Question

For a 10m diameter reactor full of spherical iron beads (r=1.5cm), the minimum height for fluidization is 50m, and the minimum porosity is 0.1. The volumetric flow rate is controlled and kept at 0.5L/s. For which fluids listed below will the reactor act as a packed bed and which will act as a fluidized bed? Assume laminar flow.

Ethylene glycol

Silicone oil

Bromine

Acetone

Answer 1

We will find the minimum fluidisation velocity of the iron beads in each of the fluids and compare it with the velocity (obtained from fixed flowrate of 0.5 L/s)
ρ_iron = 7.87 g/cc

(1) Properties of Ethylene glycol:
ρ_{ethylene glycol} = 1.11 g/cc
µ_{ethylene glycol} = 0.0162 Pa s

(2) Properties of Silicone Oil:
ρ_{silicone oil} = 0.971 g/cc
µ_{silicone oil}= 0.02 Pa s

(3) Properties of Bromine:
ρ_bromine = 3.12 g/cc
µ_bromine = 0.00095 Pa s

(4) Properties of Acetone:
ρ_acetone= 0.784 g/cc
µ_acetone = 0.000316 Pa s

(1) For ethylene glycol:

Using the first equation to find the pressure drop.

ΔP = (7.87-1.11) x 1000 x (1-0.1) x 9.8 x 50
ΔP = 2981160 Pa

Similarly calculating for all the fluids:

Using the second equation to find the minimum fluidisation velocity:
LHS = 2981160/50
= 59623 Pa/m

RHS = ((150 x 0.0162) x V x (1-(0.1))²)/((0.03)2 x (0.1)³) - ((1.75 x 7870 x V2)/(0.03)) x (1-0.1)/(0.1)³
RHS = 2187000 V - 58275000 V²

On solving the quadratic equation:
V = 0.0446 m/s

A generalised equation for all the fluids:
ΔP/50 = (135000000 x µ x V) - (52500 x ρ x V²)

Velocity of fluid in reactor = (0.5 x 10^-3)/((3.14/4) x (10²)) m³/s x 1/m²
V = 6.369 x 10^-6 m/s

Comparing this with the minimum fluidisation velocity, the reactor will act as a packed bed for all the fluids.