effects of agitation speed and temperature on minimum … · 2001-04-26 · 0.8

HWAHAK KONGHAK Vol. 40, No. 2, April, 2002, pp. 237-245

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(2001� 11� 5� ��, 2002� 1� 10� � )

Effects of Agitation Speed and Temperature on Minimum Fluidization Velocity of Cohesive Particlesin a Mechanically Agitated Fluidized Bed

Dal-Hee Bae, Ho-Jung Ryu†, Dowon Shun, Gyoung-Tae Jin, Dong-Kyu Lee* and Jeong-Hoo Choi**

Fluidization Research Center, Korea Institute of Energy Research, Daejeon 305-343, Korea*Department of Industrial Chemistry Engineering, Chungbuk National University, Chongju 361-763, Korea

**Department of Chemical Engineering, Konkuk University, Seoul 143-701, Korea(Received 5 November 2001; accepted 10 January 2002)

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Abstract − To interpret the effects of agitation speed and temperature on the minimum fluidization velocity, bed and distri-

butor pressure drop and pressure fluctuation signal have been measured in a high temperature mechanically agitated fluidized

bed(0.05 m i.d. and 1.31 m high) using bentonite(mean particle diameter: 3.7µm, apparent density: 1,681 kg/m3) as bed mate-

rial. Fluidization of very fine cohesive powder is possible if mechanical energy is introduced into the bed by agitation. Mea-

sured minimum channeling velocity and minimum fluidization velocity increased with increasing bed temperature, however,

increased after an initial decrease with increasing agitation speed. The empirical correlation, considering the temperature effectbut no effects of agglomerate size and density, on the minimum fluidization velocity of cohesive particles has been proposed on

the basis of the experimental data of present study.

Key words: Fluidization, Channeling, Cohesive Powder, Minimum Fluidization Velocity

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&' C ��3� st()74j� �L �� N ()7�,� >†To whom correspondence should be addressed.E-mail: [email protected]

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bed pressure dropbed weight per unit surface

Table 1. Bed behavior with variations of fluidization index and fluidization quality[7]

FI QF Bed behavior

0.8<FI<1 0.7<QF<1 -Homogeneous fluidization of individual particlesFI<<1 0.8<QF<1 -Fluidization of agglomerates

-Measured Umf much higher than calculated value-At low velocity, channeling may occur

Very small Very small -Not fluidizable due to channeling or slugging-Pressure profiles are random-Bed is not expanding

Table 2. Summary of previous studies on fluidization methods of cohesiveparticles

Fluidization methods Authors

Mechanical agitation Nezzal et al.[8]Kuipers et al.[9]Park et al.[10]Tsujimoto et al.[11]

Mechanical vibration Marco et al.[12]Noda et al.[13]Mawatari et al.[14]Wank et al.[15]

Acoustic vibration Morse[16]Nowak and Hasatani[17]Leu and Huang[1]

Addition of fluidization aid Dutta and Dullea[18]Lauga et al.[19]Chirone et al.[20, 21]Nowak et al.[22]Li et al.[23]Wang[24]Brooks and Fitzgerald[25]Kato et al.[26]Zhou and Li[5]

Adjust bed geometry Park et al.[27]

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Fig. 1. Schematic diagram of experimental apparatus.1. Air compressor 17. Electric heater2. Mass flow controller 18. Heater controller3. Preheater 19. Differential pressure transducer4. Fluidized bed 10. Personal computer5. Variable speed motor 11. Temperature indicator6. rpm controller & indicator

Fig. 2. Detailed dimensions of blade.

Fig. 3. Bed and distributor pressure drop versus gas velocity(without mechan-ical agitation).

HWAHAK KONGHAK Vol. 40, No. 2, April, 2002

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Fig. 6. Minimum channeling velocity or minimum fluidization velocity ver-sus temperature.

Fig. 7. Fluidization index and fluidization quality with temperature andagitation speed.

Fig. 8. Comparison between measured minimum fluidization velocity andcalculated values.Symbols: measured values, Lines: calculated values1: Ergun[29], 2: Wen and Yu[30], 3: Baeyens and Geldart[31], Goroshko et al.[32], 5: Leva[33], 6: Davies and Richardson[34], Saxena and Vogel[35], 8: Riba et al.[36], 9: revision of Riba et al.[3correlation, 10: present correlation-Eq. (3).


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video camera! ��$� ��} �i()*�� ÑL *[� ()

*H f�$� 56�� v� .=$8� Û ��A ®} %i�

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�j! v�$� ��&N ZhouA Li[5]� �ÑL ()*�� !

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! v�$% U�5&N �� A >D! v�$� �j! 3

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L �� g¼09 �&' ��L �� = ��

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D �B. Table 4� �� ! uv$ «L Õ� ��H

µ¶$� 1IJ% �B. n� 1I{ �A ®� ��

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$ «=�� K(4� st()74j Ç� Úµ$-N Û ��

�A ®� �� ! 3Â$� st()74j ��

$ «L Bq&N� f�` D aB. L� �� j! 3Â$

«= Kusakabe [37], Nezzal [8], IwadateA Horio[4]� v��

�� A st()74j ÇH Õ� st()74j ��

� ��$� �� j! 3Â$� ��H f�$¯&1 � �

�j �� j! 3Â$� st()74j �� $

«L Bq&N� f�` D aB.

Knowlton[38]} st()74j� �L Õ� ��|� ijk7

� �C st()74j� k75~} 1I4 D �(°j v�Ç��

ý�. W� D �&' ��L 56� �� Òj! >�$ «=

�i�� v�L st()74j ÇH �� $� (C��

�(effective particle size)! %&N 3Â$%, � ÇH st()74j

�� $� %i�� st()74j! 3Â` ¥H D¹$¯

B. Û ��j Õ� st()74j �� i�� v�� s

t()74j ÇH ��$� (C ��(effective agglomerate

size)! %&N 3Â$% � ÇH �� $� ijk7� �C

st()74j ÇH 3Â=�òB. (C �� 3Â�� Û

�� hÌÆ�A õ�.8N ij. Î.l� �° st()74j

. Î.$� 5~H 1I� Riba [36]� ��H f�$¯B. Fig. 8

Table 3. Minimum fluidization velocity correlations[in SI unit]

Author Correlation

Ergun[29]

Wen and Yu[30]

Baeyens and Geldart[31]

Goroshko et al.[32]

Leva[33]

Davies and Richardson[34]

Saxena and Vogel[35]

Riba et al.[36]

1.75

εmf3 φs

------------dpUmfρg

µ-------------------

2 150 1 εmf–( )

εmf3 φ s

2----------------------------

dpUmfρg

µ-------------------

2 dp

3ρg ρp ρg–( )g

µ2----------------------------------=+

Umfµ

ρgdp

---------- 1135.7 0.048Ar+ 33.7–( )=

Ar 1823Remf1.07 21.27Remf

2+=

Umfµ

ρgdp

---------- Ar

1400 5.2 Ar+-----------------------------------

=

Umf

7.169 104– dp1.82 ρp ρg–( )0.94g×

ρg0.006µ0.88

----------------------------------------------------------------------=

Umf

7.8 10 4– dp2 ρp ρg–( )g×

µ----------------------------------------------------=

Umfµ

ρgdp

---------- 25.282 0.057Ar+ 25.28–( )=

Umfµ

ρgdp

---------- 0.0154dp

3ρg2g

µ2--------------

0.66ρp ρg–

ρg

--------------- 0.7

=

�� 40� �2� 2002� 4�

�� 243

� 95&N n¼� �} �i�� v�� st()74j ÇH Table 3

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0ôB.

%i�� st()74j! �Ò_ uv$ «=�

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g�� L Ç|H v�$� �6 9/# h��B. �°�

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�� st()74j! uv` D �� H g¼$%� $¯B.

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j. Î.$� ¥&N uv0� Riba [36]� �� +,! Û&N

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ÂL st()74j� k75~} Fig. 8� 105 �&N n¼09�B.

(r2=0.996) (3)

Û �� = �i�� 3Â� �� . qùL Ê«

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= �ò&' Fig. 9� 1IJôB. © �� ÞJ�� D� ��

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I{ �A ®� ��ÞJ�� D. Î.l� �° ��A �

�� È(da/dp). Ït$� 5~H 1IKB. Û ��

(3)� �= 3Â� �i�� (C ��A �� È

(da,eff/dp)� Õ �%|� 1I{ Ç|� (fL Ê«� ÇH 1IK&

', �� (3)� v�� st()74j ÇH ��$� (C ��

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L� st()74j� �O� ij�~� �M$�, Û �� g¼

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�C Î.5~H uv$ de� BC �� È= �B ×pq&N

%i�� st()74j! uv` D �H ¥&N f

Í0ôB. $8� hgq&N� �� A �j� �L (4,

ij, ��G�� ~� �L Ù.q� ��A lm � Ç|H �Ò$

x v� Y uv` D �� >V� Úµ$' �! �N&N �

�� st()74j� �O� ij� �~� �L �B �L =

�� Úµ$B.

4. � �

Û �� hÌÊ«�� O9¾ ÆPH µ¶$o B¬� ®B.

(1) Geldart �2 C ��3� 4$� ��1� �� 56 3q

� ¸-� a� 56�� RST� @91 ()7�,! (8$ 9

/Q&' 3q ¸-� �= ()7. .=$¯B.

(2) stRST4jA st()74j� ij. Î.l� �° Î.

$� 5~H 1IJô&' ¸-4j. Î.l� �° ÏtL Ð B¼

Î.$� 5~H 1IJôB.

(3) Õ� st()74j ��H D�$� Û hÌ�� v�� i

jk7� �C st()74j� k75~H uv` D �� H

g¼$¯B.

Umfµ

ρgda eff,

----------------- 2.895 103– da eff,3 ρg

2g

µ2----------------------

ρp ρg–

ρg

-----------------

0.686

×=

Table 4. Correlations on the agglomerate diameter [in SI unit]

Authors Equations

Morooka] et al.[3]

Iwadate and Horio[4]

Zhou and Li[5]

da

hw 1 εa–( )32πδdpεa

----------------------- 3µUmf a,–

ρaUmf a,2

12-----------------

-----------------------------------------------=

dank mf, Ha 1 εa–( )

12πδ2Dbρag Ps–( )-------------------------------------------=

nk 1.61ε 1.48– ε 0.82<( )=

Db Dbm–Dbo Dbm–----------------------- 0.3

Lc

Dt

-----– exp=

ρa ρg–( )gda2 0.33ρgU

2ε 4.8– 0.996π

-------------πV6ρa

3

k---------------

1 5⁄

+ da–

Ha

4πδ2-----------+ 0=

Ha Ha v 0=, Ha v, 0>34---BT

ε1 ε0–

ε1 ε0+--------------

=+=

3hνe

16 2-------------+

N12 n0

2–( )2

N12 n0

2+( )3 2⁄

---------------------------

n8

9π2 k1 k2+( )2-------------------------------

da1da2

da1 da2+-------------------=

k 1 ν2–πE

-------------=

V 1.5Ps n, Dbgε( )1 2⁄

=

Db 0.652 At U Umf–( )[ ]2 5⁄=

Fig. 9. The ratio of agglomerate diameter to particle diameter versusparticle Archimedes number.


244 ��

édés

y

77

nd

ree-

.

lu-

Kim,

rk,

J.:

l-

r-

86).

ara,

n,

ase

182

� ��

Ar : Archimedes number, ρg(ρp−ρg)gdp3/µ2 [-]

A t : cross-sectional area of bed [m2]

B : Boltzmann’s constant [J/K]

da : agglomerate diameter [m]

da,eff : effective agglomerate diameter [m]

Db : bubble diameter [m]

Db0 : initial formation bubble diameter [m]

Dbm : maximum attainable bubble diameter [m]

dp : particle diameter [mm]

Dt : column diameter [m]

g : gravitational acceleration [m/s2]

h : Planck’s constant [Js]

Ha : Hamaker constant [J]

hw : Lifshitz-van der Waals constant [J]

k : function of Poisson’s ratio and Young’s modulus of agglomerate i

[Pa−1]

Lc : settled bed height [m]

N1 : index of refraction of particle

nk : coordination number [-]

nk,mf : coordination number of agglomerates at minimum fluidization

condition [-]

Ps : particle pressure [Pa]

Ps,n : dimensionless average particle pressure of non-sticky system [-]

r2 : correlation coefficient [-]

Remf : Reynolds number at minimum fluidization velocity, dpUmf ρg/µ[-]

T : temperature [K]

U : superficial gas velocity [m/s]

Uch : minimum channeling velocity [m/s]

Umf : minimum fluidization velocity [m/s]

Umf,a : minimum fluidization velocity of bed of agglomerates [m/s]

V : relative velocity of agglomerate [m/s]

��

δ : microscale gap between agglomerate or particle surfaces [m]

ε : bed voidage [-]

εa : agglomerate voidage [-]

εmf : void fraction in a bed at minimum fluidizing condition [-]

µ : gas viscosity [kg/m-s]

ν : Poisson’s ratio [-]

νe : UV adsorptive frequency [s-1]

ρa : agglomerate density [kg/m3]

ρg : gas density [kg/m3]

ρp : apparent particle density [kg/m3]

φs : sphericity of particle [-]

��

1. Leu, L. P. and Huang, C. T.: AIChE Symp. Ser., 90, 124(1994).

2. Chaouki, J., Chavarie, C., Klvana, D. and Pajonk, G.: Powder Tech-

nology, 43, 117(1985).

3. Morooka, S., Kusakabe, K., Kobata, A. and Kato, Y.: Chem. Eng. Jpn.,

21, 41(1988).

4. Iwadate, Y. and Horio, M.: Powder Technology, 100, 223(1998).

5. Zhou, T. and Li, H.: Powder Technology, 102, 215(1999).

6. Lettieri, P., Yates, J. G. and Newton, D.: Powder Technology, 110,

117(2000).

7. Nezzal, A., Guigon, P. and Large, J. F.: Colloque Génie des Proc

Compiègne(1991).

8. Nezzal, A., Large, J. F. and Guigon, P.: “Fluidization VIII,” edited b

Large, J. F. and Laguerie, C., Engineering Foundation, New York,

(1995).

9. Kuipers, N. J. M., Stamhuis, E. J. and Beenackers, A. A. C. M.: Chem.

Eng. Sci., 51(11), 2727(1996).

10. Park, J., Kim, J., Cho, S. H., Han, K. H., Yi, C. K. and Jin G. T.: Korean J.

Chem. Eng., 16, 659(1999).

11. Tsujimoto, H., Yokoyama, T., Huang, C. C. and Sekiguchi, I.: Powder

Technology, 113, 88(2000).

12. Marco, E., Santos, A., Menendez, M. and Santamaria, J.: Powder

Technology, 92, 47(1997).

13. Noda, K., Mawatari, Y. and Uchida, S.: Powder Technology, 99, 11(1998).

14. Mawatari, Y., Koide Tetsu, Yokawa, K., Ozawa, M., Uchida, S. a

Noda, K.: “The Seventh Asian Conference on Fluidized-Bed and Th

Phase Reactors,” edited by Uchida, S. and Morooka, S., 167(2000)

15. Wank, J. R., George, S. M. and Weimer, A. W.: Powder Technology,

121, 195(2001).

16. Morse, R. D.: Ind. Eng. Chem., 47, 1170(1955).

17. Nowak, W. and Hasatani, M.: “The Third Asian Conference on F

idized-Bed and Three-Phase Reactors,”edited by Chun, H. S. and

S. D., 423(1992).

18. Dutta, A. and Dullea, L. V.: AIChE Symp. Ser., 87, 281(1991).

19. Lauga, C., Chaouki, J., Klvana, D. and Chavarie, C.: Powder Tech-

nology, 65, 461(1991).

20. Chirone, R., Massimilla, L. and Russo, S.: “Fluidization VII,” edited by

Potter, O. E. and Nicklin, D. J., Engineering Foundation, New Yo

545(1992).

21. Chirone, R., Massimilla, L. and Russo, S.: AIChE Symp. Ser., 48, 41(1993).

22. Nowak, W., Hasatani, M. and Derczynski, M.: AIChE Symp. Ser., 89,

296(1993).

23. Li, H., Legyos, R., Bereton, C. M. H., Grace, J. R. and Chaouki,

Powder Technology, 60, 121(1990).

24. Wang, Z. L.: PhD Dissertation, Beijing, Institute of Chemical Meta

lurgy, Academia Sinica, Chinese(1995).

25. Brooks, E. F. and Fitzgerald, T. J.: “Fluidization V,” edited by Øste

gaard, K. and Sørensen, Engineering Foundation, New York, 217(19

26. Kato, K., Takarada, T., Koshinuma, A., Kanazawa, I. and Sugih

T.: “Fluidization VI,” edited by Kunii, D. and Toei, R., Engineering

Foundation, New York, 351(1989).

27. Park, J., Kim, J., Cho, S. H., Han, K. H., Yi, C. K., Jin G. T. and So

J. E.: “The Sixth Asian Conference on Fluidized-Bed and Three-Ph

Reactors,” edited by Chun, H. S. and Kim, S. D., 329(1998).

28. Davidson, J. F., Clift, R. and Harrison, D.: “Fluidizaion,” 2nd ed., Aca-

demic Press, New York, 31(1985).

29. Ergun, S.: Chem. Eng. Prog., 48, 89(1952).

30. Wen, C. Y. and Yu, Y. H.: AIChE J., 12, 610(1966).

31. Baeyens, J. and Geldart, D.: Int. Symp. on Fluidization, Toulouse,

(1973).

32. Goroshko, V. D., Rozembaum, R. B. and Toedes, O. H.: Izvestiya Vuzov,

Neft’ i Gaz, 1, 125(1958).

33. Leva, M.: “Fluidization,” McGraw-Hill, New York(1959).

�� 40� �2� 2002� 4�

�� 245

34. Davies, L. and Richardson, J. F.: Trans. Inst. Chem. Engrs., 44, T293

(1966).

35. Saxena, S. C. and Vogel, G. J.: Trans. I. Chem. E., 55, 184(1977).

36. Riba, J. P., Routie, E. and Coudere, J. P.: Can. J. Chem. Eng., 56,

26(1978).

37. Kusakabe, K., Kuriyama, T. and Morooka, S.: Powder Technology,

58, 125(1989).

38. Knowlton, T. M.: “Fluidization VII,” edited by Potter, O. E. and Nicklin,

D. J.: “Engineering Foundation,” New York, 27(1992).

39. Sugihra, M.: Res. Assoc. Powder Technol. Japan, 3, 21(1966).


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