incipient flu1dization of polydisperse beds

INŻYNIERIA CHEM ICZNA I PROCESOWA 4, 769-786 (1988)

Andrzej Biń, N u h u A k a w u I r m i y a

INCIPIENT FLU1DIZATION OF POLYDISPERSE BEDS

In s ty tu t Inżyn ierii C hem icznej i P rocesow ej P o litech n ik i W arszaw skie j

W pły n ę ło 24 II 1988

A d d itio n a l ex p erim en ta l d a ta fo r th e beg inn ing , m in im u m a n d co m p le te flu id iza tio n velocities for b in a ry a n d te rn a ry m ix tu res o f sand , d ia to m ite a n d u rea p a rtic les hav e been p rov id ed . T h e ow n ex p e rim en ta l d a ta a n d som e m o re recen t ones d u e to o th e r a u th o rs o n ubf, umf a n d ucf c an reaso n a b ly ac cu ra te ly be co rre la te d by th e E rg u n ty p e e q u a tio n w ith c o n s ta n ts suggested by V aid a n d Sen G u p ta o r by W en a n d Y u if th e b ed p a ra m e te rs a re a p p ro p ria te ly ca lcu la ted . V alid ity o f som e o th e r re la tio n sh ip s, a lso th o se invo lv in g bed p o ro sities , hav e been checked .

U zy sk an o dalsze d a n e d o św ia d cza ln e o k reśla jące p o czą tk o w ą , m in im a ln ą o raz ca łk o w itą p ręd k o ść fiu idyzacji d la dw u- i tró jsk ład n ik o w y ch m ieszan in p iask u , d ia to m itu i m oczn ik a . W łasne dan e d o św ia d cza ln e o ra z now sze d a n e in n y ch a u to ró w d la иы , umC i uc, m o ż n a z w y sta rcz a jącą d o k ład n o śc ią sk o re lo w ać za p o m o c ą ró w n a n ia ty p u E rg u n a ze s ta ły m i p o d a n y m i p rzez V aida i Sen G u p tę o ra z przez W en a i Y u, jeśli p a ra m e try z ło ża z o s ta n ą ob liczo n e w o d p o w ied n i sposób . S p ra w d zo n o p rz y d a tn o ść innych zależności, ró w n ież tych , k tó re zaw iera ją p o ro w a to śc i złoża, d o o k re ś la n ia w spo m n ian y ch p rędkości.

В с т а т ь е п о лучен ы д о п о л н и т е л ь н ы е эк сп ер и м ен тал ь н ы е д ан н ы е, х ар ак те р и зу ю щ и е н ач а л ьн у ю , м и н и м а л ь н у ю с к о р о сти п севд о о ж и ж ен и я , а так ж е с к о р о с ть п о л н о го п севд оож и ж ен и я, д л я д вух- и тр ех к о м п о н ен тн ы х см есей .ча сти ц песка, д и а т о м и т а и м оч еви н ы . С о б ствен н ы е эк сп ер и м ен тал ь н ы е д а н н ы е и новей ш и е д ан н ы е други х и ссл ед о в ател ей д л я иы , ит1 и ucf м ож н о б ы л о со п о с т а в и т ь с б о л ь ш о й степ е н ью то ч н о сти п ри п о м о щ и у р авн ен и я Э р ган а с п о сто ян н ы м и , п р и в о д и м ы м и Б а й д о м и С ен Г у п то м , а так ж е В еном и Ю . Т а к а я в о зм о ж н о с т ь со п о ста вле н и я в о зм о ж н а б ы л а в случае с о о т в е т с т в у ю щ е го р асч ета п а р а м е т р о в сл о ев части ц . П р о вер ен а п р и го д н о с т ь о стал ь н ы х эм п и р и ч ески х уравн ен и й , в т о м числе и тех , в к о то р ы х у чи ты вается п о р и с т о с т ь сл о я .

IN T R O D U C T IO N

In practical applications of fluidized bed technique polydisperse beds of solid particles are encountered most frequently. In such beds solid particulate materials of different size, shape and/or density are used. Typical examples of such beds are coal with limestone added (as a desulfurization agent in combustion process), far- maceutical and pesticide powder products, agriculture seeds etc. When such systems are fluidized, a dynamic mixing/segregating equilibrium is set up wjiich is mainly a function of denisty and size of particles and of the gas flow rate. Fluidization

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770 A. B iń , N . A k a w u Irm iya

theories operate with the surplus (u —Mmf) or the ratio u/um[ (fluidization number) values so that the um( and/or other inherent characteristic parameters for the incipient fluidization of polydisperse beds are of primary relevance.

Most of the experimental works devoted to the incipient fluidization of polydisperse beds concern binary mixtures and the results of these works allow to gain insight into general behaviour of polydisperse beds made up of more than two different components. The majority of these works concentrated on determination and correlation of um[ (Rem[) for multicomponent particulate beds, less attention being paid to other accompanying parameters inherent in the incipient fluidization of such beds. In this paper more experimental data for the incipient fluidization of mixtures of different solid particles have been provided and an attempt to obtain some generalized correlations for the own as well as other authors’ data has been presented.

T H E O R E T IC A L B A C K G R O U N D

When a binary mixture of particulate solids is fluidized, typically one species will have a lower value of wmf than the other. Thus, the lower umf species will fluidize at a velocity uF (the fluid component) and the higher umf at uP (the packed component). If there is a density difference, the heavier component (@H) will tend to sink, i.e. becomes jetsam, while the ligther (^L) to rise, i.e. becomes flotsam. If there is no density difference, the bigger (dB) component becomes jetsam and the smaller (ds) flotsam. It is this segregating tendency and the segregation rate arising from it which causes some difficulty in umf measurements for such systems.

Figure 1 presents the effect of mixing/segregation state on the relationship between bed pressure drop and superficial gas velocity idealized [2]. In case (A) the completely mixed bed with only a small difference in size and of equal density can be achieved. In this case, a unique measure of the minimum fluidization velocity, uM, can be obtained from the intersection of the pressure drop plots. In case (B), when one component is both considerably bigger and denser (and therefore of um[, uP) than the other, the system remains completely segregated, with pure flotsam at the top and pure jetsam at the bottom. To obtain a value of wmf some special definition must be adopted, since at uF < u < uP the upper part of the bed is well fluidized while the bottom One is packed. Similar intersection of the pressure drop plots as before yields a vale of us, apparent minimum fluidization velocity. In the majority of cases some intermediate mixing/segregation equilibrium is reached (C), and similar intersection of the pressure drop plots leads to a value of uMS. In this case an experimental procedure used in determination of uMS can affect its value (fast or slow de- fluidization).

For the cases (B) and (C) from this description one can distinguish between the beginning fluidization velocity, иы ( = mf ) and the complete fluidization velocity, uc{ { = Up). More exactly, иы is slightly higher than for a pure component (mf ), while uc{ is


Fluidization of polydispcrse beds 771

slightly reduced with respect to »P,iwhich effects result from the presence of the other components. The minimum fluidization velocity, umf, follows from the intersection of the pressure drop plots versus superficial gas velocity for a packed and a fluidized bed and its apparent meaning is clearly evident from Fig. 1. Despite its artificial character um{ has most frequently been measured and correlated for multicomponent mixtures, thus providing quite often some underestimation of the necessary conditions for complete fluidization [3, 5, 8 , 9, 12, 14-18, 21-24].

Fig . 1. V ario u s d efin itio n s o f th e m in im u m flu id iza tio n velocity fo r a b in a ry system : A — perfectly m ixed bed , В — com p le te ly seg reg a ted bed,

C — p a rtia lly m ix ed /seg reg a ted bed Rys. 1. R óżne definicje m in im alnej p ręd k o śc i flu idyzacji d la u k ła d u d w u sk ład n ik o w eg o : A — złoże d o sk o n a le w ym ieszane, В — złoże ca łkow icie segregow ane, С — złoże częściow o

w ym ieszane/seg regow ane

There were numerous attempts to correlate umf for multicomponent systems (mostly binary systems), and a list of such correlations is given for example by T h o n g l i m p et al. [3]. Most commonly the well known and established for practical applications for single-component system Ergun equation was used to correlate um[ (and/or иы and ucf):

K l Re^[ + K 2Rem[ = Ar. (1)

In calculations of dimensionless numbers (Ar and Rem[) the appropriate values of the particle diameter and density for the mixture must be used. For binary systems the following definitions are usually recommended:

1 /Gr = Z Xi/Qi’ i = 1

(2)

W m C j = I x M iQ i)- i = 1

(3)

Rowe and N ienow [4 ] proposed a sem i-theoretical equation for uM of a multi- com ponent bed made up o f particles with equal density

l - 6 i 2 — n I In[x i + (rf1/^2 )x2+ . . . ] 1- 3/n, (4)

where n was given empirically as 1.053. This equation can be extended to the case of binary mixtures of particles different in density as well as in size.


772 A. Biń , N. A k a w u Irm iya

Cheung et al. [5 ] proposed a purely empirical equation for binary mixtures of the same density

■ um = uF{uP/uF)Xp (5)

provided d j d s < 3, which later turned out to be also applicable for different density components.

Chiba et al. [2] derived an equation for completely mixed beds

«м = uAejQF)(dJdF)2 (6)

obtained for laminar flow regime and under assumption of constant voidage. The mean particle diameter is here defined as d3i0 (volume to number mean). For completely segregating case the st>me authors suggested an equation

(1 Wp/np)Xp -f- Mp/up

O b a ta et al. [6 ] showed that us resulting from Eq. (7) is actually a harmonic mean o f uh and uP taking each weight fraction of the tw o-com ponent mixture.

Much less information is available for ubf and wcf. V aid and G u p ta [7 ] suggested two correlations for Reb[ and Rec{ obtained on the basis of the available at that time experimental data on solid — liquid and solid — gas systems. These correlations are of the Ergun type, Eq. (1), with different pairs of and K 2 for the beginning and complete fluidization, respectively. .

Ś c i ą ż k o et al. [8 , 9, 13] studied incipient fluidization of mixtures of coal, char and glass beads (the mixtures were made up of the same material but with different size fractions) and suggested semi-theoretical equations of the type

CRem = Ar, (8)

where Re means Rebf, Rem[ or Rec{, respectively, and with different values of С and the power exponent m. The same authors listed a few published correlations for Rec( due to other authors. Among them that given by K n o w l .t o n [10] seems to be of some interest

Rect = Z*,-Remfii, (9)

where Remf t should be calculated with the aid of Wen and Yu equation (resulting directly from Eq. (1)):

Remf, i = (33.72 + 0.0408 A r f 5- 33.7. ( (10)

H artm an et al. [11] approxim ated their experimental data for uc[ collected for mixtures of ballotini and coal ash with the following empirical relationship

Mcf = ^ m f .P ^ m f .F A W .p ) * ' • O l )

Recently, N o d a et al. [12] published some experimental data on wcf for binary systems of particles with different sizes and densities (sand, glass beads, wood,


F l u i d i z a t i o n o f p o l y d i s p c r s c beds 7 7 3

Marten shot, soya beans, small beans and rubber) and correlated them using Eq. (1) and giving A.', and K 2 by

K , = 36 ( < W ( 4 e P))~ ° 196> (12)

K 2 = U 0 0 (d PQF/(d FQPj) °-296 (13)

for completely mixed beds, and

K 2 = 6400(dPQ F/(d f g p)) “ 1 8 6 (14)

for partially mixed beds with dP/d F > 3.Apart from the above mentioned parameters for the incipient fluidization

parameters a remark should be made on the minimum bubbling velocity (ubm). This corresponds to the gas superficial velocity at which the first bubble appears and constitutes a boundary between two kinds of fluidization, that is particulate (homogeneous) and aggregative (heterogeneous) fluidization. In the case of essentially monodisperse systems wmh will be greater than umf for powders belonging to group A according to the Geldart’s classification, and »mb = hmf for powders belonging to group B . For the mixtures the situation is more complex since bubbles may appear either below or above um( [13]. Ś c i ą ż k o and B a n d r o w s k i [13] studied the minimum bubbling velocity for the mixtures of coal and char and suggested a correlation for Remb of the type similar to Eq. (8 ).

Variation of иы and uc[ with the mixture composition for binary and ternary systems can be presented in a form resembling phase equilibrium diagrams [1, 17, 18—20]. Such diagrams enable easier assessment of segregation properties of different mixtures of the same initial materials. For the particle diameter ratios less than three such diagrams are closed, whereas for these ratios greater than 3 they remain open.

For each of the above mentioned parameters of the incipient fluidization of polydisperse beds a characteristic bed voidage accompanies. The most accessible from the direct measurements is a packed bed voidage, e0, dependent only upon the mixture composition and the shape of particles. The bed voidage at the beginning of fluidization, ebf, does not differ significantly from e0. Much more difficult problem is involved with determination of emf and ec/ for polydisperse beds. These voidages depend upon the bed composition as well as on hydrodynamic conditions. Ś c i ą ż k o

and B a n d r o w s k i [13] suggested some empirical relationship which can eventually be used to calculate emf and ксГ knowing s0, R eP and Ar, however, it is not clear if this relationship is sufficiently general and applicable for any solid mixture. Usually, the authors do not give detailed information on ebf, Bmf and ecf.

E X P E R IM E N T A L

Determination of the main parameters for the incipient fluidization has been carried out in a typical equipment which main parts consisted of a transparent glass column of internal diameter 39 mm and height of 1.0 m, a rotameter and U-tube


774 A. Biń , N . A k a w u Irm iya

T a b l e 1. P hysica l p ro p e rtie s o f n a rro w frac tio n s T a b l i c a 1. W łaściw ości fizyczne w ąsk ich frakcji

M a teria łSize ran g e d e s “ mf smf G e ld a r t’s

[m m ] .[m m ] [k g /m 3] [m /s ] g ro u p

Si 0.383-0 .430 0.408 2670 0.21 0.512 B -D

s 2 0.600-1 .02 0.810 2640 0.45 0.490 D

s 3 1.20-1.50 1.35 2610 0.81 0.497 D

s 4 1.50-2.00 1.75 2610 1.05 0.497 DD? 0.43-0 .55 0.49 1950 0.17 0.583 В

d 2 0 .55-0 .60 0.57 1950 0.19 0.661 B -D

D 3 0 .60-1 .02 0.81 1950 0.33 0.675 B -D

d 4 1 .02- 1.20 1.11 1950 0.47 0.677 D

d 5 1.20-1.50 1.35 1950 0.70 0.672 D

D 6 1.50-2.00 1.75 1950 0.81 0.675 DU ? 4 .0 -5 .0 4.5 1335 1.28 0.482 Du 2 5.0-6 .0 5.5 1335 1.51 0.507 D

1 S — sand; 2 D — diatomite; 3 U — urea.

T a b l e 2. P h y sica l p ro p e rtie s o f b in a ry m ix tu res T a b l i c a 2. W łaściw ości fizyczne m ieszan in d w u sk ła d n ik o w y ch

М ясс f ra r tin n M e an p artic ie M e an p a rtic ieM a te ria l

x F x jd iam e te r

[m m ]d ensity[k g /m 3]

U 1 + U 2 0.50 0.50 4.95 1335s 4 + d 4 0.32 0.68 • 1.48 2335s 4 + u 2 0.71 0.29 2.18 2040s 4 + d 6 0.40 0.60 1.75 2299

Р з + ° 6 0.40 0.60 1.20 1950d 5 + d 6 0.40 0.60 1.57 1950d 6 + d 4 0.40 0.60 1.42 1950D 3 + D j 0.80 0.20 0.53 1950D 3 + D [ 0.60 0.40 0.58 1950D 3 + D ! 0.40 0.60 0.64 1950

D 3 + D l 0.20 0.80 0.72 1950S3 + D 5 0.50 0.50 1.35 2232

d 5 + d 6 0.80 0.20 1.42 1950D 5 + D 6 0.60 0.40 1.49 1950D s + D 6 0.40 0.60 1.57 1950D 5 + D6 0.20 0.80 1.65 1950S 3 + S4 0.80 0.20 1.42 2610S 3 + S4 0.60 0.40 1.49 2610s 3 + s 4 0.40 0.60 1.57 2610s3+s4 0.20 0.80 1.65 2610


Fluidization of polydisperse beds 775

T a b l e 3. P h y sica l p ro p e rtie s o f te rn a ry m ix tu res T a b l i c a 3. W łaściw ości fizyczne m ieszan in tró jsk ład n ik o w y ch

M uss frac tionM e an p artic le M e an p artic le

M a te ria l d ia m e te r d ensityXF Xm Xp

[m m ] [k g /m 3]

D j + D 2 + D 3 0.40 0.20 0.40 0.59 1950D t + D 2 + D 3 0.3Ó 0.40 0.30 0.58 1950D ; + D 2 + D 3 0.20 0.60 0.20 0.56 1950

+ D 2 + D 3 0.10 0.80 0.10 0.54 1950S j + D 2 + D 3 0.29 0.35 0.36 0.36 2115

d 2 + S 2 + U 2 0.40 0.41*

0.19 0.77 1919

manometers for measurements of the pressure drop across the bed. The column was equipped with a gas distributor which had three layers: the bottom and the top layers were screen distributors made of a fine and thicker gauze, respectively. The middle layer was packed with coarse sand particles of size 2 mm which served, as a flow uniforming device for fluidizing air. The auxiliary equipment used consisted of a pressure regulating valve and an oil filter to remove oil droplets from the air stream. Two sets of the U-tube manometers were used: one, the so-called two-fluid manometer, filled with water and xylene, for more accurate readings, and another filled with water. All experiments were conducted at the ambient conditions and prior to each run the bed was firstly fluidized and then suddenly stopped to obtain a completely mixed system.

During an experimental run the basic parameters were measured: the net pressure drop across the bed, the bed static and dynamic heights, the pressure drop across the gas distributor and the gas flow rate, gas temperature and pressure. By slowly increasing or decreasing gas flow rates the corresponding pressure drop across the bed and the bed heights were recorded.

The following materials have been used in the experiments: sand, urea and diatomite. The main physical properties of the narrow fractions of these materials are listed in Table 1. The narrow fractions were then used to prepare binary and ternary mixtures of the same but differing in size materials or of different materials. In Tables2 and 3 the basic physical properties of the binary and the ternary mixtures used are given. The mean particle diameters and the mean density of such mixtures given in the Tables were calculated from Eqs. (2) and (3), respectively.

R E S U L T S A N D D IS C U S S IO N

On the basis of the experimentally determined plots of the pressure drop across the bed versus the superficial gas velocity in the column the values of the characteristic velocities for the incipient fluidization were obtaned. In the case of the narrow fractions a sharp transition from the packed into the fluidized state was observed yielding a single minimum fluidization velocity (Fig. 2).


776 A. Biń, N. A kaw u I rm iy a

F ig . 2. Bed p ressu re d ro p vs, superficial gas velocity for n a r ro w frac tio n s o f sand

Rys. 2. S p ad ek c iśn ien ia w z łożu w funkcji p ozo rnej p ręd k o śc i gazu d la w ąsk ich frakcji p iask u

О Ю u [m/s] 2.0

Unlike narrow fractions, mixtures of particles with different size and/or density tended to either segregate or partially segregate. For example, the binary mixtures of sand and diatom ite (with dm = 1.48 mm) and sand and urea (with dm = 2.18 mm) showed a tendency for partial segregation while the binary mixture of urea (with dm = 4.95 mm) indicated a tendency for total segregation (Figs. 3 and 4). A curvature

r - i 1<* О OL

d?< 1.2

1.0

0.8

0.6

OA

02

0.2 OA 06 0.8 1.0 1.2 1.4 1.6 U [m/s]

Fig. 3. Bed p ressu re d ro p vs. superficial gas velocity for b inary m ix tu res o f sand an d d ia to m ite an d sandan d u rea

Rys. 3. S p ad ek c iśn ien ia w z iożu w funkcji p o zo rn e j p ręd k o śc i gazu d la d w u sk ła d n ik o w y ch m ieszaninp ia sk u i d ia to m itu o ra z p ia sk u i m o czn ik a


Fluidization of polydisperse beds 7 7 7

Fig . 4. Bed p ressu re d ro p vs. superficial gasvelocity fot u re a ^

Rys. 4. S p adek c iśn ien ia w z łożu w funkcji < p o zo rn e j p ręd k o śc i gazu d la m o czn ik a

0.4

0,3

0.2

0.1

0O 0.4 0 8 1.2 1.6 2.0 U [m/s]

noticed for the packed bed plot for the urea particles indicates that the gas flow conditions were in the transition or the turbulent flow regimes.

Variation of um[ for the binary mixtures of sand and diatomite with the mass fraction of the one of the components is shown in Fig. 5. The corresponding “phase diagrams” for иы and ucf are plotted in Fig. 6 . For the materials studied the size ratio

Fig. 5. D ep en d en ce o f th e m in im um flu id iza tio n F ig . 6. D ep en d en ce o f th e beg in n in g an d com p-velocitv o n th e flo tsam m a te ria l m ass frac tio n fo r lete flu id iza tio n velocities on th e flo tsam m a teria l

b in a ry m ix tu res o f sa n d a n d d ia to m ite m ass frac tio n fo r b in a ry m ix tu res o f sand an d Rys. 5. Z a leżn o ść m in im alnej p ręd k o śc i fluidyza- d ia to m itecji o d zaw a rto śc i sk ła d n ik a lżejszego d la dw u - Rys. 6. Z a leżn o ść p oczątkow e j i ca łkow ite j fluidy-

sk ła d n ik o w y ch m ieszan in p ia sk u i d ia to m itu zacji o d zaw arto śc i sk ła d n ik a lżejszego d la d w u sk ład n ik o w y ch m ieszan in p ia sk u i d ia to m itu


778 A. Biń , N . A k a w u Irm iya

of the jetsam and the flotsam particles was less than 3 so that the equilibrium diagrams were found to be closed. The area between the curves of ubf and uc[ varies

, with this ratio.An increase in the mass fraction of the finer material resulted in a decrease of wbf

and мсГ. Also, it can be noted that иы of the mixtures is greater than um{ of the pure fine fraction. This effect can be attributed to the presence of coarse particles which as a jetsam material remain unfluidized at the bottom of the bed. On the other hand, addition of a finer fraction decreases all incipient fluidization velocities, in particular uc[, as compared to the minimum fluidization velocity of a coarser material. This well known effect of “fluidization improvement” may be interpreted in terms of reduction of the region of partly fluidized bed and affecting gas bubbles size distribution, most likely promoting formation of smaller and stable gas bubbles [ 8 ].

Figure 7 demonstrates the bed height versus the gas superficial velocity for

0 1.0 2.0 U [m/s]

F ig . 7. D ep en d e n ce o f th e bed h e ig h t o n superficial gas velocity Rys. 7. Z ależn o ść w ysokości z ło ża o d p o zo rn e j p ręd k o śc i gazu

a ternary diatomite mixture and a binary urea mixture. The plots shown a typical behaviour of the group В (or D) materials according to the Geldart’s classification which is characterized by a distinct transition from the packed bed straight to the aggregative bed. Most of the materials studied in this work showed such a fluidization behaviour.

The bed expansion curves served also for calculating the average bed voidages corresponding to the minimum fluidization velocity. The bed voidage varied from the packed state value, £0, to that observed in the fluidized state. For the coarser particles (e.g. those belonging to group B) the minimum fluidization voidage, emf,



coincides with emb and it can be concluded that

£ 0 < £ m b = e m f (15)

Figures 8-10 show dependences of Reb{, Rem{ and Recf on Ar for the mixtures made up of the narrow fractions. For comparison possibly all available experimental data (mainly for Remf) due to different authors are also indicated. In these diagrams

Fig . 9. R e la tio n sh ip R e mf = / (Ar) fo r th e m in im u m flu id iza tio n velocity

1 — E q . (1) with = 24,6 and K 2 = 1650; 2 — equation due to G o r o s h k o et al. [26] Remf = Ar/( 1400 + 5.22 Aro s); 3 — E q. (8)

with С = 1047 and m = 1.0925 [9]. The remaining symbols are defined in Fig. [8]

Rys. 9. Z a leżn o ść R e mf = f (Ar) d la m in im alnej p ręd k o śc i flu idyzacji

1 — równ. (1) ze stałymi K, = 24,6 i K 2 — 1650; 2 — równanie G o r o s z k o i in. [26] Remf = Ar/( 1400 + 5,22 Лг1/2); 3 — równ. (8)

ze stałymi С = 1047 i m = 1,0925 [9]

Own doto

▼ U1 ♦ U2

A U? ♦ Si,■ D ♦ S binar* '• D + D !y5,,ms» S * S* ♦ * ternary syst. -

* [1] v [17 ]

some relationships suggested by different authors have also been given. For dependences of Rebf and Rec( on Ar the relationships recommended by V a id and Sen G u p t a [7 ] corresponding to Eq. (1) seem to approximate with a reasonable accuracy the own experimental data as well as some additional data due to the other authors which were not included in the considerations of V a id and Sen G u p t a [7 ]. Larger

Fig. 8. R e la tio n sh ip R e bf = f (Ar) fo r th e beg in n in g flu id iza tio n velocity

1 - Eq. (1) with К , = 52 and K 2 = 1883 [7]; 2 - Eq. (8) with С = 2242 and m = 1.0783 [9]; 3 - Eq. (8) with С = 846 and

m = 1.045 [13]

Rys. 8. Z a leżn o ść R ebt = f (Ar) d la p o czą tk o w e j p ręd k o śc i flu idyzacji

1 — równ. (1) ze stałymi K t = 52 i K 2 = 1883 [7]; 2 — równ. (8) ze stałymi С = 2242 i m = 1,0783 [9]; 3 — równ. (8) ze stałymi

С = 846 i m = 1,045 [13]


780 A. Biń , N. A k a w u Irmiya

Fig. 10. R e la tio n sh ip R e cf = f (Ar) fo r th e c o m p lete flu id iza tio n velocity

I - Eq. (I) with K, = 18.3 and K2 = 877 [7]; 2 - Eq. (8) wilh С = 874 and m = 1Д893 [9]. The remaining symbols are defined

in Figs. 8 and 9

Rys. 10. Z a leżn o ść R e c{ = f (Ar) d la p ręd k o śc i ca łk o w ite j fluidyzacji

1 - równ. (1) ze stałymi K , = 18,3 i K2 = 877 [7]; 2 - równ. (8) ze stałymi С = 874 i m = 1,1893 [9]. Pozostałe symbole zostały

oznaczone na rys. 8 i 9

deviations from these relationships occur for the mixtures with large differences in particle diameters and/or densities of the components, cf. data of G e l p e r i n et al. [1] and C m k n and K e a i r n s [17]. In Fig. 8 lines which show dependences of Reb( and Remb on Ar due to Ś c i ą ż k o et al. [9, 13] are plotted. It can be seen that the lines describing Reb[ versus Ar due to these authors differ only slightly from the correlation of Vaid and Sen Gupta. However, the line for Remb is distinctly shifted, demonstrating that иы differs from umb for polydisperse materials.

In Fig. 9 a plot of Remf = / (Ar) shows that it is in good agreement with Eq. (1). Furthermore, the commonly recommended values of K l and K 2, e.g. those as in Wen and Yu Eq. (10) or the well known correlation due to G o r o s h k o et al. [26], for the narrow fractions seem also be applicable for polydisperse mixtures. The line due to Ś c i ą ż k o et al. [9] is somewhat shifted from the remaining lines and agrees well with the data of L u c a s et al. [24]. ,

Figure 10 demonstrates the experimental data for Rec[ (and uc{) as a plot against Ar. The scatter of these data is considerable, in particular these due to B e n a et al. [25] and G elp er in et al. [1]. It is interesting to point out that the former authors provided about 106 data points for different mixtures of glass beads and crushed calcite and tested from binary to seven-component mixtures.

Application of some of the equations quoted in the references and presented in the theoretical section has been tested for the own data points. Although formally a full statistical test would be most decisive in verification of validity of these equations in a manner demonstrated by Ś c i ą ż k o et al. [9], however, it has been decided to simplify such an analysis by introducing a sensitivity parameter, S, according to T h e o e a n o u s et al. [27]. S is the slope of the least-squares line through the points on a plot of the predicted versus measured values of a given variable (umf or uc[).

The results of this verification are presented in Table 4. It can be concluded that


Fluidization of polydisperse beds 7 8 1

T a b l e 4. V erifica tion o f va lid ity o f d ifferen t e q u a tio n s p red ic tin g inc ip ien t flu id izatio n velocities fo r o w n ex p e rim en ta l d a ta

T a b l i c a 4. W ery fikacja s to so w aln o śc i ró żn y ch za leżności o k reśla jący ch p rędkości p o c z ą tk u flu idyzacji d la w łasnych d an y ch dośw iadcza ln y ch

Eq.M e an absol. e r ro r [ % ]

Sensitiv ityp a ra m e te r

R em ark s

(4)(5)(6)

M in im u m fluid

42 7.9

19.2

iza tio n velocity

0.953 0.926 1.18

F o r b in a ry m ix tu res F o r b in a ry an d te rn a ry m ix tu res F o r b in a ry m ix tu res u n d e r a s su m p tio n o f co m plete ly m ixed beds

(9)

(1 1 )( 1) a n d (12), (13)

C o m p le te fluid

24

10.9 17.5

za tio n velocity

1.04

0.913 0.798

| F o r b in a ry a n d te rn a ry m ix tu res

F o r b in a ry m ix tu res

Eq. (5) gives best agreement with the experimental data on wmf. It is interesting to note that this equation is also applicable for binary mixtures of different density components and for ternary mixtures (at least those tested in this work). A graphical check of validity of this equation is shown in Fig. 11. It is seen that for some data the equation underestimates the values of um{ what is manifested by a value of S lower than 1 .

In the case of uc{ best agreement has been obtained by using Eq. (11) due to H a r t m a n et al. [11]. Also in this case the equation can be extended to the ternary systems (Fig. 12). The maximum deviation from Eq. (11) was about 30%.

Attempts to establish some empirical relationship of similar type for иы failed. It could only be observed that the values of иы did not differ much from wmf F (the average difference for the own experimental data was about 18%, the maximum: 79% for the mixture D 2 + S2 + U 2).

From these comparisons an interesting conclusion can be drawn that the best predictive equations for both umf and Mcf in polydisperse systems are of empirical form, differing significantly from each other, but having mass fractions of correspondingly fletsam and jetsam materials as a power exponent. To apply these equations the minimum fluidization velocities of pure flotsam and pure jetsam components have to be known. In this respect Eq. (1) is of more general use (although less accurate) since only basic physical properties of the bed are necessary.

Further considerations may involve relationships which take into account bed voidages at the incipient fluidization. In the case of monodisperse solid the well known equation due to Ergun proved to be effective and most frequently applied in practice


782 A. B iń , N . A k a w u Irmiya

Fig. 11. C o m p a riso n o f u“ flc p red ic ted by E q. (5) w ith th e ex p e rim en ta l d a ta . S ym bols a re defined in Fig. 8 Rys. 11. P o ró w n a n ie ob liczo n y ch z ró w n . (5) z d an y m i dośw iad cza ln y m i. Z naczen ie sym boli o k reś lo n o

n a rys. 8Fig. 12. C o m p ariso n o f u“ lc p red ic ted by Eq. (11) w ith th e experim en ta l d a ta . Sym bols a re defined in Fig. 8 Rys. 12. P o ró w n a n ie и°“ ob liczo n y ch z ró w n . (11) z d an y m i dośw iad cza ln y m i. Z naczen ie sym boli

o k re ś lo n o n a rys. 8

For spherical particles фв = 1 and Eq. (16) implies that relationship of a form Re/( 1—e) = J '[ A r s 3/( 1 —e)2] can be tested (cf. [9]) accounting for different values of Re and e (at the beginning, minimum and complete fluidization velocities). More exactly the shape factor of particles should be included in these variables, however, this is usually not known with sufficient confidence, in particular there would be a problem of definition of this parameter for polydisperse beds. The results of such tests for Reb( and Rem{ are shown in Figs. 13 and 14. For comparison the curve following from Eq. (16) under assumption that фв = 1 is also plotted, together with lines which have been given by Ś c i ą ż k o et al. [9]. The own data points are rather

I •

Fig. 13. R ela tionsh ip Rebf/(1 — ebf) vs. A teU ( \ — cbf)2 fo r th e ow n ex p e rim en ta l d a ta

1 — Hq. according to Śc ią ż k o et al. [9]. Symbols are defined in Fig. 8

Rys. 13. Z a leżn o ść R ebf/(1 — ebf) o d Ar£bf/(1 — ebf)2 d la w łasnych d an y ch dośw iad cza ln y ch

t — równanie według Ścieżko i in. [9]. Znaczenie symboli określono na rys. 8



Fig. 14. Relationship R e J { \ - z m!) vs. А п ^ Ц \ - е .тГ)2 fo r th e ow n ex p e rim en ta l d a ta

1 — Eq. (16) with (f>s = 1; 2 — Eq. according to Ś c i ą ż k o et al. [9]. Symbols are defined in Fig. 8

Rys. 14. Z ależność o d A r e ^ / ( l - f i mf)2d la w łasnych d an y ch d o św ia d cza ln y ch

1 — równ. (16) przy <j)s = 1; 2 — równanie według Ś c i ą ż k o i in. [9]. Znaczenie symboli określono na rys. 8

lower than the mentioned two types of approximations and a significant scatter is also evident. In the case of the minimum fluidization velocity there was good agreement between the data obtained for narrow fractions with those for the binary and ternary mixtures what indicates that no systematic error is involved in these results. A possible explanation for the observed discrepancies between the own data points and the approximations due to Ś c ią ż k o et al. [9] may stem from differences in the shape factors for the materials used in this work and in the authors’ work. On the other hand, the voidage function e3/ ( l —e)2 is highly sensitive to the values of voidage of the bed and for the majority of the beds studied in this work the voidage was in the range 0.50-0.65.

Ś c i ą ż k o et al. [9] recommended an empirical equation enabling to calculate bed voidages at the minimum and the complete fluidization:

1= 6.31 ^0.2746^-0.235-7 (17)

if the static bed voidage, s0, is known. The validity of this equation for the own data points has been checked for narrow fractions as well as for binary and ternary mixtures. Good agreement with Eq. (17) for 93% of the own data on cmf within the claimed accuracy limit has been obtained.

C O N C L U S IO N S

1. Additional experimental data for the beginning, minimum and complete fluidization velocities for binary and ternary mixtures of sand, diatomite and urea particles have been provided. The studied mixtures exhibited tendencies to partial or to total segregation.

11 — Inż. Chem. i Proc. 4/88Pobrano z http://repo.pw.edu.pl / Downloaded from Repository of Warsaw University of Technology 2022-02-23

784 A. B iń , N. A k a w u Irmiya

2. The own experimental data and some more recent ones due to different authors concerning иы and uc{ can reasonably accurately be predicted with the aid of Eq. (1), following from the well known Ergun equation, and validity of the numerical constants K x and K 2 as suggested by V aid and G u p ta [7] has been confirmed, if the bed parameters (dm and gm) are calculated from Eqs. (2) and (3).

3. Eq. (1) has also been found to be applicable to predict um{ for polydisperse beds. The values of K x and K 2 in this equation agreed well with those resulting for narrow fractions and in particular with those recommended by Wen and Yu.

4. Validity of some empirical equations suggested in the references for um[ and ucf has been tested. Eq. (5) due to C h eu n g et al. [5] for predicting um{ and Eq. (11) due to H artm an et al. [11] for predicting uc{ have been found to give the best agreement- with the experimental data.

5. Some relationships involving bed voidages at the incipient fluidization have been checked for the own experimental data. Possible explanations for the observed discrepancies from the relationships recommended by Ś c ią ż k o et al. [9 ] have been offered.

S Y M B O L S - O Z N A C Z E N IA

С — c o n s ta n t in E q. (8)s ta ła w rów n. (8)

d — p artic le size śred n ica cząs tk i

m

di — p artic le size o f th e i-th frac tio n śred n ica cząs tk i i-tej frakc ji

m

dm — m ean p a rtic le size defined by E q. (3)śred n ia ś red n ica cząstk i zd efin io w an a w rów n. (3)

m

9 — g rav ita tio n a l acce le ra tio n p rzysp ieszen ie ziem skie

m 2/s

н ь — b ed heigh t w ysokość złoża

m

K U K 2 — c o n s ta n ts in E q. (1) s ta łe w rów n. ( 1)

m — p o w er ex p o n e n t w y k ład n ik po tęg o w y

A P — bed p ressu re d ro psp a d ek c iśn ien ia w z ło żu

N /m 2

S — sensitiv ity p a ra m e te r p a ra m e tr czułości

и — superficial gas Velocity p o z o rn a p rę d k o ść gazu

m /s

X — m ass frac tio n o f partic les u łam ek m aso w y cząstek

«0 — sta tic bed vo idagep o ro w a to ść sta ty c zn a złoża

E — bed vo idage p o ro w a to ść złoża

— gas d y n am ie v iscosity d y n am iczn a lep k o ść gazu

P a s



o g — gas d ensity gęstość gazu

os — so lid d ensityg ęsto ść fazy stałej

<f)s — sh a p e fac to r o f partic les czynn ik k sz ta łtu cząs tk i

k g /m 3

k g /m 3

SUBSCRIPTS - INDEKSY DOLNE

b f — beg in n in g o f flu id iza tion p o czą tek fluidyzacji

cf — co m p le te flu id iza tio n p e łn a flu idyzacja

' F — flo tsamm a te r ia ł lżejszy (lub o m niejszej średnicy)

m b — m in im u m b u b b lin gp o c z ą te k p ęch erzo w an ia

m f — m in im u m flu id iza tion p o czą tek fluidyzacji

M — co m p le te ly m ixed bedzłoże całkow icie w ym ieszane

M S — p a r tia lly m ixed bedzłoże częściow o w ym ieszane

P — je tsa mm a te r ia ł cięższy (lub o w iększej średnicy)

S — com p le te ly seg rega ted bedzłoże całkow icie segregow ane

[1 ] N . I. G el pe r in , W . G . A in sh t ein , G . A. N o so v , W . W . M a m o sh kin a , R ebrova , T eo r. O sn . K him . T ek h n ., 1, 383 (1967).

[2 ] S. C h ib a , T. C h ib a , A. W . N ie n o w , H . K o b a y a sh i, P o w d e r T ech n o lo g y , 22, 255 (1979).[3 ] V. T h o n g l im p , N. H iq u il l y , С. L a g u er ie , P o w d e r T echno logy , 39, 223 (1984).[4 ] P. N . R o w e , A. W . N ie n o w , C hem . E n g n g Sci., 30, 1365 (1975).[5 ] L. Y. L. C h e u n g , A. W. N ie n o w , P. N . R ow e, C hem . E n g n g Sci., 29, 1301 (1974).[ 6] E. O b a ta , H . W a ta n a b e , N . E n d o , J. C bem . E ng. Ja p a n ., 15, 23 (1982).[7 ] R. P . V a id , P. Sen G u p t a , C an . J. C hem . E ng „ 56, 292 (1978).[ 8] M . Śc ią ż k o , J. Ba n d r o w sk i, L. Sa r o ff , Inż. C hem . i P roc ., 6, 531 (1985).[9 ] M . Śc ią ż k o , J. Ba n d r o w sk i, L. Sa r o ff , Inż. C hem . i P roc ., 6, 735 (1985).

[1 0 ] Т. M . K n o w l t o n , A IC h E Sym p. Ser., 73 (161), 22 (1977).[1 1 ] M . H a r tm a n , К . Svoboda , V. V esf.ly , C h em ick e L isty , 79, 247 (1985).[1 2 ] К . N o d a , S. U c h id a , Т. M a k in o , H . K amo, P o w d e r T echno logy , 46, 149 (1986)[13 ] M . Śc ią ż k o , J. Ba n d r o w sk i, C hem . E n g n g Sci., 40, 1861 (1985).

d i m e n s i o n l e s s n u m b e r s - l ic z b y b e z w y m i a r o w e

A r = gd 3Qt ( e , - Q j / l i l A rch im edes n u m b er liczba A rch im edesa R ey n o ld s n u m b e r fo r partic les liczba R ey n o ld sa d la cząstek

R e = u d Q jn t

R E F E R E N C E S


786 A. Biń , N. A k a w u I rmiya

[1 4 ] W. R. A. G oossens, G . L. D u m o n t , G . L. Spa e pe n , C hem . Eng. P ro g r., Sym p. Ser., 67, (116), 38 (1971).

[1 5 ] S. U c h id a , H . Y am a d a , J. T A D A , J. C h in ese ln s t. C hem . Eng., 14, 257 (1983).[1 6 ] A. K u m a r , P. Sen G u p t a , In d ia n J. T echno l., 12, 225 (1974).[1 7 ] J. L. P . C h en , D . L. K ea irn s , C an . J. C hem . Eng., 53, 393 (1975).[1 8 ] W . C. Y a n g , D . L. K e a irn s , Ind . E ng. C hem . F u n d a m ., 21, 228 (1982).[1 9 ] W. C. Ya n g , [ in :] E n cy c lo p ed ia o f F lu id M echan ics, C h a p te r 26, E d. N . P. C herem isinoff, G u lf Publ.

C o m p ., 1986.[2 0 ] N. B. K o n d u k o v , М . H . So sn a , T eo r. O sn . K h im . T ek h n o l., 1, 775 (1967).[2 1 ] W , K . L ew is, E. R. G i l l i l a n d , W . C. B a u e r , Ind . Eng. C hem ., 41, 1104 (1949).[2 2 ] M . J. L o c k e t t , G . G u n n a r s o n , C hem . E ngng Sci., 28, 666 (1973).[2 3 ] H . A n g e l in o , J. P . C o u d e r c , R. M o to c z y n s k i , N . L acom be, G en ie C h jm ique, 102, 1290 (1969).[2 4 ] A. L u c a s , J. A r n a ld o s , J. C a s a l , L. P u ig ja n e r , C hem . Eng. C o m m u n ., 41, 122 (1986).[2 5 ] ’ J. Ben a , J. H a v a ld a , J. Ii .av sk y , M . Ba fr n ec , C oll. C hechosl. C hem . C o m m u n ., 33, 2833 (1968).[2 6 ] W . D. G o r o sh k o , R. B. R o ze n b a u m , О . M . T od es, Izv. V yssh. U cheb . Z aved ., N eft i G az , 1, 125

(1958).[2 7 ] T . G . T h e o fa n o u s , R. N . H o u z e , L. K . B ru m f ie ld , In t. J. H e a t M ass T ran sfe r, 19, 613 (1976).[2 8 ] A. K . B in , C an . J. C hem . E ngng , 64, 854 (1986).

A. B in , N u h u A k a w u Irm iya

P O C Z Ą T E K F L U ID Y Z A C JI Z Ł Ó Ż P O L ID Y S P E R S Y JN Y C H

S t r e s z c z e n i e

W p rz y p a d k u flu idyzacji m ieszan in cząs tek sta łych ró żn iący ch się w ielkością lu b gęstością w ystępuje ten d en c ja d o segregacji z łoża , co u tru d n ia p o m ia ry o ra z definicję m in im alnej p rędkości fluidyzacji w tak ich u k ład ach . R óżn ice w w ielkości o ra z gęstości cząs tek w iążą się z różn icam i w w ielkości um[ d la czystych frakcji, z k tó ry c h u tw o rz o n a je s t m ieszan ina . Z tego w zględu m o ż n a w yróżn ić p ręd k o ść p o czą tk u flu idyzacji (ub{), p rę d k o ść m in im a ln ą flu idyzacji (umf) o ra z p rę d k o ść ca łkow ite j fluidyzacji (ucf), p rzy czym w arto śc i umf za leżą od p rzy ję teg o sp o so b u jej o k reślan ia , a w szczególności od s to p n ia w ym ieszan ia złoża.

W p racy o m ó w io n o za leżności za lecan e p rzez ró żn y ch a u to ró w ,,z a k tó ry ch p o m o cą m o żn a określić w ym ien ione wyżej p ręd k o śc i c h a ra k te ry z u ją c e p rzejście m ieszan iny cząstek sta łych w s ta n fluidalny. Z w ró c o n o p rzy tym uw agę n a zróżn ico w an ie ' p o ro w a to śc i z ło ża d la ró żn y ch p ręd k o śc i o k reśla jących sto p ień p rze jśc ia w s ta n flu idalny.

W części dośw iad cza ln e j o m ó w io n o w yniki p o m ia ró w p ręd k o śc i ch arak te ry zu jący ch przejście w s ta n flu ida lny d la trzech m ate ria łó w : p ia sk u , d ia to m itu i m o czn ik a o ra z ich dw u- i tró jsk ład n ik o w y ch m ieszan in . B a d an e m ieszan iny cech o w ała ten d en c ja d o częściow ej lu b całkow itej segregacji. W łasne w yniki p o m ia ró w p ręd k o śc i ch a rak te ry zu jący ch p o c z ą te k flu idyzacji o ra z now sze d an e innych au to ró w m o ż n a z w y sta rcz a jącą d o k ła d n o śc ią sk o re lo w ać za p o m o c ą rów n. (1 ), p rzy czym w ró w n an iu tym a k tu a ln e są w arto śc i s ta łych K 1 i K 2 su g e ro w an e p rzez V a ida i Sen G u pt^ [7 ] w p rz y p a d k u ubf i uQ{ o raz p rzez W ena i Y u w p rz y p a d k u um[, jeśli d o tego ró w n a n ia p o d sta w i się w łaściw ości z łoża (dm i g m) ob liczo n e z rów n. (2) i (3). S p ra w d z o n o p o n a d to p rz y d a tn o ść n iek tó ry ch zależności em pirycznych od o b liczan ia umf i ucf, w k tó ry c h u d z ia ł m aso w y o d p o w ied n ich frakcji (xF lu b x P) w ystępu je w w y k ład n ik u po tęgow ym : rów n . (5) d la umf o ra z rów n. (11) d la ucf, s tw ie rdzając , że d a ją o n e najlepsze zgodności z d an y m i d o św iadczalnym i.

S p ra w d zo n o ró w n ież zależności, w k tó ry c h w y stęp u ją p o ro w a to śc i z łoża c h a rak te ry zu jące jego przejście w s ta n flu idalny. P rz e d s ta w io n o m ożliw e p rzyczyny stw ie rd zo n y ch d la w łasnych dośw iadczeń o d ch y leń od tych zależności.


incipient flu1dization of polydisperse beds

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