EXPERIMENT 8: FIXED AND FLUIDIZED BED
OBJECTIVES
The objectives of this experiment are to determine the pressure drop through the fixed and fluidized
bed for air and water systems, to verify the Kozeny-Carman equation, and to observe the onset of
fluidization.
THEORY
Fixed and fluidized beds are used in many chemical engineering processes such as ion exchange,
drying, catalytic reactions, combustion, etc. In these processes, liquids or gases flow through beds
of solid particles. When a fluid is passed at a very low velocity up through a bed of solid particles,
the particles do not move. This is the fixed bed position and in this case, the pressure drop is
calculated by the Ergun equation.
∆𝑃 𝐷𝑝
𝜀3
(1 − 𝜀)
= 150
+ 1.75
2
𝐿 𝜌(𝑉𝑠𝑚 ) (1 − 𝜀)
𝑅𝑒
𝐷𝑝 = equivalent spherical diameter of the particle (μ)
𝐿 = height of the bed (m)
𝜌 = density of the fluid (kg·m-3)
𝜇 = dynamic viscosity of the fluid (N·s·m-2)
𝑄
𝑉𝑠𝑚 = superficial velocity (m·s-1) (𝑉𝑠𝑚 = 𝐴 where 𝑄 is the volumetric flow rate of the fluid and 𝐴
is the cross-sectional area of the bed).
𝑀𝑎𝑠𝑠 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠
𝜀 = bed voidage = 1-: 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑥 𝑇𝑜𝑡𝑎𝑙 𝐵𝑒𝑑 𝑉𝑜𝑙𝑢𝑚𝑒
𝐷𝑝 𝑉𝑠𝑚 𝜌
𝑅𝑒=Reynolds’ number based on superficial velocity=
𝜇
At low Re values (Re/(1-ε) < 10), where the viscous forces are more important, the Ergun equation
can be written to be
∆𝑃 𝐷𝑝
𝜀3
(1 − 𝜀)
= 150
2
𝐿 𝜌(𝑉𝑠𝑚 ) (1 − 𝜀)
𝑅𝑒
This equation is called the Kozeny-Carman equation.
At high Re values (Re/(1-ε)≥1000), where the viscous forces are negligible and inertial forces are
dominant, the Ergun equation is written to be
∆𝑃 𝐷𝑝
𝜀3
= 1.75
𝐿 𝜌(𝑉𝑠𝑚 )2 (1 − 𝜀)
This equation is called the Burke-Plummer equation.
If the fluid velocity is steadily increased, the pressure drop, and the drag on individual particles
increase, and eventually the particles start to move and become suspended in the fluid. The more
force is applied to the particles, the less gravitational forces between the particles. The terms
fluidization and fluidized bed are used to describe the conditions of fully suspended particles since
the suspension behaves as a dense fluid. The pressure drop across the bed, ∆𝑃, at fluidization equal
to the weight of the bed per unit area of cross-section and can be found using the following
equation:
∆𝑃 = 𝑔(1 − 𝜀)(𝜌𝑝 − 𝜌)𝐿
𝑔 = gravitational acceleration=9.81 N·m-2
𝜌𝑝 = particle density (kg·m-3)
Consider a vertical tube partly filled with a fine granular material, shown in Figure 1. The top of
the tube is open and there is a porous plate at the bottom to support the granular material and to
distribute the flow uniformly over the entire cross-section. Air is admitted below the distributor
plate at a low flow rate and passes upward through the bed without causing any particle motion. If
the particles are small enough, the flow between the particles becomes laminar and the pressure
drop across the bed is directly proportional to the superficial velocity. As the velocity is increased
gradually, the pressure drop also increases, but the particles do not move and the bed height
remains the same. At a certain velocity, the pressure drop across the bed counterbalances the force
of gravity on the particles or the weight of the bed, and any further increase in velocity causes the
particles to move. This is shown with point A in Figure 1. Sometimes the bed expands slightly
with the grains still in contact since just a slight increase in 𝜀 can offset an increase of several
percent in superficial velocity and keep ∆𝑃 constant. With a further increase in velocity, the
particles become separated enough to move about in the bed, and true fluidization begins (point
B). Once the bed is fluidized, the pressure drop across the bed remains constant but the bed height
continues to increase with increasing flow. If the flow rate of the fluidized bed is gradually reduced,
the pressure drop remains constant and the bed height decreases. The line BC was observed as a
result of increasing the speed. However, the final bed height may be greater than the initial value
for the fixed bed, since solids dumped in a tube tend to pack more tightly than solids slowly settling
from a fluidized state. The pressure drop at low velocities is then less than in the original fixed
bed.
Figure 1. Pressure drop and bed height vs. superficial velocity for a bed of solids.
EXPERIMENTAL SET-UP
The Armfield CEL Fixed and Fluidised Bed apparatus shown in Figure 2 facilitates the study of
flow through fixed and fluidized particle beds. The apparatus consists of two clear acrylic
cylindrical columns for air and water, each column diameter 50 mm and height 550 mm with
sintered bronze bed plates. Separate manometers are provided for measurement of bed pressure
drop in the columns. Water is circulated from a sump tank through a control valve and variable
area flowmeter to the appropriate column by a pump. An overflow returns the water to the sump
tank. Air supply to the second column by diaphragm pump via a bypass control valve and variable
area flow meter. Air is discharged to the atmosphere.
Figure 2. Armfield CEL Fixed and Fluidized Bed apparatus
EXPERIMENTAL PROCEDURE
Be sure that the unit is connected to the electrical supply.
For air system

The test column is filled to a height of 165 mm with the fine grade of ballotini (267
microns).

Check that the value read on the manometer is zero, if not, it is set to be zero.

Start the compressor.

Adjust the airflow control valve to give a flow rate of 1 L/min and wait until the pressure
drop stabilizes. When stabilized, record pressure drop, and bed height.

Increase the airflow rate with increments of 1 L/min up to 14 L/min and following the
stabilization period record the pressure drop, bed height, and bed state for each flow rate.

Decrease the airflow rate to 1 L/min with the same increments suggested above and record
the pressure drop, bed height, and bed state for each flow rate.

Close the airflow control valve.

Stop the compressor.
For the water system

The test column is filled to a height of 335 mm with the coarse grade of ballotini (485
microns)

Check that the value read on the manometer is zero, if not, it is set to be zero.

Turn on the water pump.

Adjust the water flow control valve to give a flow rate of 0.1 L/min and wait until the
pressure drop stabilizes. When stabilized, record pressure drop, and bed height.

Increase the water flow rate with increments of 0.1 L/min up to 0.9 L/min and following
the stabilization period record the pressure drop, bed height, and bed state for each flow
rate.

Decrease the water flow rate to 0.1 L/min with the same increments suggested above and
record the pressure drop, bed height, and bed state for each flow rate.

Close the water flow control valve.

Turn off the water pump.

Determine particle density by weighing a known volume of the ballotini.
RESULTS AND CALCULATIONS

The table below should be filled in for each experiment set.
Flow rate (L/min) Bed Pressure Drop (mm H2O) Bed Height (mm) Bed State

Calculate the pressure drop (mm H2O) for both increasing and decreasing airflow rates.

Calculate the pressure drop (mm H2O) for both increasing and decreasing water flow rates.

Plot the pressure drop (mm H2O) versus air velocity (cm/s) curve for both increasing and
decreasing airflow rates.

Plot the pressure drop (mm H2O) versus water velocity (cm/s) curve for both increasing
and decreasing water flow rates.

Plot the variation of bed height against the air velocity.

Plot the variation of bed height against the water velocity.

Determine the minimum fluidization velocity by using the experimental data for air and
water systems.

Calculate the theoretical minimum fluidization velocity for air and water systems.
DISCUSSIONS

Comment on the variation of bed pressure drop against the velocity for air and water
systems.

Comment on the variation of bed height against the velocity for air and water systems.

Compare the theoretical minimum fluidization velocity with the experimental one for
water and air systems and discuss your findings.
REFERENCES
Armfield Limited Engineering Teaching and Research Equipment Instruction Manual, Fixed,
and Fluidised Bed Apparatus, 1997.
Daugherty L. R., Fluid Mechanics for Engineering Applications, McGraw-Hill, 1989.
De Nevers N., Fluid Mechanics for Chemical Engineering, Mc Graw-Hill, 1991.
Geankoplis J. C., Transport Processes and Unit Operations, Prentice-Hall Inc., New Jersey, USA
1993.
McCabe L.W., Smith C. J., Harriot P., Unit Operations of Chemical Engineering, McGraw-Hill,
New York, 2001.