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Elutriation of fine particles from batch gas—solid fluidized bed — at sufficiently high freeboard height —
65
Elutriatitin~oifFiqe Particles fkoti &itch Gas-Solid at Sufficietitl~ Hi& Freeboard Height YOSHIZO MATSUNO=, HIGASHlTANI+
HIROYUKI
KAGE,
TETSUYA
Department of Indusfrial Chem.istry and +Department logy, 1-I Sensuicho, (Received
Tobata. Kitahyushu,
NAGAMITSU,
of Environmental
Fluidized Red -
HISAMORI
YAMAGUCHI
Science, Kyzshu
Institute
and KO
of Techno-
804 (Japan)
January 20.1982)
SUMMARY
An experimental and semi-theoretical work on tha elutriation of fine particles from a fluidtied bed was carried out. The fluid&zing equipment, consisting of an iron pipe of 3 in id., was designed in such a way that its freeboard height can be adjusted properly_ At the different freeboard heights and air flow rates, the accumulated weights of fine particles with time were measured. The same procedure was repeated for different initial contents of the fine particles in the bed_ In order to interpref the experimental results, a simple model was constructed by assuming that the fine particles were transported only by convection of gas. The model included two parameters; one was a critical height above which the transport of fine particles was controlled by convection of gas, and the other was the elutriation rate constant_ The critical height was estimated experimentally. The eluiriation mte constant was determined by a mefhod proposed in this work_ It was found that the elutriation rate constant was independent of the freeboard heighf and that its value was consistent with the calculated value based on the correlation of Wen and Hashinger [3] _ Further, a physical meaning of the elutriation rate constant was elucidated from this model.
*To whom correspondence should be sent. Mailing Address; Yoshizo Matsuno, Department of Industrial Chemistry, Kyushu Institute of TechnoIogy, l-l Sensuicho, Tobata, Kitakyusbu, 804 (Japan)_
0032-5910/82/0000-00001$02.75
INTRODUCTION When the fluidized bed is composed of particles of different sizes, the smaller particles will be carried out from the fluidized bed if the gas velocity exceeds the terminal velocities of the smaller particles. The elutriation of fine particles from the fluidixed bed is important in air pollution control, recovery of the valuable materials, estimation of the reaction yields and sekctivities in the freeboard, etc. Since Leva [l] and Osberg and Charlesworth [2] found, from experiments with two particles of different sizes, that the reciprocal of the concentration of fine particles in the bed is exponentially proportional to the elapsed time, macroscopic views of the elutriation of fine particles have been oriented toward clarifying the correlation between the elutriation rate constant and the operational variables by many investigators [3 - 6]_ Wen and Hashinger [3] and Yagi and Aochi [4] have contributed to the establishment of a new concept of the elutriation rate constant_ Kunii and Levenspiel [‘7] have proposed a correlation between the elutiation rate constant and the operating parameters based on the experiment carried out by Lewis et al_ [8] on the entrainment from a continuous fluidized bed. In addition, the estimation of the TDH (Transport Disengaging Height) is important for both the analysis of the gas and particle behaviors in the freeboard and for industrial applications. Zenx and Weil [9] have proposed a method of estimating the TDH_ As they pointed out, this method may not be accurate when the bed diameter and/or
0 Ekevier Sequoia/Printed
in the Netherlands
66
6 Prnw-ereguh 7cErdryer
Fig_ 1. Schematic
diagram of experiment_
Fig_ 2_ FIuidizing
equipment_
superficialgasveIocityissmalLUndersucha condition, slugging, sire segregation and velocityfluctuationin thefreeboard can take place_
Theobjectiveofthispaperistoinvestigate the concentration change at a suf5ciently highfreeboardandtocom&ðeelufriation rate constant and the TDH with operating variables_
EXPERIMENTAL
EQDIPMENT
AND
wasprepared asthelowerpart(a)_ Pressure taps were provided every 50 mm along~the wall oftbispipe segment to measure the e~andedh~ghtofthebedby-a.methodof Miyauchi [lO].Theupperpart (C)wasthe outlet which was connect& to a cyclone separator_ A 10 mm thick poly(me$hyl methacrylate)plateoflmm bore and 6.5. mmsquarepitchservedasadistribut.or_ To preventelectrostaticchargesbetween theparticlesandbetweentheparticleand thewallofthebed,agroundwhzwaswound around the flanges of the column, which madethemeas*urementsfairlyreproducible_ Glassbeadswereusedasthefluidixingparticles_Theaveragediametersofthefiueand coarse particleswere 0.00565 and O-0161 cm,respectively_Thetotalweightoffineand coarseparticlescharged inthebedatthe heginningofeverynmwas2000g.Thegas (airatroomtemperature)wassupplied at a velocity well below the terminal velocity of thefineparticlessoastopreventthembeing entrainedwhilemixingtheparticlessufficientlybeforethenmwasstarted_Thedesiredgasflowratewasadjustedbyregulating valves_Particleswerecollectedbythecyclone separator at a suitable interval_These collectedp~~eswereclassifiedbytheuse of screens, and the fiue particleswere weighedonabaIance_Preliminaryobservationsindicatedthatnegti~bleamountsoffine particlesweredeated attheairoutletof thecycloneseparator, Theexperimentswererepeatedbychangingthefreeboardh~~tandtheairnowrateTheeffectoftheinitialcontentofthefine partich?sinthebedwasalsoinvestigated. The-experimental conditions are summarixedinTable1,
PROCEDURE THEORETICAL
Aschematicdiagramoftheexperimentis showninFig_l_Thecolumnwasmade~ofan ironpipeof3 in(81mm)i_d_Thefluidizing equipmentwas constructed by combining threepartsasshoWninPig_ 2:Inorderto adjustthefreeboardheight,piecesofpipeof Iengths2000mm,~~Omm;650mm,500 mm;300-~~dlOO'mmw~prep~to be inserted aS part (b)i-Z3ycombiningthese piecesofpipesuitably~~thefreeboard~height could be changed-A Segment650 mm:Iong-m ..
CONSIDERATION
AspointedoutbyWenandHashinger[3] and other investigators[7,9,11,12],the entrainmentoftheparticlesiscausedbythe fluctuation of gas velotiitycaused by the intermittent.burstingactionofbubblesjust above the bed surfsce.Asthe particlesare carried up to a sufficientheight,it is reasonabletoconsiderthattheyarecontrolledbytheconve;ction-ofthegasflowbecause ofthen&ligibledirecteffe&oftheb&sting .-.
TA&El :
Ekperimentzdconditions
(1)Operatingconditions~
Initi&totalweig& ofpa+les,g Initi$ content of &ES, F,,, wt.%
2000
2000 15
10
Airflowrate,x/min
80
s"p+icialgasve~ocity,cmls Freeboard he&h&cm
28.6
100
120
20
36-4 46-S 30-350
25
100
140
36.4 35-215
57-6
(2)Characteristicsofpartides Particlesused:glasbeads Density,gfcm3 Sizerange,,Y
fine
coarse 2.52 80 -100
2.52 250 -280
0.0161
0.00565
Averagediieteqcm
24.3
197.5
Terminalvelocity,cm/s
By solving eqn_ (2), using the separation variables method, eqn. (3) is obtained_ c(z,t)
= cs exp I-ku,(
t -z/4)
J
(3)
where ca and are integration constants. The accumulated weight of the fine particles, ~(z,t), at any height z and elapsed time t after the beginning of the run w5il give the concentration of fine particles, c&t), as Fig.3. Scheme
ofelutriation model_
%c(Gt)
aw(z,t)
=
ar [
action of bubbles at such a high freeboard_ Thus, a mass balance for the fine particles in the shell, Sdz, as shown in Fig. 3, can be given by, (Sdz)
Substitution
awkt) [
~=SC~Cl,-U&IZ+,, &
(1)
where c is the concentration of the fine particles in the freeboard, S is the cross-sectional area of the column, t is the time elapsed just after the gas begins to flow out at the bed surface (z = 0), and u, is the relative velocity between the gas velocity U, and the terminal velocity of the fine particles ut_ From eqn. (l), we get
ac at=--“%
ac
(2)
at
I
(4)
z
of eqn. (3) into eqn. (4) gives
1
=
Szqzo expf-ku,(t --z/u,)]
(5)
z
Next we integrate eqn- (5) under a fixed height z. It should be noted that the lower limit of integration for time t must be Z/U,, since it takes this time for the entrained particles to reach the distanze z_ Therefore, we get w(z,t)
= (Sc&k)Cl
-
exp(--k+(t
-z/24))]
(6) According to Wen and Hashinger [S] and the- following equation others 14,5,71, holds above the TDH,. i.e. z > z,_.nn
-!+V
(7)
6i3
Fig. 4. Change of accumulated
weight of frieswith t_
where W is equal to W. - w and W. is the initial weight of the fine particles. Let us consider that the fine particles are collected at an arbitrary height z. After the particles leave the bed surface, as mentioned before, it takes t = z/y before they reach z_ Just then the particles w-RI be collected. In order to determine the accunxdated weight of fine particles, ru(z,t), eqn_ (7) sho-uId be integrated with respect to time &om z/u, to f at height z. That is
Fig_ 5. Relationship and pressure drop.
w(z,t)
= W,fl
-
expt-k(t
-z/u,))1
(8)
Comparing eqn_ (8) with eqn. (6), we get a relationship between the eIutiation rate constant k in this work and & proposed previously [3,4] as follows: &=ku,
ctz,t)
w,
-w(z,t)
=- c,
(11)
wo
Substituting eqn. (11) obtain
into eqn. (lo),
W, - w(z, t))
we
(12)
Equation (10) or (12) gives a physicaI meaning of the elutriation rate constant_ That is to say, k is a constant which is proportional to the ratio of the contientration to the total weight of fine particles remaining below any height z. If we know this ratio at any freeboard height, we can determine the ehrtriation rate constant. EXPERIMENTAL RESULTS AND DISCUSSION
(9)
where k is expressed as k=&,l&
height from distributor
the initial weight of fine particles in the bed, respectively_ From eqns. (3) and (6), combined with eqn. (lo), we can obtain the following relationship :
k = Sc(z, t)/(
and
between
(10)
From eqn. (3), c, is found to be the fine particle concentration at t.7 z&, and W,, is the weight ~offine part&s remaining below-z just before the fine particIes &a& &It c&r be also seen &&at,when z = 0, c,, and W, co& respond to the concentration of fine particles blownup from the bed surface-at t = 0 and
Figure 4 shows the cumulative weight of fine particles cohected by the cyclone separator as a function of time -at a fixed freeboard height z. It is noted that the changes in w with-t become quite siniilar above a certain height_ The -data on the changes in w with t under other conditions are available. elsewhere [13,14] . Figure 5 shows how the pressurechanges with the height from the distributor for various gas flow rates. The pressure gradients seem to change slightly with the gas flow, but
69
I4
1
loo
1
300
2%
Fig.6.Change ofkwithheightandconstancy above a certain height r,
of k
Fig. 8. Comparison of kt in this work with those of other investigators_
uokmm so
3040 -4 E 03 z= “Z2 P z
1
60 0
0
0
0
10
Fo lOwtofe
20 Mcmls)
Fig. 7_ Variation
30
of k with u, or ug_
+$200 3 iO0 I
0 this is negligible_ Therefore, it is decided, using Miyauchi’s method [lo], that the bed
surface from the distributor is 30 cm in spite of the change of gas flow rates_ The value of k can be obtained as follows: c&t) is determined according to eqn. (4), by graphically differentiating the accumulated weight of fine particles with time shown in Fig. 4. Then, applying eqn. (12), we determine the k for any time at a fixed height. The average value of k for each t is plotted against z in Fig. 6. The range of deviation of k for each t is shown by a symbol (I) in Fig. 6. The k, which is determined by the method mentioned above, is plotted against u, in Fig. 7_ Figure 8 compares the & obtained from the experimental results with the & values c&uIated from previously proposed correlations [3_5].Inthispapereqn.(9)isused_k,in this work agrees fairly well with the correlation of Wen and Hashinger [3] when u, is
laIge.
’ As pointed iut by Wen and Hashinger [ 31, ’
k, in eqn. (8) should be constant above a
certain height and this height is defined as the “critical height?‘, which we designate z,. It is difficult to determine the value of
10
Ur
20
30
40
Fig. 9. Estimated values of zc from Fig. 6 and TDH from Zenz and Weil’s nomograph.
z, accurately, but Fig_ 6 seems to indicate a method of estimating z,. The vaiue of z, is determined approximately, by interpolation as shown in Fig. 6. Figure 9 shows the estimated value of z,, thus obtained, against U, or z+ an (= TDH) obtained by interpolation on the nomograph proposed by Zenzand WeiI [9] isakoplotted forcomparison. It is not expected that z, wih be found to
be much larger than +nH_ The reason for the difference is not clear. As to the influence of free board on the weight of fine particles removed from the bed, Wen and Hashinger [3] carried out an expeziment with three different heights of the freeboard, and they concluded that & remains constant if the freeboard height is greater than 23.5 in. This value is too small compared with z, obtained in this work_ Since they did not state their experimental conditions, it is impotible to determine the reason for the discrepancy. Zenz and WeiI [9] conducted an experiment with a twodimensional fhiidized bed and
1.
Fig_ lo_ Effectof initial content of fines in bed
on
k.
obtained large values of hx_ As their equipment was large (2 ft diam.) and the particles used were cracking catalysts, our work cannot be compared with their data, The inconsistency between z, and hE was due to the slugging phenomena which occmred because of the small diameter of the experimental equipment used in this work. Figure 10 shows the change of k or h with the initial fine contents F,,. As pointed out by Wen and Hashinger [3], k remains nearly constant below 25 wt.%_ This was in agreement with the present work_
;_ .-of kt in this Work a&qz fairIy Well with ‘th&& obtained by Wenand_IIa&inger 133 _ :- .: 1 (4) A critical height-z,, which may Corres~ pond to the TDH, &s.o@t&in~~&xpez+entall~. This value-obtained in this work is about three times greater than that obtained by ... Zenz and Weil[9] _ (5) k is independent of S’s under the present experimental conditions. This result agrees with the findings by Wen and Hashinger [3] .
ACKNOWLEDGEMENT
The authors are indebted to Drs. R. Toei and R. Matsuno at Kyoto University in Japan and Dr. C. Y. Wen at West Virginia University in the U.S.A. for their enthusiastic discussions throughout this project.
LIST C
OF SYMBOLS
concentration of fine particles t, g/cm3
fal CONCLUSION
Fo. Using a batch fluidized bed with a sufficiently high freeboard, this experiment was carried out in order to investigate the effect of the freeboard height on the elutriation rate constant_ A theoretical model was proposed to clarify a physical meaning of the elutriation rate constant.. Within the operating conditions, the following conclusions were drawn. (1) The accumulated weight of the fine.particles, w, at a sufficiently high freeboard is expressed by eqn. (6) or (8). (2) A physical meaning of the elutriation rate constant k in eqn. (3) is -clarified_ It is a constant proportional to the-ratio of concentration of the fine particles at height z to -the total weight bf fine particles still remaining below that height. k is expressed by. eq+ (10) and_eqn, (12). It is also correlatedwith~_by,eqn_ (9) : ._ -: _(3) -The ehitriation rate constaut k is' nearly constant in spite of the.change of i-when z is greziter +than 2~ & -(= ~kz&j-is compared. .: .with those obtained previously. The values
h k
kt P
Q
S
at z and
concentration of fine particles at t = x/u, g/cm3 initial content of fine particles in bed, wt.% length of column segment, mm elutriation rate constant in eqn (3) and related to k, by eqn. (9), cm-’ elutriation rate con&ant defined by eqn U), s-r press-, -20 volumetric flow rate of gas, I/s cross-sectional area of fluidixed bed, cm2 elapsedtimea&rrunisstarted,s superficial gas velocity, cm/s relative velocity of gas, u. - ~4, cm/s terminal velocity of fine particles, cm/s accumuIated weight- of fine particles collected by cyclone separator up to t, g weightof fine particles which remains below any height z, g init@ weight of fine particles in the sy&cm,:g :__-. -; : : :-:~ freeboard height frorq bed surface, cm critical height &om bed surface, cm. Jiansport disengaging height, cm.. . . .
:
7 D; Kunii and-d.-LevenspieI, &Chem. Eng_ Jpn.. 2 (1969) 84 - 88. 8 W; K. &ewis, E_ R. Gilliland and +_ M. La&, C&em. Eng_ Progr- Symp. Ser., 58 [1962) 65 7s.
REFERENCES M_ Leva, Chem. Eng. Rogr.., 4 7 (1951) 39 - 45. G. L. Osbeg and D. H. Char&worth, Chem. EngProgr_, 47 (1951) 566 - 570_ C. Y. W~II and R. F. Hashinger, Am. Inst. Chem. Eng_ J., 6 (1960) 220 - 226. S. Yagi and T_ Aochi, Sot. Chem. Eng.. SPring Meeting, Jpn., (1955) 89 - 92. I. Tanaka, II. Shin&a+ H_ Hirose and Y. Tanaka, J. Chem_ Eng. Jpn.. 5 (1972) 51- 56. M. Leva and C. Y. Wen, in J. F. Davidson and D. Harrison (I&Is_), Fluidization. Academic Press, 1971, pp_ 627 - 650_
F. A. Zenz and N. A. Weil, Am. Ins_ Chem. Engd., 4 (1958) 472 - 479. T. Miyauchi, J_ Chem. Eng. Jpn.. 7 (1975) 201207. M. Horio. A. Taki. Y_ S_ Hi&h and L Mu&i. in J. R. Grace and J. M. Matsen (Eds_), Fluidiration, PIenum Press, New York, 1980. pp. 509 - 518. S_ Morooka, K_ Kawazumi and K. Kate. Sot. Chem. Eng., Fall Meeting. Jpn., (1979) 508 509. IL Fukumoto, Bachelor’s Thesis, Elutriation of Fine Particles at a Sufficiently High Freeboard Height of a Batch Fluidbed Bed, Kyushu In&_ Tech.. Jpn.. (1981). T_ Nagamitsu, Master’s Thesis, Ektiation of Fine Particles from a Batch Fluidized Bed, Kyushu InA Tech.. Jpn., (1981).
Elutriatitin~oifFiqe Particles fkoti &itch Gas-Solid at Sufficietitl~ Hi& Freeboard Height YOSHIZO MATSUNO=, HIGASHlTANI+
HIROYUKI
KAGE,
TETSUYA
Department of Indusfrial Chem.istry and +Department logy, 1-I Sensuicho, (Received
Tobata. Kitahyushu,
NAGAMITSU,
of Environmental
Fluidized Red -
HISAMORI
YAMAGUCHI
Science, Kyzshu
Institute
and KO
of Techno-
804 (Japan)
January 20.1982)
SUMMARY
An experimental and semi-theoretical work on tha elutriation of fine particles from a fluidtied bed was carried out. The fluid&zing equipment, consisting of an iron pipe of 3 in id., was designed in such a way that its freeboard height can be adjusted properly_ At the different freeboard heights and air flow rates, the accumulated weights of fine particles with time were measured. The same procedure was repeated for different initial contents of the fine particles in the bed_ In order to interpref the experimental results, a simple model was constructed by assuming that the fine particles were transported only by convection of gas. The model included two parameters; one was a critical height above which the transport of fine particles was controlled by convection of gas, and the other was the elutriation rate constant_ The critical height was estimated experimentally. The eluiriation mte constant was determined by a mefhod proposed in this work_ It was found that the elutriation rate constant was independent of the freeboard heighf and that its value was consistent with the calculated value based on the correlation of Wen and Hashinger [3] _ Further, a physical meaning of the elutriation rate constant was elucidated from this model.
*To whom correspondence should be sent. Mailing Address; Yoshizo Matsuno, Department of Industrial Chemistry, Kyushu Institute of TechnoIogy, l-l Sensuicho, Tobata, Kitakyusbu, 804 (Japan)_
0032-5910/82/0000-00001$02.75
INTRODUCTION When the fluidized bed is composed of particles of different sizes, the smaller particles will be carried out from the fluidized bed if the gas velocity exceeds the terminal velocities of the smaller particles. The elutriation of fine particles from the fluidixed bed is important in air pollution control, recovery of the valuable materials, estimation of the reaction yields and sekctivities in the freeboard, etc. Since Leva [l] and Osberg and Charlesworth [2] found, from experiments with two particles of different sizes, that the reciprocal of the concentration of fine particles in the bed is exponentially proportional to the elapsed time, macroscopic views of the elutriation of fine particles have been oriented toward clarifying the correlation between the elutriation rate constant and the operational variables by many investigators [3 - 6]_ Wen and Hashinger [3] and Yagi and Aochi [4] have contributed to the establishment of a new concept of the elutriation rate constant_ Kunii and Levenspiel [‘7] have proposed a correlation between the elutiation rate constant and the operating parameters based on the experiment carried out by Lewis et al_ [8] on the entrainment from a continuous fluidized bed. In addition, the estimation of the TDH (Transport Disengaging Height) is important for both the analysis of the gas and particle behaviors in the freeboard and for industrial applications. Zenx and Weil [9] have proposed a method of estimating the TDH_ As they pointed out, this method may not be accurate when the bed diameter and/or
0 Ekevier Sequoia/Printed
in the Netherlands
66
6 Prnw-ereguh 7cErdryer
Fig_ 1. Schematic
diagram of experiment_
Fig_ 2_ FIuidizing
equipment_
superficialgasveIocityissmalLUndersucha condition, slugging, sire segregation and velocityfluctuationin thefreeboard can take place_
Theobjectiveofthispaperistoinvestigate the concentration change at a suf5ciently highfreeboardandtocom&ðeelufriation rate constant and the TDH with operating variables_
EXPERIMENTAL
EQDIPMENT
AND
wasprepared asthelowerpart(a)_ Pressure taps were provided every 50 mm along~the wall oftbispipe segment to measure the e~andedh~ghtofthebedby-a.methodof Miyauchi [lO].Theupperpart (C)wasthe outlet which was connect& to a cyclone separator_ A 10 mm thick poly(me$hyl methacrylate)plateoflmm bore and 6.5. mmsquarepitchservedasadistribut.or_ To preventelectrostaticchargesbetween theparticlesandbetweentheparticleand thewallofthebed,agroundwhzwaswound around the flanges of the column, which madethemeas*urementsfairlyreproducible_ Glassbeadswereusedasthefluidixingparticles_Theaveragediametersofthefiueand coarse particleswere 0.00565 and O-0161 cm,respectively_Thetotalweightoffineand coarseparticlescharged inthebedatthe heginningofeverynmwas2000g.Thegas (airatroomtemperature)wassupplied at a velocity well below the terminal velocity of thefineparticlessoastopreventthembeing entrainedwhilemixingtheparticlessufficientlybeforethenmwasstarted_Thedesiredgasflowratewasadjustedbyregulating valves_Particleswerecollectedbythecyclone separator at a suitable interval_These collectedp~~eswereclassifiedbytheuse of screens, and the fiue particleswere weighedonabaIance_Preliminaryobservationsindicatedthatnegti~bleamountsoffine particlesweredeated attheairoutletof thecycloneseparator, Theexperimentswererepeatedbychangingthefreeboardh~~tandtheairnowrateTheeffectoftheinitialcontentofthefine partich?sinthebedwasalsoinvestigated. The-experimental conditions are summarixedinTable1,
PROCEDURE THEORETICAL
Aschematicdiagramoftheexperimentis showninFig_l_Thecolumnwasmade~ofan ironpipeof3 in(81mm)i_d_Thefluidizing equipmentwas constructed by combining threepartsasshoWninPig_ 2:Inorderto adjustthefreeboardheight,piecesofpipeof Iengths2000mm,~~Omm;650mm,500 mm;300-~~dlOO'mmw~prep~to be inserted aS part (b)i-Z3ycombiningthese piecesofpipesuitably~~thefreeboard~height could be changed-A Segment650 mm:Iong-m ..
CONSIDERATION
AspointedoutbyWenandHashinger[3] and other investigators[7,9,11,12],the entrainmentoftheparticlesiscausedbythe fluctuation of gas velotiitycaused by the intermittent.burstingactionofbubblesjust above the bed surfsce.Asthe particlesare carried up to a sufficientheight,it is reasonabletoconsiderthattheyarecontrolledbytheconve;ction-ofthegasflowbecause ofthen&ligibledirecteffe&oftheb&sting .-.
TA&El :
Ekperimentzdconditions
(1)Operatingconditions~
Initi&totalweig& ofpa+les,g Initi$ content of &ES, F,,, wt.%
2000
2000 15
10
Airflowrate,x/min
80
s"p+icialgasve~ocity,cmls Freeboard he&h&cm
28.6
100
120
20
36-4 46-S 30-350
25
100
140
36.4 35-215
57-6
(2)Characteristicsofpartides Particlesused:glasbeads Density,gfcm3 Sizerange,,Y
fine
coarse 2.52 80 -100
2.52 250 -280
0.0161
0.00565
Averagediieteqcm
24.3
197.5
Terminalvelocity,cm/s
By solving eqn_ (2), using the separation variables method, eqn. (3) is obtained_ c(z,t)
= cs exp I-ku,(
t -z/4)
J
(3)
where ca and are integration constants. The accumulated weight of the fine particles, ~(z,t), at any height z and elapsed time t after the beginning of the run w5il give the concentration of fine particles, c&t), as Fig.3. Scheme
ofelutriation model_
%c(Gt)
aw(z,t)
=
ar [
action of bubbles at such a high freeboard_ Thus, a mass balance for the fine particles in the shell, Sdz, as shown in Fig. 3, can be given by, (Sdz)
Substitution
awkt) [
~=SC~Cl,-U&IZ+,, &
(1)
where c is the concentration of the fine particles in the freeboard, S is the cross-sectional area of the column, t is the time elapsed just after the gas begins to flow out at the bed surface (z = 0), and u, is the relative velocity between the gas velocity U, and the terminal velocity of the fine particles ut_ From eqn. (l), we get
ac at=--“%
ac
(2)
at
I
(4)
z
of eqn. (3) into eqn. (4) gives
1
=
Szqzo expf-ku,(t --z/u,)]
(5)
z
Next we integrate eqn- (5) under a fixed height z. It should be noted that the lower limit of integration for time t must be Z/U,, since it takes this time for the entrained particles to reach the distanze z_ Therefore, we get w(z,t)
= (Sc&k)Cl
-
exp(--k+(t
-z/24))]
(6) According to Wen and Hashinger [S] and the- following equation others 14,5,71, holds above the TDH,. i.e. z > z,_.nn
-!+V
(7)
6i3
Fig. 4. Change of accumulated
weight of frieswith t_
where W is equal to W. - w and W. is the initial weight of the fine particles. Let us consider that the fine particles are collected at an arbitrary height z. After the particles leave the bed surface, as mentioned before, it takes t = z/y before they reach z_ Just then the particles w-RI be collected. In order to determine the accunxdated weight of fine particles, ru(z,t), eqn_ (7) sho-uId be integrated with respect to time &om z/u, to f at height z. That is
Fig_ 5. Relationship and pressure drop.
w(z,t)
= W,fl
-
expt-k(t
-z/u,))1
(8)
Comparing eqn_ (8) with eqn. (6), we get a relationship between the eIutiation rate constant k in this work and & proposed previously [3,4] as follows: &=ku,
ctz,t)
w,
-w(z,t)
=- c,
(11)
wo
Substituting eqn. (11) obtain
into eqn. (lo),
W, - w(z, t))
we
(12)
Equation (10) or (12) gives a physicaI meaning of the elutriation rate constant_ That is to say, k is a constant which is proportional to the ratio of the contientration to the total weight of fine particles remaining below any height z. If we know this ratio at any freeboard height, we can determine the ehrtriation rate constant. EXPERIMENTAL RESULTS AND DISCUSSION
(9)
where k is expressed as k=&,l&
height from distributor
the initial weight of fine particles in the bed, respectively_ From eqns. (3) and (6), combined with eqn. (lo), we can obtain the following relationship :
k = Sc(z, t)/(
and
between
(10)
From eqn. (3), c, is found to be the fine particle concentration at t.7 z&, and W,, is the weight ~offine part&s remaining below-z just before the fine particIes &a& &It c&r be also seen &&at,when z = 0, c,, and W, co& respond to the concentration of fine particles blownup from the bed surface-at t = 0 and
Figure 4 shows the cumulative weight of fine particles cohected by the cyclone separator as a function of time -at a fixed freeboard height z. It is noted that the changes in w with-t become quite siniilar above a certain height_ The -data on the changes in w with t under other conditions are available. elsewhere [13,14] . Figure 5 shows how the pressurechanges with the height from the distributor for various gas flow rates. The pressure gradients seem to change slightly with the gas flow, but
69
I4
1
loo
1
300
2%
Fig.6.Change ofkwithheightandconstancy above a certain height r,
of k
Fig. 8. Comparison of kt in this work with those of other investigators_
uokmm so
3040 -4 E 03 z= “Z2 P z
1
60 0
0
0
0
10
Fo lOwtofe
20 Mcmls)
Fig. 7_ Variation
30
of k with u, or ug_
+$200 3 iO0 I
0 this is negligible_ Therefore, it is decided, using Miyauchi’s method [lo], that the bed
surface from the distributor is 30 cm in spite of the change of gas flow rates_ The value of k can be obtained as follows: c&t) is determined according to eqn. (4), by graphically differentiating the accumulated weight of fine particles with time shown in Fig. 4. Then, applying eqn. (12), we determine the k for any time at a fixed height. The average value of k for each t is plotted against z in Fig. 6. The range of deviation of k for each t is shown by a symbol (I) in Fig. 6. The k, which is determined by the method mentioned above, is plotted against u, in Fig. 7_ Figure 8 compares the & obtained from the experimental results with the & values c&uIated from previously proposed correlations [3_5].Inthispapereqn.(9)isused_k,in this work agrees fairly well with the correlation of Wen and Hashinger [3] when u, is
laIge.
’ As pointed iut by Wen and Hashinger [ 31, ’
k, in eqn. (8) should be constant above a
certain height and this height is defined as the “critical height?‘, which we designate z,. It is difficult to determine the value of
10
Ur
20
30
40
Fig. 9. Estimated values of zc from Fig. 6 and TDH from Zenz and Weil’s nomograph.
z, accurately, but Fig_ 6 seems to indicate a method of estimating z,. The vaiue of z, is determined approximately, by interpolation as shown in Fig. 6. Figure 9 shows the estimated value of z,, thus obtained, against U, or z+ an (= TDH) obtained by interpolation on the nomograph proposed by Zenzand WeiI [9] isakoplotted forcomparison. It is not expected that z, wih be found to
be much larger than +nH_ The reason for the difference is not clear. As to the influence of free board on the weight of fine particles removed from the bed, Wen and Hashinger [3] carried out an expeziment with three different heights of the freeboard, and they concluded that & remains constant if the freeboard height is greater than 23.5 in. This value is too small compared with z, obtained in this work_ Since they did not state their experimental conditions, it is impotible to determine the reason for the discrepancy. Zenz and WeiI [9] conducted an experiment with a twodimensional fhiidized bed and
1.
Fig_ lo_ Effectof initial content of fines in bed
on
k.
obtained large values of hx_ As their equipment was large (2 ft diam.) and the particles used were cracking catalysts, our work cannot be compared with their data, The inconsistency between z, and hE was due to the slugging phenomena which occmred because of the small diameter of the experimental equipment used in this work. Figure 10 shows the change of k or h with the initial fine contents F,,. As pointed out by Wen and Hashinger [3], k remains nearly constant below 25 wt.%_ This was in agreement with the present work_
;_ .-of kt in this Work a&qz fairIy Well with ‘th&& obtained by Wenand_IIa&inger 133 _ :- .: 1 (4) A critical height-z,, which may Corres~ pond to the TDH, &s.o@t&in~~&xpez+entall~. This value-obtained in this work is about three times greater than that obtained by ... Zenz and Weil[9] _ (5) k is independent of S’s under the present experimental conditions. This result agrees with the findings by Wen and Hashinger [3] .
ACKNOWLEDGEMENT
The authors are indebted to Drs. R. Toei and R. Matsuno at Kyoto University in Japan and Dr. C. Y. Wen at West Virginia University in the U.S.A. for their enthusiastic discussions throughout this project.
LIST C
OF SYMBOLS
concentration of fine particles t, g/cm3
fal CONCLUSION
Fo. Using a batch fluidized bed with a sufficiently high freeboard, this experiment was carried out in order to investigate the effect of the freeboard height on the elutriation rate constant_ A theoretical model was proposed to clarify a physical meaning of the elutriation rate constant.. Within the operating conditions, the following conclusions were drawn. (1) The accumulated weight of the fine.particles, w, at a sufficiently high freeboard is expressed by eqn. (6) or (8). (2) A physical meaning of the elutriation rate constant k in eqn. (3) is -clarified_ It is a constant proportional to the-ratio of concentration of the fine particles at height z to -the total weight bf fine particles still remaining below that height. k is expressed by. eq+ (10) and_eqn, (12). It is also correlatedwith~_by,eqn_ (9) : ._ -: _(3) -The ehitriation rate constaut k is' nearly constant in spite of the.change of i-when z is greziter +than 2~ & -(= ~kz&j-is compared. .: .with those obtained previously. The values
h k
kt P
Q
S
at z and
concentration of fine particles at t = x/u, g/cm3 initial content of fine particles in bed, wt.% length of column segment, mm elutriation rate constant in eqn (3) and related to k, by eqn. (9), cm-’ elutriation rate con&ant defined by eqn U), s-r press-, -20 volumetric flow rate of gas, I/s cross-sectional area of fluidixed bed, cm2 elapsedtimea&rrunisstarted,s superficial gas velocity, cm/s relative velocity of gas, u. - ~4, cm/s terminal velocity of fine particles, cm/s accumuIated weight- of fine particles collected by cyclone separator up to t, g weightof fine particles which remains below any height z, g init@ weight of fine particles in the sy&cm,:g :__-. -; : : :-:~ freeboard height frorq bed surface, cm critical height &om bed surface, cm. Jiansport disengaging height, cm.. . . .
:
7 D; Kunii and-d.-LevenspieI, &Chem. Eng_ Jpn.. 2 (1969) 84 - 88. 8 W; K. &ewis, E_ R. Gilliland and +_ M. La&, C&em. Eng_ Progr- Symp. Ser., 58 [1962) 65 7s.
REFERENCES M_ Leva, Chem. Eng. Rogr.., 4 7 (1951) 39 - 45. G. L. Osbeg and D. H. Char&worth, Chem. EngProgr_, 47 (1951) 566 - 570_ C. Y. W~II and R. F. Hashinger, Am. Inst. Chem. Eng_ J., 6 (1960) 220 - 226. S. Yagi and T_ Aochi, Sot. Chem. Eng.. SPring Meeting, Jpn., (1955) 89 - 92. I. Tanaka, II. Shin&a+ H_ Hirose and Y. Tanaka, J. Chem_ Eng. Jpn.. 5 (1972) 51- 56. M. Leva and C. Y. Wen, in J. F. Davidson and D. Harrison (I&Is_), Fluidization. Academic Press, 1971, pp_ 627 - 650_
F. A. Zenz and N. A. Weil, Am. Ins_ Chem. Engd., 4 (1958) 472 - 479. T. Miyauchi, J_ Chem. Eng. Jpn.. 7 (1975) 201207. M. Horio. A. Taki. Y_ S_ Hi&h and L Mu&i. in J. R. Grace and J. M. Matsen (Eds_), Fluidiration, PIenum Press, New York, 1980. pp. 509 - 518. S_ Morooka, K_ Kawazumi and K. Kate. Sot. Chem. Eng., Fall Meeting. Jpn., (1979) 508 509. IL Fukumoto, Bachelor’s Thesis, Elutriation of Fine Particles at a Sufficiently High Freeboard Height of a Batch Fluidbed Bed, Kyushu In&_ Tech.. Jpn.. (1981). T_ Nagamitsu, Master’s Thesis, Ektiation of Fine Particles from a Batch Fluidized Bed, Kyushu InA Tech.. Jpn., (1981).