is 50 oC and the velocity is 150 m/min. Determine the diameter (cm) of the pipe transporting this stream, using Kay’s rule in your calculations.

Answer 1

To find pipe diameter we should know volumetric flow rate and velocity.

We can find volumetric flow rate by PV= ZnRT

P - Pressure = 10 atm = 1013.25 kPa

V - Volumetric flow

Z - Compressibility factor

n - molar flow = 35 kmol/hr = 0.00972 kmol/s

T - temperature = 50 °C = 323.15 K

R - gas constant = 8.314 kJ/kmol K

Z can be calculated from compressibility factor chart relating , Z, P_r and T_r

P_r - reduced Pressure, T_r - reduced temperature

P_r = P/P_c and T_r = T/T_c

For a mixture, kays rule

_Pc^' = y1*P_c1 + y₂*P_c2

T_c^' = y1*T_c1 + y₂*T_c2

y₁ - mole fraction of H₂

y2 - mole fraction of Butene

T_c1 - Critical temperature of hydrogen = 33.15 K

_Pc1 - Critical pressure of hydrogen = 1300 kPa

T_c2 - Critical temperature of butene = 419.29 K

_Pc2 - Critical pressure of butene = 40050 kPa

given y₁ = 0.15 y₂ = 0.85

P_c^' = (0.15*1300)+(0.85*40050)

P_c^'= 34237 kPa

_Tc^' = (0.15*33.15)+(0.85*419.29)

T_c^' = 361.369 K

P_r = P/P_c^'

= 1013.25/34237

=0.03

T_r = T/T_c^'

= 323.15/361.369

=0.9

From compressibility chart, for P_r = 0.03 and T_r = 0.9 , Z value is approximately 1

V = ZnRT/P

= 1*0.00972*8.314*323.15/1013.25

= 0.026 m³/s

velocity v = 150 m/min

= 150/60

=2.5 m/s

Flow area A = V/v = 0.026/2.5

=0.0104 m²

Diameter = (4A/3.14)^0.5 *100

Diameter = 11.5 cm