1. Fluidization & Mapping of Flow Regimes
건국대학교 화학공학과
최정후

2. Fluidization A type of fluid-solid contact
Fluidization is the operation by which solids particles are transformed into a fluid-like state through suspension in a gas or liquid.

3. Various forms of contacting of a batch of solids by fluid (Kunii and Levenspiel, 1991)

4. Bubbling, turbulent, and fast fluidized bed; spouted bed (Kunii and Levenspiel, 1991)
Turbulence
Uniform temperature

5. Figure: Circulating fluidized bed combustor (Foster Wheeler type).

6. Liquid-like behavior of gas fluidized beds (Kunii and Levenspiel, 1991)

7. Solids circulation between two beds
Contacting schemes with gas fluidized beds (Kunii and Levenspiel, 1991)
Crosscurrent
Solids circulation between two beds
Countercurrent

8. Operating principle for solids circulation between two beds (Kunii and Levenspiel, 1991)

9. Types of contacting gas and solids (Kunii and Levenspiel, 1991)
Gas flow
Solids flow

10. Advantages and disadvantages of fluidized beds for industrial operation
Broad residence time distribution of the gas due to dispersion and bypass in the form of bubbles.
Broad residence time distribution of solids due to intense solids mixing.
Erosion of internals.
Attrition of catalyst particles.
Difficult Scale-up due to complex hydrodynamics.
It has the ability to process large volumes of fluid.
Excellent gas-solid contacting.
Heat and mass transfer rates between gas and particles are high when compared with other modes of contacting.
No hot spot even with highly exothermal reaction.
Ease of solids handling.

11. Process variables
The ease with which particles fluidize and the range of operating conditions that sustain fluidization vary greatly among gas-solid systems. They are affected by numerous factors: size (size distribution), shape and density of solids; velocity, density and viscosity of gas; and column size(diameter, height).

12. Gas velocity: superficial gas velocity
Gas Properties:
Air density:
Air viscosity:
Gas velocity: superficial gas velocity

13. Screens; particle size analysis
microne

14. Specific surface mean particle diameter
dp: particle diameter
x: weight fraction
Shape factor

15. Particle Density True density
- It uses true particle volume that excludes pore volume in particle. The concern is down to how small to determine the pore volume.
Apparent density
- It uses the apparent particle volume.
- It is the apparent density that is used in calculation relating to fluidization.
Bulk density
- It uses the volume that includes the apparent particle volume and the void volume among particles. Bulk density is used in calculating the size of storage.

16. Pore classification (by Dubinin): 1) Macropore: 기공 폭>1000 Å, 모세관 응축이 없음 2) Mesopore: Å, 증기압 강하가 발생 3) Micropore: 5-14 Å (1 Å=10-10 m)

17. Hg porosimetry

19. Table: Repose angle for solid particles (adapted from Kunii and Levenspiel, 1991)
Solids
Mean bulk density
[kg/m3]
Repose Angle, θr
[deg]
Calcium oxide, powdered
433 43
Catalyst, fluid cracking, 60μm
         TCC beads, 3mm
513
729 32 35
Coke, pulverized
400 34
Dolomite, pulverized
738 41
Glass bead, 290μm
            5.4mm
1470
1360 26
Iron powder, 130μm-3.6mm
40-42
Lead shot, mm
23-33
Limestone, pulverized 47
Portland cement
1630 39
Sand, 480μm
1460 37
Steel balls, mm
33-37
Wheat
770 23

20. Gas fluidization:
u: drag
dp: (gravity-buoyance)

21. Pressure drop versus velocity
For the relatively low flow rates in a fixed bed, the pressure drop is approximately proportional to gas velocity, and usually reaching a maximum Δpmax, slightly higher than the static pressure of bed .
With a further increase in gas velocity, the fixed bed unlocks, in other words, the voidage increases from εm to εmf resulting in a decrease in pressure drop to the static pressure of the bed.
With gas velocities beyond minimum fluidization, the bed expands and gas bubbles are seen to be present. Despite this rise in gas flow, the pressure drop remains practically unchanged.

22. Pressure drop in fixed bed (Ergun, 1952)
uo : superficial gas velocity [m/s]
dp : particle diameter [m]
: gas density [kg/m3]
Lm: static bed height [m]
: gas viscosity [kg/m•s]
: shape factor [-]
: void fraction in bed -]
: frictional pressure drop [Pa]

23. Fluidization without carryover of particles
Minimum Fluidization velocity, umf
When a bed of particles resting on the distributor, its onset of fluidization occurs when
[drag force by upward moving gas]=
[(Weight of particles)]
[(pressure drop across bed)(cross sectional area of tube)] = [(volume of bed)(solid fraction)(specific weight of solids)]
with Δp always positive,

24. By rearranging, we find for minimum fluidizing conditions that1
By rearranging, we find for minimum fluidizing conditions that 2
Ergun equation (1952) 3
The superficial velocity at minimum fluidizing conditions, Umf, is found by combing equation 2 and 3.

25. In more simplified forms
umf 4
where Rep,mf and Ar are defined as
In more simplified forms 5 6 7

26. umf
Superficial fluid velocity at which the packed bed becomes a fluidized bed is known as the minimum fluidization velocity, umf.
Sometimes referred to as the velocity at incipient fluidization.
umf increases with particle size and particle density and is affected by fluid properties.

27. Wen and Yu (1966) equation on Umf
hence Umf ∝ Tb-n
where Tb : bed temperature, n : 0.6~1.0
hence Umf ∝ Tb0.5

28. umf
가능한 한 측정하여 사용한다.

29. Particle classification diagram (Geldart, 1973)

30. Geldart's classification of powders
Group A (Aeratable): (e.g., ammoxidation of propylene) small mean particle size and/or low particle density (<~1.4 g/cm3), gas bubbles appear at minimum bubbling velocity (umb).
Group B (Sand-like): (e.g., starch) particle size 40 μm to 500 μm and density 1.4 to 4 g/cm3, gas bubbles appear at the minimum fluidization velocity (umb).
Group C (Cohesive): very fine particle, particle size < 30 μm, difficult to fluidize because inter-particle forces are relatively large, compared to those resulting from the action of gas.
Group D (Spoutable): (e.g., roasting coffee beans) large particle, stable spouted beds can be easily formed in this group of powders.

31. Particle terminal velocity
Ut: particle terminal velocity [m/s]
dp: particle diameter [m]
p: particle density [kg/m3]
g: particle density [kg/m3]
g: acceleration of gravity, 9.8 [m/s2]
Cd: drag coefficient [-]
Cd=24/Rep for Rep  5.8, Cd=10/Rep0.5 for 5.8 < Rep  540, Cd=0.43 for 540 < Rep
Rep: particle Reynolds number , dpUg/

32. Terminal velocity of single free-falling particles (Kunii and Levenspiel, 1991)

33. References
D. Geldart, Powder Technology, 7, 285 (1973). D. Geldart and A.R. Abrahamsen, Powder Technology, 19, 133 (1978). D. Kunii and O. Levenspiel, “Fluidization Engineering,” Chapter 1 & 3, 2nd edition, Butterworth-Heinemann, Boston USA (1991). G.-S. Lee, “Pressure fluctuations and mixing characteristics in turbulent fluidized beds,” Ph.D. Thesis, KAIST, Daejeon, Korea (1990). H.-J. Ryu, “Slug characteristics and transition velocity to turbulent fluidization in gas fluidized beds,” Ph.D. Thesis, Konkuk University, Seoul, Korea (2000).