Design of Packed Tower with Berl Saddle packing

7000 kg/hr of air, at a pressure of 7 atm abs and a temperature of 127oC is to be passed through a cylindrical tower packed with 2.5 cm Berl saddles. The height of the bed is 6 m. What minimum tower diameter is required, if the pressure drop through the bed is not to exceed 500 mm of mercury?
For Berl saddles,
D p = (1.65 x 105 Z Vs1.82 r 1.85 )/Dp1.4
where
D p is the pressure drop in kgf/cm2, Z is the bed height in meter, r is the density in g/cc, Dp is nominal diameter of Berl saddles in cm, Vs is the superficial linear velocity in m/sec.

Data:

Mass flow rate = 7000 kg/hr = 1.944 kg/sec

Height of bed (Z) = 6 m

Dp = 2.5 cm

760 mm Hg = 1 kgf/cm2 = 1 atm

D p = 500 mm Hg = (500/760) x 1 kgf/cm2 = 0.65 kgf/cm2

Formula:

Ideal gas law:

PV = nRT

Formula given,

D p = (1.65 x 105 Z Vs1.82 r 1.85 )/Dp1.4

Calculations:

r = Mn/V = MP/(RT) = 29 x 7 x 1.01325 x 105 / (8314 x (273 + 127) ) = 6.185 kg/m3 = 6.185 x 10-3 g/cc

D p = (1.65 x 105 Z Vs1.82 r 1.85 )/Dp1.4

0.65 = (1.65 x 105 x 6 x Vs1.82 x (6.185 x 10-3 )1.85 ) / 2.51.4

Vs1.82 = 4.603 x 10-5

Vs = 0.029 m/sec.

Volumetric flow rate = mass flow rate/density = 1.944/6.185 = 0.3144 m3/sec

Cross sectional area = Volumetric flow rate / Vs = 0.3144 / 0.029 = 10.84 m2

Required Minimum Diameter (D) = (A x (4/p) )0.5 = (10.84 x 4/p)0.5 = 3.715 m.