Fixed and Fluidized Bed for Good Manufacturing

Fixed and fluidized bed

1. CBE 150A –Transport Spring Semester 2014
Fixed and Fluidized Beds

2. CBE 150A –Transport Spring Semester 2014
Goals
•Describe forces that act on a bed of particles.
•Describe how pressure drop and bed height (or void
fraction) vary with fluid velocity.
•Apply basic equations to compute pressure drop
across the bed, the bed height and the diameter of the
bed.
•List advantages and disadvantages of fluidized beds.

3. CBE 150A –Transport Spring Semester 2014
Flow Through a Bed of Particles

4. CBE 150A –Transport Spring Semester 2014
Response to Superficial Flow
Fluid does not impart enough drag to overcome gravity and particles do
not move. Fixed Bed.
At high enough velocities fluid drag plus buoyancy overcomes the
gravity force and the bed expands. Fluidized Bed.
Low Velocity
High Velocity
p for Increasing u
0
Until onset of fluidization p increases, then becomes constant.
Bed Length for Increasing u
0
L is constant until onset of fluidization and then begins to increase.

5. CBE 150A –Transport Spring Semester 2014
Response to Superficial Velocities

6. CBE 150A –Transport Spring Semester 2014
Fixed Bed
How do we calculate the pressure drop across a fixed
bed?
Start with the MEB:fb
f
hgL
p


 2
4
2
V
D
L
fh
f 






For pipe flow we determined:

7. CBE 150A –Transport Spring Semester 2014
Pressure Drop
For now make the following assumptions:
•Horizontal Bed (or small L)
Gravity not important.
•Particles pack uniformly giving rise to continuous
flow channels
•Bed can be modeled as bundle of small pipes.
•Flow is laminar (f = 16/Re).

8. CBE 150A –Transport Spring Semester 2014
Laminar Flow





















2
16
4
2
V
D
L
Re
p
f f
D
VL


2
32

?
?
What are the proper velocity and diameter?

9. CBE 150A –Transport Spring Semester 2014
Velocity
L
bS = Volume of Bed
eL
bS = Volume Available for Flow
For a unit length of bed:SuSue
0
Mass
Balancee
0uu

10. CBE 150A –Transport Spring Semester 2014
Diameter
Since this is not true pipe flow must use hydraulic radius.






 

perimeterwetted
flowforareasectionalcross
D
h4 








areasurfacewetted
flowforavailablevolume
D
h4
Multiply by L/L

11. CBE 150A –Transport Spring Semester 2014
Diameter










sb
b
h
aSL
SL
D
e
e
1
4
a
sis the ratio of particle surface area to volume.
The denominator above is then the particle volume
multiplied by a
sor the particle surface area.p
s
DR
R
a
64
3
3
4
2



For a sphere: 
ph DD










e
e
16
4

12. CBE 150A –Transport Spring Semester 2014
Laminar Flow
3
2
2
0172
e
e 

pD
Lu
p
In actuality the above equation does not account for the tortuous path
through the bed and L is much longer. Experimental data show that a
numerical constant of 150 should replace the 72.
Blake-Kozeny equation. Assumes e < 0.5 and Re
p< 10.

e
fp
p
uD
Re
0
1
1

 
3
2
2
01150
e
e 

pD
Lu
p

13. CBE 150A –Transport Spring Semester 2014
Turbulent Flow
One cannot use the Hagen-Poiseuille approximation
when flow is turbulent. After substituting in D
hand
velocity correction
3
2
013
e
e 

p
D
Luf
p
Experimentally:000,1
p
Re
Burke-Plummer Equation 
3
2
0175.1
e
e 

p
D
Lu
p

14. CBE 150A –Transport Spring Semester 2014
Intermediate Flow
Ergun Equation
75.1
150
1
3
2
0



p
p
ReL
D
u
p
e
e

Note: equation can be used with gases using average gas density
between inlet and outlet.   
3
2
0
3
2
2
0 175.11150
e
e
e
e 



p
b
p
b
D
Lu
D
Lu
p

15. CBE 150A –Transport Spring Semester 2014
Fixed Bed “Friction Factor”

16. CBE 150A –Transport Spring Semester 2014
Irregular Shapes
To increase surface area and liquid solid contact, many
particles are often of irregular shape. In that case the
particle is treated as a sphere by introducing a factor called
sphericity F
swhich allows calculation of an equivalent
diameter.particleparticle
p
particle
sphere
s
VS
D
a
a
/
6
F
Where D
pis the diameter of a sphere of the same volume
as the particle

17. CBE 150A –Transport Spring Semester 2014
Example: Cube3
2
6
aV
aS


What is diameter of sphere of volume a
3
?aD
Da
p
p
31
33
6
6



 
81.0
66
6
6
3131






F

a
a
s

18. CBE 150A –Transport Spring Semester 2014
Sphericity
Note entries for cubes and cylinders. For convenience, some just
calculate a nominal (average) diameter and assign a sphericity of unity.
For greatest contact area want lower sphericity.

19. CBE 150A –Transport Spring Semester 2014
Adsorbent Mesh Sizes
6 X 8 Mesh d
p= (0.132 + 0.0937) / 2 = 0.113 in (0.0094 ft)

20. CBE 150A –Transport Spring Semester 2014
Irregular Shapes
So the final Ergun equation is: 
3
2
0
3
2
22
0 175.11150
e
e
e
e 
F


F

ps
b
ps
b
D
Lu
D
Lu
p

21. CBE 150A –Transport Spring Semester 2014
Fluidization (Refinery Application)

22. CBE 150A –Transport Spring Semester 2014
Fluidization (Drug Application)

23. CBE 150A –Transport Spring Semester 2014
Fluidization
At fluidization, the gravity force on the particles in the bed
must be balanced (F
k= 0) by the drag, buoyancy, and
pressure forces.   01
21  gLppSF
fpbk e
Substituting the Ergun equation for the pressure drop. 










F

F
 75.1
1150
0
3
2
0
fpsps
f
fp
uDD
u
g

e
e



24. CBE 150A –Transport Spring Semester 2014
Minimum Fluidization Velocity
This equation can be used to calculate the minimum
fluidization velocity u
mfif the void fraction e
mfat incipient
fluidization is known. 
 









F

F
 75.1
1150
3
2
fmfps
mf
mfps
mff
fp
uDD
u
g

e
e



25. CBE 150A –Transport Spring Semester 2014
Void Fraction at Min. Fluidization
e
mfdepends on the shape of the particles. For spherical
particles e
mfis usually 0.4 –0.45.

26. CBE 150A –Transport Spring Semester 2014
Minimum Fluidization
What if e
mf(and maybe F
s) is unknown?
Wen and Yu found for many systems:14
1
3
F
mfse

27. CBE 150A –Transport Spring Semester 2014
Bed Length at Minimum Fluidization
Once we obtain the minimum void fraction 
ballpongPingmfBedTube
ballspongPing
mfBed
S
M
L




e
,
,
1
L
Bed
S
Tube

28. CBE 150A –Transport Spring Semester 2014
Example
A packed bed is composed of cubes 0.02 m on a side. The bulk density
of the packed bed, with air, is 980 kg/m3. The density of the solid cubes is
1500 kg/m3.
•Calculate the void fraction (e) of the bed.
•Calculate the effective diameter (D
p) where D
pis the diameter of a sphere
having the equivalent volume.
•Determine the sphericityof the cubes.
•Estimate the water flow rate (m
3
/sec) required for minimum fluidization of the
solid using water at 38 C and a tower diameter of 1.0 m.

29. CBE 150A –Transport Spring Semester 2014 35.0
1500
980
11
:
3
3






m
kg
m
kg
V
V
V
andVV
VV
VVV
WWWandVVVknowWe
FractionVoid
solids
bed
bed
solids
bedbed
bed
solidssolidsbedbed
fluidfluidsolidssolids
solidssolidsfluidfluidbedbed
solidsfluidbedsolidsfluidbed


e


e



30. CBE 150A –Transport Spring Semester 2014  mDD
Da
diameterEffective
pp
p
025.0
6
02.0
6
33
33



 
81.0
66
6
6
3131






F

a
a
Sphericity
s

31. CBE 150A –Transport Spring Semester 2014  
 
 
2
4
5
3
2
3
3
2
3
222
3
2
10748.9
445.0025.081.0
99475.1
75.1
445.0
14
1
495980.9
3
994
3
1500
75.1
1150
mf
mf
mfps
mff
mfmfs
fmfps
mf
mfps
mff
fp
u
m
kg
m
u
m
kg
D
u
sm
kg
s
m
m
kg
m
kg
uDD
u
g
VelocityonFluidizatiMimimum




F

F
















F

F

e

ee

e
e


LHS
RHS Term No. 1

32. CBE 150A –Transport Spring Semester 2014  
  
  
GPM) (884.5 /sm 0558.0071.0*
4
(1.0)
flow Volumetric
233.0071.0
4959159710748.90
1597
445.0025.081.0
001.0693.0445.01150
1150
3
22
223
2
4
5
3
322322






















F

s
mm
s
ft
s
m
u
sm
kg
u
sm
kg
u
m
kg
u
sm
kg
m
u
sm
kg
cp
D
u
mf
mfmf
mf
mf
mfps
mfmf

e
e
RHS Term No. 2
Final Equation