PRESSURE DROP IN A PACKED BED AND A FLUIDIZED BED

PURPOSE To determine the relationship between pressure drop and superficial velocity for a packed bed To calculate the minimum fluidization velocity (v¿¿mf )¿ required for fluidization.

THEORYThe upward flow of a fluid through a bed of particles give rise to a fixed bed (packed bed) at low flow rates; but, if the velocity is sufficiently great, the particles will be freely supported in the fluid to give rise to a fluidized bed.

The forces acting on the particles in the bed are its own weight, buoyancy force and the drag force. At the start of fluidization, the (weight - buoyancy) force is equal to the drag force. For a fixed bed, the Ergun’s equation is applicable. It is as follows:

∆ P=sL(1−ε )

ε3 [kμs (1−ε ) v+k ' ρf v2 ] (1)

Where:

∆ P=Pressure drop

ρ f=Fluid density

ρ s=Particle density

μ=Viscosity of the fluid

v=Fluid velocity

ε=Voidage

s=Specific surfacearea of particles

L=Height of bed

k=15036

k '=1.756

For Laminar or stream line flow

∆ P=15036

(1−ε)2

ε3 s2 Lμv (2)

log ∆ P=logv+ log [15036

(1−ε )2

ε3 s2 Lμ] (3)

For Turbulent flow

∆ P=1.756

(1−ε)ε3 sL ρf v2

(4)

log ∆ P=2logv+log [ 1.756

(1−ε )ε3 sL ρ f ] (5)

Thus a plot of ∆ P vs. v on a log - log paper should be linear with a gradient of 1 for laminar flow and 2 for turbulent flow, and provides a method to determine the flow type.

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Ergun's equation could also be applied at the start of fluidization. When applied for spherical particles at minimum fluidization, the equation (1) can be modified as follows by applying

s= AV

=

4 π d2

443

π ( d3

8)=6

d

∆ Pmf=(1−εmf )

ε mf3

Ld [150 μ

(1−εmf )d

. vmf +1.75 ρ f vmf2 ] (6)

Where,

d=particle diameter

suffix(mf )=Minimum fluidizationcondition

For the flow of fluid through the bed; ∆ P vs. v on a log - log plot takes the following form:

PROCEDURE1. Check all pipe connections. 2. Check whether the appropriate orifice plate is placed on the orifice plate flow-measuring

instrument.3. Check water levels in the manometer.4. Feed the material into the packed bed/fluidized chamber. 5. Switch on the blower by inserting the 'plug to the holder. 6. Measure

a. Pressure drop across the orifice plate. b. Pressure drop across the bed with material. c. Fixed bed height at packed bed experiments and varying bed height at fluidization.

7. Take the above readings for various air flow rates. 8. Stop the blower by removing the plug. 9. Remove the material from the packed/fluidized chamber. 10. Start the blower and for the same airflow rates (note: to the same pressure drop values across the

orifice plate) measure the pressure drop across the perforated bottom plate of the bed (without material).

11. Stop blower.

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12. Measure the essential dimensions of the packed/fluidized bed. 13. Note the orifice plate diameter. 14. Measure the density and voidage of the particles used in fixed bed experiments.

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CALCULATIONS

1. Calculate the superficial velocity v corresponding to each ∆P of orifice from the following equations and tabulate in Table 2.

Volumetric flow rate Q=Cd A0 v0=Abed v (7)

Where,

A0=Area of the orifice

v0=Velocity of fluid through the orifice

Abed=Areaof the packed bed / fluidized chamber

v=Superficial velocity

Cd=Coefficient of discharge

From Bernoulli’s equation

v0=√2 gh (8)

Superficial velocity v=Cd

A0

Abed √ 2 ∆ Porifice

ρf

(9)

2. Calculate ∆ Pbed.

∆ Pbed=∆ PTotal−∆ PEmpty (10)

Table 01

Superficial velocity v

(ms-1)

∆Pbed(mmH2O) ∆Pbed(Nm-2) Packed bed Fluidized bed Packed bed Fluidized bed

3. Plot log ∆Pbed vs. log v for packed bed and fluidized conditions on log-log paper.

4. Calculate the gradient of the graph of packed bed and find out the flow condition.5. Calculate the density (ρ s¿ and voidage (ε ) of particles used in packed bed experiments.

ρ s=mass of 100 particles

volume of 100 particles

ε=

AL−Wρs

AL

6. Find the minimum fluidization velocity (v¿¿mf )¿ of the fluidized bed from the graph5

Coursework guide 1. Title page

2. Introduction

3. Procedure

4. Observation sheet

5. Calculation

6. Discussion

a. What are packed beds and fluidized beds?

b. Brief explanation on ‘what’s happening inside a packed / fluidized bed’

in a chemical engineer’s point of view.

c. Industrial applications of packed and fluidized beds. (Not a general unit

operation or a process. Specify)

d. What you learn from the practical.

e. Analysis of results (Example: what would be the cause for the hump in

the graph of log ∆Pbed vs. log v)

f. Experimental errors and suggestions to minimize those errors.

g. Improvements that you suggest for the practical, if any.

7. References (use standard methods)

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