ABSTRACT
In the Experiment 1.1. Fixed & Fluidized Bed the aim is to study on the fluidization in a gas-solid
system. Bed heights and pressure drops are observed at different air flow rates for this purpose. It
is observed that, when flow rate of air is increased the movement of particles begins after a while,
that is minimum fluidization velocity, and also bubbling in the bed is seen. In the result part,
pressure difference versus fluidization velocity graphs and bed height versus fluidization velocity
graphs are plotted. From the graphs, minimum fluidization velocity at which pressure drop nearly
becomes stable for forward direction is recorded as 10.2 cm/s while this value is 11.3 cm/s for
backward direction. Yet, minimum fluidization velocity is founded as 11 cm/s experimentally.
Moreover, assuming єmf equals to 0.4 and the flow is laminar, that is Rep < 20, minimum
fluidization velocity is calculated as 16.0 cm/s by Ergun equation. After calculation, it is proved
that the assumption of Reynold’s number of the particle is valid. Also, it is founded as 11.4 cm/s
using Yu & Wen equation with ±34% standard deviation [2].
1
Table of Contents
ABSTRACT......................................................................................................................................i
1.
INTRODUCTON......................................................................................................................1
2.
EXPERIMENTAL METHOD..................................................................................................4
2.1
Experimental Set-up..........................................................................................................4
2.2. Experimental Procedure........................................................................................................4
3.
RESULTS AND DISCUSSION................................................................................................5
4.
CONCLUSION.......................................................................................................................10
5.
REFERENCE..........................................................................................................................11
6.
APPENDIX.............................................................................................................................12
2
1. INTRODUCTON
When a liquid or gas passed at very low velocity up through a bed of solid particles, the particles
do not move, and the pressure drop is given by the Ergun 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 terms fluidization and fluidized
bed are used to describe the condition of fully suspended particles, since the suspension behaves
as a dense fluid [1]. When a packed bed of particles is subjected to a sufficient high upward flow
of fluid (gas or liquid) the weight of the particles is supported by the drag force exerted by the
fluid on the particles and the particles become freely suspended or fluidized.
When a bed of solids is kept suspended by fluid up flow, the bed can behave in various ways.
Figure 1.1 is an illustration of the stages of fluidization.
Figure 1.1 Stages of Fluidization
At very low flow rates channeling is observed since the fluid passes between the particles
through the interstices and the flow is not be distributed across the bed. In this condition, the
bed is called as fixed bed. It can be said that fixed beds are poor from the point of view of the
fluid/ solid contact. As the flow rate increases, force exerted by the fluid on the particles
becomes sufficient to lift the particle from the bed and to separate it from its neighbors. In this
condition, state is the incipient fluidization and the bed is called “fluidized bed”. Solid/ fluid
contact is improved in this state since all solid surfaces are available to the fluid.
1
As flow rate is increased more, bed goes to third stage, bubbling fluidization. This stage gives
good surface area between the solid and fluid. Particles will also show a similar effect of
bubbling water. Further increase of flow rate will give much more bubbling effects, which is
known as slugging. This stage forms bubbles through the diameter of bed, they move up like
a piston. Both the slugging and channeling stages are not desired in fluidizing systems.
Conditions for Fluidization
Consider a vertical tube partly filled with a solid material and 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 quite small, flow in the channels between the particles will
be laminar and the pressure drop across the bed will be proportional to the superficial
velocity. As the velocity of air is gradually increased the pressure drop increases but the
particles do not move and the bed height remains the same. This is a region where the Ergun
equation for a packed bed can be used to relate the pressure drop to the velocity. When u mf is
reached, particles become separated enough to move about in the bed and fluidization begins.
When the bed is fluidized, the pressure drop across the bed stays constant but the bed height
continues to increase with increasing flow. If the flow rate to the fluidized bed is gradually
reduced, the pressure drop remains constant and the bed height decreases. 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. Figure 1.2
2
represents
the
pressure
drop
behavior
with
different
air
velocities.
Figure 2.2 Pressure drop versus air velocity for a bed of solids
An equation covering the entire range of flow rates can be obtained by assuming that the viscous
losses and the kinetic energy losses are additive. The result is called Ergun equation:
(1.1)
Minimum Fluidization Velocity
Minimum fluidization velocity can be obtained by an equation setting the pressure drop across
the bed equal to the weight of the bed per unit area of cross section;
∆ p=g ( 1−ε ) ( ρ p− ρ ) L
At incipient fluidization,
∆p
=g ( 1−ε M ) (ρ p −ρ)
L
(1.2)
ε
is the minimum porosity,
εM .
Thus
(1.3)
3
Using Equation (1.3) and Ergun equation (1.1) for
∆p
at the point of incipient fluidization
L
gives a quadratic equation for the minimum fluidization velocity,
V́ 0M :
150 μ V́ 0 M (1−ε M ) 1.75 ρ V́ 0 M 2 1
+
=g( ρ p−ρ)
Φ S D p ε 3M
Φ 2s D2P
ε 3M
(1.4)
According to Kunii et al.[2] particle Reynolds number less than 20, Ergun equation can be reduced
to Kozeny-Carman equation. Which is expressed as below.
(1.5)
P 150u  (1   ) 2

 3
h s2 D p2

which can be derived to Eqn-1.6 in order to get minimum fluidization velocity.
(1.6)
umf 
D ( p   f )g  
2
p
3 2
mf s
150 
1   mf
2. EXPERIMENTAL METHOD
2.1 Experimental Set-up
The equipment used in the experiment is a vertical Plexyglass cylinder of internal diameter of 44
mm and glass beads of ~375 µm as bed material, through which air flows. At the lower end of the
cylinder, there exists a distributor chamber so that fluid flow can be uniform. This stainless steel
4
sintered plate distributor support the bed and excessive pressure drop does not occur in the
system.
The set-up also contains an air compressor (P1), pressure reservoir (D2), pressure safety valve
(PSV), air bypass valve (V2), rotameter (FI2), and a U-tube manometer (PdI2) as shown below;
2.2. Experimental Procedure
Firstly, the unit is connected to the electrical supply. Then, bypass valve, V2, is opened
completely while flowmeter, FI2, is closed completely. The compressor, P1, is started and air
flow is adjusted to 200 nL/h in the rotameter. After pressure drop becomes stable, the value of
pressure drop in mm Cl4 is noted with the bed height. In the rotameter, the air flow is increased
with increments of 100 nL/h up to 500 nL/h and for every flow the data of pressure drop and
height is recorded. From 500 nL/h, the air flow is increased to 900 nL/h with the increments of 20
nL/h. The recording step is repeated. When increasing the air flow rate from 900 nL/h to 1600
nL/h with the increments of 100 nL/h, the same procedure is followed. Finally, air flow rate is
decreased with the same increments up to 200 nL/h. When the first movement and bubbles are
observed, the flow rate is signed for both increasing and decreasing.
5
3. RESULTS AND DISCUSSION
In the experiment air flow rate, height of the bed and pressure drop along the cylinder is recorded
and data is given in Table-3.1
Table 3.1 Recorded data and corresponding fluidization velocities
FORWARD
Flow Rate
(nL/h)
200
300
400
500
520
540
560
580
*600
620
640
660
**680
700
720
740
760
780
800
820
840
860
880
900
1000
1100
1200
1300
1400
***1500
1600
u (cm/s)
3.7
5.5
7.3
9.1
9.5
9.9
10.2
10.6
11.0
11.3
11.7
12.1
12.4
12.8
13.2
13.5
13.9
14.6
14.6
15.0
15.4
15.7
16.1
16.4
18.3
20.1
21.9
23.8
25.6
27.4
29.2
ΔP
(mm CCl4) h (cm)
42
15.7
63
15.8
85
15.8
105
15.6
126
15.4
132
15.4
137
15.5
138
15.5
139
15.5
140
15.6
140
15.7
140
15.8
140
15.9
140
16.0
140
16.1
140
16.2
140
16.3
141
16.4
141
16.4
141
16.5
142
16.7
142
16.7
142
16.8
143
17.0
146
17.5
148
18.0
150
19.0
154
19.0
150
19.5
152
20.0
156
20.5
BACKWARD
Flow Rate
(nL/h)
1600
1500
1400
1300
1200
1100
1000
900
880
860
840
820
800
780
760
740
720
700
680
660
640
620
600
580
560
540
520
500
400
300
200
ΔP
u (cm/s) (mm CCl4) h (cm)
29.2
156
20.5
27.4
154
20.5
25.6
152
19.5
23.8
154
18.5
21.9
148
18.0
20.1
146
17.5
18.3
146
17.0
16.4
143
16.5
16.1
143
16.5
15.7
142
16.4
15.4
142
16.3
15.0
142
16.3
14.6
142
16.2
14.3
142
16.2
13.9
142
16.1
13.5
142
16.0
13.2
142
16.0
12.8
142
15.9
12.4
142
15.9
12.1
141
15.8
11.7
140
15.7
11.3
140
15.6
11.0
140
15.5
10.6
139
15.5
10.2
137
15.4
9.9
134
15.4
9.5
130
15.4
9.1
126
15.3
7.3
102
15.3
5.5
68
15.3
3.7
52
15.3
6
Data at Table-3.1 marked with (*) indicates the flow rate where the fluidization is observed at the
first time. Moreover, data with mark (**) is the place where the bubbling observed during the
experiment and finally data with (***) is the place where slug occurred.
On the experimental set-up there is a ruler attached to the cylinder in order to ease measurement
of the bed height. However at the beginning bed height is measured with another ruler in order to
confirm. Those two measurements were not the same, in the calculations and curve plotting the
height data is used as the ones verified according to the latter one. However, it is still expected
some deviations from actual bed height, since all portions of the bed cannot be measured.
According to the data fluidization velocity is calculated for each flow rate and pressure drop vs.
velocity curve is plotted. Figure-3.1 is given below as the pressure drop vs. fluidization velocity.
250
200
150
Pressure drop, ΔP (mmH2O)
forward
backward
100
50
0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
Fluidization velocity, u (cm/s)
Figure 3.3- Pressure drop over fluidization velocity
Minimum fluidization velocity is the least velocity needed to lift the particles from the bed. At
this point pressure drop becomes constant and upward forces exerted on the particles are equal to
the force due to weight of the particles. According to Figure-3.1 the minimum fluidization
velocity is determined as the data where the change in pressure drop becomes nearly zero.
7
For forward direction (where flow rates have increasing order) this point is found as 10.2 cm/s
with 191 mm H2O and for backward direction it is found as 11.3 cm/s with 195 mm H2O.
Figure-3.2 indicates the bed height over fluidization velocity.
18.0
16.0
14.0
12.0
10.0
Bed height, h (cm)
8.0
forward
backward
6.0
4.0
2.0
0.0
0.0
5.0 10.0 15.0 20.0 25.0 30.0 35.0
Fluidization velocity, u (cm/s)
Figure 3.4- Bed height over fluidization velocity
According to Figure-3.2 bed height is constant until the fluidization begins. After that point it
starts to increase with increasing fluidization velocity. This behavior occurs as expected
according to theory. Additionally, this behavior was observed more clearly at the backward
direction. The increase in height occurs after the point where the fluidization begins, because
until that point the flow rate of fluidization velocity are not enough to lift the particles apart.
Minimum fluidization velocity can be calculated by Ergun equation (Eqn-1.1) as given in
introduction section.
∆P
is chosen as the point where the fluidization begins during the experiment. Viscosity term
h
μ is assumed the viscosity of air at room temperature [1]. This assumption may cause some
deviations since the temperature of air was not exactly at 20 °C. In Ergun equation there is also a
8
term for sphericity, denoted as
, and was taken as 1. By that all glass beam particles were
s
assumed as spheres which may not be the actual case. Additionally particle diameter was noted as
375 μm on average at the manual of the experiment and calculated by that value. However, each
particles cannot be exactly in that size and taking averages of it would cause deviations, also.
Finally, the void fraction ε is expected as 0.4 from equation
is the bulk density and has a value of 1.5 (g/cm3) and
where
  1
b
p
b
is the density of
p
particle and introduced to the equation as 2.5 (g/cm3). However the value 0.4 is for particles
without air flow (stable particles). Therefore it is expected as more than that value when
fluidization starts for particles, since particles become a little apart from each other at the
fluidization. To find the void fraction Eqn-1.2 is used which takes the basis of force balance [3].
(1902 Pa)  (9.81m / s 2 )(1   mf )(2500  1.204kg / m3 )  (0.11m)
Density of fluid (air) is found by ideal gas law and pressure drop and height is determined from
the experimental data. From equation below the εmf is found as 0.3, which is not a reasonable
value for void fraction at minimum fluidization, since it is less than 0.4.
To determine a theoretical value for εmf Wen Yu constant (K1 and K2) can be used where K2/2K1
equals to 33.7 and 1/K1 equals to 0.0408. These constants gives relations between εmf and ϕs.
Solution gives two equations with four distinct root. Only one of them has a reasonable value of
0.415 as εmf (other two have complex roots and last one was less than 0.4).
Reynolds number is assumed as the less that 20 for minimum fluidization conditions and
fluidization velocity is found as 16.0 cm/s by Eqn-1.6.
9
To verify the laminar flow (Rep < 20) assumption, particle Reynolds number is calculated as 4.25
with introducing the found velocity by
equation. The result indicates that the
Re p 
D pu  f

assumption is valid.
Minimum fluidization velocity is also calculated with Wen and Yu equation also. According to
Yu-Wen
, (K1) and
1.75
 mf3 s
, (K2) values are constant for many kinds of particles and
150(1   mf )
 mf3 s2
this may cause ±34% standard deviation [2] for fine particles Wen and Yu equation is
D pumf  f


 D 3p  f (  p   f ) g 
2
  (33.7)  0.0408 


2


 
1/ 2
 33.7
From that equation umf is found as 11.4 cm/s.
So far, minimum fluidization velocity values are determined in five different ways and those
values are summarized at Table-3.2.
Method used for finding umf
umf (cm/s)
Experimental observations
11.0
Graphical readings
10.2 (forward) & 11.3 (backward)
Ergun equation
16.0
Yu and Wen equation
11.4
Literature
10
11
4. CONCLUSION
In the experiment, Fixed and Fluidized Bed, the phenomenon of fluidization in a gas-solid system
is investigated. During the experiment, pressure difference and fixed-fluidized bed height values are
recorded with the different air flow rates. Fluidization velocity, pressure drop and bed height
measured are tabulated at each air flow rate. The pressure drop (mm H 2O) versus fluidization velocity
(cm/s) curve is plotted for both increasing and decreasing air flow rates. Additionally, the variation of
bed height against the fluidization velocity is plotted. Minimum fluidization velocity is found as 10.2
cm/s and 11.3 cm/s from the pressure drop versus fluidization velocity graph for forward and
backward direction of flow, respectively. Minimum fluidization velocity is also determined as 11.0
cm/s with the help of experimental observations whereas it is found as 11.4 cm/s by using Wen and
Yu equation and 16.0 cm/s by Ergun equation.
12
5. REFERENCE
1. McCabe, W.L.,.Smith, J.C and Harriott P., "Unit Operations of Chemical Engineering",
7th ed., McGraw Hill, N.Y., 2005.
2. Kunii, D. and Levenspiel, O.,”Fluidization Engineering”, 2nd ed., ButterworthHeinemann, 1991.
3. Che 410 – Chemical Engineering Lab 2 web page – lab manual and web notes.
13
6. APPENDIX
Sample Calculations
Calculation of Fluidization Velocity:
The calculation is made for 500 nL/h
u=
Q
A
where bed area, A;
2
π∗D2 π∗(4.4 cm)
2
A=
=
=15.2cm
4
4
3
3
L
cm
1
h
cm
Q=500 *1000
*
=138.9
h
L
3600 s
s
3
138.9 cm /s
u=
=9.14 cm/s
15.2 cm2
Conversion of ∆P from mm CCl4 to mm H2O
ρ1 × g1 ×h1=ρ2 × g2 ×h2
where g1 = g2
ρ1
=1.39 g/cm3
14
h1
= 105 mm
ρ2
=0.997 g/cm3
1.39
h2
g
3
×105 mm=0.997 g/cm ×h2
3
cm
=146.4 mm
Calculation of Minimum Fluidization Velocity by Ergun Equation
umf 
D p2 (  p   f ) g  mf3 s2
150 
1   mf
(375  106 m)2 (2500  1.204kg / m3 )(9.81m / s 2 ) 0.4153 12
150(0.0175 10 3 kg / m s)
1 0.415
umf  0.160m / s  16.0cm / s
umf 
Calculation of Minimum Fluidization Velocity by Yu & Wen Equation
(375 106 m)(umf )(1.204kg / m3 )
(0.0175 103 kg / m s )

 (375  106 m)3 (1.204kg / m3 )(2500  1.204kg / m3 )(9.81m / s 2 ) 
  (33.7)  0.0408 

(0.0175 103 ) 2

 

2
1/ 2
 33.7
 (375 106 m)3 (1.204kg / m3 )(2500  1.204kg / m3 )(9.81m / s 2 )
  5082.11
(0.0175 103 ) 2



 [(33.7)2  0.0408  5082.11]1/ 2  33.7  2.95
 umf  0.114m / s  11.4cm / s
15
16