MODELING OF AGGLOMERATION IN A FLUIDIZED BED.

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fluidized bed, whereas the velocity influences the rate of particle collision as well as the particle .... mass flow rate of initial and entrained gas, kg/h x = distance ...
MODELING OF AGGLOMERATION I N A FLUIDIZED BED

A. Rehmat, C. Huang,* R. C a r t y I n s t i t u t e of Gas Technology Chicago, I l l i n o i s 60616 H. Hariri, H. Arastoopour

I l l i n o i s I n s t i t u t e of Technology Chicago, I l l i n o i s 60616 ABSTRACT A f l u i d i z e d bed c o n t a i n i n g a c e n t r a l j e t was o p e r a t e d w i t h low-temperature m e l t i n g m a t e r i a l s t o o b t a i n t h e r a t e of a g g l o m e r a t i o n a s w e l l a s t o measure t h e t e m p e r a t u r e d i s t r i b u t i o n w i t h i n t h e f l u i d i z e d bed. The r a t e of a g g l o m e r a t i o n was o b t a i n e d as a f u n c t i o n of o p e r a t i n g p a r a m e t e r s such a s t e m p e r a t u r e and v e l o c i t y . The a g g l o m e r a t i o n r a t e d e f i n e d , as t h e r a t e of change i n t h e number of p a r t i c l e s of a p a r t i c u l a r s i z e , was determined from t h e p a r t i c l e p o p u l a t i o n b a l a n c e u s i n g t h e experimental data. The a g g l o m e r a t i o n model developed t o p r e d i c t t h e a g g l o m e r a t i o n r a t e c o n s t a n t based on t h e t e m p e r a t u r e d i s t r i b u t i o n i n t h e f l u i d i z e d bed and t h e r a t e of e n t r a i n m e n t of p a r t i c l e s i n t o t h e j e t y i e l d e d v a l u e s f o r t h e r a t e c o n s t a n t s s i m i l a r t o the experimental values. INTRODUCTION Fluidized-bed systems have been used in many c o a l c o n v e r s i o n and o t h e r c h e m i c a l processes. The f l u i d i z e d beds a r e sometimes o p e r a t e d under a g g l o m e r a t i n g c o n d i t i o n s t o maximize c o a l u t i l i z a t i o n . T h e o p e r a t i n g c o n d i t i o n s in such c a s e s a r e chosen t o Under s u i t a b l e o p e r a t i n g p r e v e n t t h e o n s e t of s i n t e r s and d e f l u i d i z a t i o n ( 1 , 2 , 3 , 4 ) . c o n d i t i o n s , a s h a g g l o m e r a t i o n p r o v i d e s a very e f f e c t i v e means of a s h removal from a coal g a s i f i e r (5). A d i s t i n g u i s h i n g f e a t u r e of a n ash-agglomerating c o a l g a s i f i e r is a r e g i o n where t h e t e m p e r a t u r e of t h e a s h p a r t i c l e s is h i g h enough t o make t h e s u r f a c e s s t i c k y s o t h a t when t h e y c o l l i d e w i t h e a c h o t h e r , t h e y a d h e r e t o e a c h o t h e r t o produce a g g l o m e r a t e s . The r a t e of t h e f o r m a t i o n of t h e s e a g g l o m e r a t e s depends upon s e v e r a l f a c t o r s such as t h e o x i d a n t d i s t r i b u t i o n w i t h i n t h e bed, t h e o v e r a l l f l u i d i z a t i o n v e l o c i t y , and t h e a s h p r o p e r t i e s . The o x i d a n t d i s t r i b u t i o n p r i m a r i l y i n f l u e n c e t h e f o r m a t i o n of t h e l o c a l i z e d zone of h i g h t e m p e r a t u r e w i t h i n t h e f l u i d i z e d bed, whereas t h e v e l o c i t y i n f l u e n c e s t h e rate of p a r t i c l e c o l l i s i o n as w e l l a s t h e p a r t i c l e e n t r a i n m e n t w i t h i n t h i s zone. Based on t h e s e f a c t o r s , a mathematical model f o r a g g l o m e r a t i o n has been developed t o p r e d i c t t h e r a t e of a g g l o m e r a t i o n i n a f l u i d i z e d bed c o n t a i n i n g a c e n t r a l j e t . These r a t e s are t h e n compared w i t h t h o s e o b t a i n e d from t h e a c t u a l e x p e r i m e n t s . EXPERIMENTAL APPARATUS AND PROCEDURE The a p p a r a t u s c o n s i s t s of a 15.2-cm-ID g l a s s f l u i d i z e d - b e d column, a m e t a l s e c t i o n p o s i t i o n e d b e n e a t h t h e g l a s s column f o r t e m p e r a t u r e measurement end sampling, a g a s d i s t r i b u t o r , a j e t and f l u i d i z i n g a i r h e a t i n g s y s t e m , t e m p e r a t u r e c o n t r o l l i n g and t e m p e r a t u r e measurement d e v i c e s , and f l o w r e g u l a t i o n and measurement I n t h e e x p e r i m e n t , t h e j e t and t h e f l u i d i z i n g a i r t e m p e r a t u r e s systems ( F i g u r e 1 ) . ___.I__-

I _ _

*Dr. Huang is c u r r e n t l y a t Nalco Chemical, N a p e r v i l l e , I l l i n o i s . 176

w e r e v a r i e d and t h e t e m p e r a t u r e d i s t r i b u t i o n and t h e a g g l o m e r a t i o n of t h e p a r t i c l e s in t h e bed were measured. P o l y e t h y l e n e and p o l y o l e f i n p a r t i c l e s were used as bed m a t e r i a l . Two t y p e s of gas d i s t r i b u t o r s were used: a f l a t porous p l a t e w i t h a c e n t r a l j e t and a p o r o u s cone w i t h a c e n t r a l j e t . The j e t g a s t e m p e r a t u r e w a s a d j u s t e d t o a v a l u e above t h e m e l t i n g t e m p e r a t u r e of t h e bed m a t e r i a l . The f l u i d i z i n g a i r ( a u x i l i a r y a i r ) t e m p e r a t u r e was g e n e r a l l y m a i n t a i n e d lower t h a n t h e s o f t e n i n g t e m p e r a t u r e of t h e bed m a t e r i a l t o a v o i d s i n t e r f o r m a t i o n on t h e d i s t r i b u t o r . EXPERIMENTAL RESULTS F i g u r e 2 shows t h e e f f e c t of j e t t e m p e r a t u r e on t h e a g g l o m e r a t i o n f o r a f l a t porous d i s t r i b u t o r w i t h h i g h - d e n s i t y p o l y e t h y l e n e bed m a t e r i a l . The measure. of a g g l o m e r a t i o n i s t h e w e i g h t p e r c e n t a g e of p a r t i c l e s g r e a t e r than 850 ym, which i n c r e a s e d l i n e a r l y w i t h r e s i d e n c e time a t each t e m p e r a t u r e l e v e l . The p e r c e n t a g e of a g g l o m e r a t e s also i n c r e a s e d l i n e a r l y w i t h t h e f l u i d i z i n g g a s and bed t e m p e r a t u r e s ; however, t h e j e t a i r t e m p e r a t u r e was found t o have t h e most s i g n i f i c a n t e f f e c t on t h e agglomeration r a t e . Another i m p o r t a n t f a c t o r a f f e c t i n g t h e r a t e of a g g l o m e r a t i o n in f l u i d i z e d beds is t h e r a t e of p a r t i c l e e n t r a i n m e n t i n t o t h e h i g h - t e m p e r a t u r e j e t r e g i o n . The e n t r a i n m e n t r a t e depends on t h e s t r e s s d i s t r i b u t i o n among t h e p a r t i c l e s i n t h e v i c i n i t y of t h e j e t r e g i o n . The d i r e c t i o n , m a g n i t u d e , and component of t h e s t r e s s toward t h e j e t r e g i o n depends on t h e cone a n g l e . F i g u r e 3 compares t h e a g g l o m e r a t i o n o b t a i n e d w i t h gas d i s t r i b u t o r s having h a l f - c o n e a n g l e s of 30", 4 5 ' , 60". and 90" ( f l a t ) a f t e r 2 , 4 , 6 , and 8 h o u r s of s t e a d y - s t a t e o p e r a t i o n . The a g g l o m e r a t i o n i n c r e a s e d as t h e cone a n g l e d e c r e a s e d up t o 45'However, ?hen the cone angle was d e c r e a s e d t o 30", t h e a g g l o m e r a t i o n was found t o be l e s s t h a n t h a t w i t h cone a n g l e of 4 5 " . This i m p l i e s t h a t , a l t h o u g h t h e s t e e p e r i n v e r t e d cone d i r e c t e d t h e s t r e s s on t h e p a r t i c l e s in t h e cone s e c t i o n more e f f e c t i v e l y toward t h e j e t zone, t h e amount of p a r t i c l e s i n t h e cone s e c t i o n d e c r e a s e d r e s u l t i n g i n lower e n t r a i n m e n t of t h e p a r t i c l e s . Because of t h i s c o m p e t i t i v e e f f e c t , t h e r e e x i s t s an optimum cone a n g l e f o r t h e maximum r a t e of a g g l o m e r a t i o n . T h i s h a l f - c o n e a n g l e is a p p r o x i m a t e l y 4 5 " . The optimum a n g l e c a n be a f u n c t i o n of p a r t i c l e - s i z e d i s t r i b u t i o n , shape and s u r f a c e roughness of t h e p a r t i c l e s , and t h e j e t and t h e fluidfzing air velocities. The t e m p e r a t u r e d i s t r i b u t i o n i n s i d e t h e bed was p l o t t e d u s i n g t e m p e r a t u r e measurements a t more t h a n 50 l o c a t i o n s i n s i d e the f l u i d i z e d bed. A t y p i c a l t e m p e r a t u r e d i e t r i b u t i o n p r o f i l e in t h e a r e a near t h e porous cone d i s t r i b u t o r is i l l u s t r a t e d in F i g u r e 4 . More d a t a c o n c e r n i n g o t h e r o p e r a t i n g c o n d i t i o n s a r e g i v e n e l s e w h e r e . (6). DATA ANALYSIS I n a f l u i d i z e d bed o p e r a t e d under a g g l o m e r a t i n g c o n d i t i o n s , t h e r a t e of a g g l o m e r a t i o n between p a r t i c l e s of two d i f f e r e n t s i z e s is p r o p o r t i o n a l t o t h e p r o d u c t of t h e i r c o n c e n t r a t i o n s . The p r o p o r t i o n a l i t y c o n s t a n t is c a l l e d t h e agglomeration r a t e c o n s t a n t .

TO d e f i n e t h e r a t e of a g g l o m e r a t i o n , we have adopted a d e f i n i t i o n t h a t is a n a l o g o u s t o t h e r a t e of chemical r e a c t i o n . In a c h e m i c a l r e a c t i o n , t h e r a t e of r e a c t i o n is d e f i n e d i n t e r m s of t h e r a t e of change in t h e number of moles of a p a r t i c u l a r component i n t h e r e a c t i n g s y s t e m due t o i t s r e a c t i o n . In the a g g l o m e r a t i o n p r o c e s s , what is changed d u r i n g t h e p r o c e s s is t h e p a r t i c l e - s i z e d i s t r i b u t i o n . T h e r e f o r e , i t i s a p p r o p r i a t e t o d e f i n e t h e r a t e of a g g l o m e r a t i o n of p a r t i c l e s of a p a r t i c u l a r s i z e a s t h e r a t e of change i n t h e number of p a r t i c l e s of t h a t s i z e . Due t o t h e d i f f i c u l t y i n measuring t h e number of p a r t i c l e s of a p a r t i c u l a r s i z e per u n i t volume of t h e f l u i d i z e d bed, it h a s been found c o n v e n i e n t 177

t o e x p r e s s t h e r a t e of a g g l o m e r a t i o n of t h e p a r t i c l e s in terms of i t s r a t e of change p e r u n i t mass of t h e bed m a t e r i a l . S i n c e t h e o v e r a l l r a t e of a g g l o m e r a t i o n is a measure of t h e r a t e of change in t h e number of p a r t i c l e s of v a r i o u s s i z e s , t h e p a r t i c l e s i z e is d e f i n e d in a manner t h a t is meaningful and f a c i l i t a t e s t h e n u m e r i c a l computation i n t h e p a r t i c l e p o p u l a t i o n b a l a n c e . It is assumed t h a t a l l p a r t i c l e s are made up of u n i t p a r t i c l e s of mass mo and d i a m e t e r do. T h i s assumption i m p l i e s t h a t p a r t i c l e s i z e is d i s c r e t e and each p a r t i c l e has a mass e q u a l t o an i n t e g e r times t h e mass of a u n i t p a r t i c l e . The p a r t i c l e whose mass is I times t h e mass of a u n i t p a r t i c l e ( I x no) is c a l l e d p a r t i c l e s i z e I. N(1) is d e f i n e d a s t h e number of p a r t i c l e s of s i z e I p e r u n i t mass of bed m a t e r i a l and is c a l l e d t h e mass number d e n s i t y of p a r t i c l e s of s i z e I. The rate of a g g l o m e r a t i o n of p a r t i c l e s of s i z e I can be e x p r e s s e d a s :

R(1)

P

dt

The v a l u e of t h e r a t e of a g g l o m e r a t i o n R(1) is dependent upon o p e r a t i n g v a r i a b l e s , i n c l u d i n g t h e t e m p e r a t u r e d i s t r i b u t i o n in t h e bed, v e l o c i t y , and p a r t i c l e - s i z e distribution. I f w e assume t h e a g g l o m e r a t i o n p r o c e s s a s i n v o l v i n g t h e c o l l i s i o n of a s i n g l e p a r t i c l e of s i z e I and a s i n g l e p a r t i c l e of s i z e J, t h e n i t i s r e a s o n a b l e t o assume t h a t t h e g e n e r a t i o n r a t e of agglomerates (I t J ) forming from p a r t i c l e s of s i z e I and p a r t i c l e s of s i z e J is p r o p o r t i o n a l t o t h e c o l l i s i o n frequency between t h e s e particles. As t h e number of c o l l i s i o n s between p a r t i c l e s of any two p a r t i c u l a r s i z e s is p r o p o r t i o n a l t o t h e product of t h e i r mass number d e n s i t i e s , t h e r a t e of g e n e r a t i o n of a g g l o m e r a t e s of s i z e (I t J ) from p a r t i c l e s o f s i z e s I and J is:

Here, KI,J is t h e a g g l o m e r a t i o n r a t e c o n s t a n t . P a r t i c l e P o p u l a t i o n Balance f o r Batch P r o c e s s . In t h e p o p u l a t i o n b a l a n c e of t h e p a r t i c l e s of a p a r t i c u l a r s i z e I , a l l t h e p o s s i b l e combinations l e a d i n g t o t h e f o r m a t i o n o r consumption of s i z e I p a r t i c l e s are t o be c o n s i d e r e d s i n c e p a r t i c l e s of s i z e I combines w i t h o t h e r p a r t i c l e s t o form a g g l o m e r a t e s of l a r g e r s i z e s ; on t h e o t h e r hand, s m a l l e r p a r t i c l e s may s t i c k t o g e t h e r and form a g g l o m e r a t e s of s i z e I. Using E q u a t i o n 1, t h e r a t e of g e n e r a t i o n of a g g l o m e r a t e s of s i z e I from s m a l l e r p a r t i c l e s is:

S i m i l a r l y , t h e r a t e of consumption of p a r t i c l e s of s i z e I due t o a g g l o m e r a t i o n is:

where L i s t h e s i z e of t h e l a r g e s t p a r t i c l e s t h a t e x i s t in t h e bed. The p o p u l a t i o n b a l a n c e f o r p a r t i c l e s of s i z e I in b a t c h p r o c e s s can t h u s be w r i t t e n a s :

Computation of Agglomeration Rate C o n s t a n t . For t h e computation of t h e a g g l o m e r a t i o n r a t e c o n s t a n t from t h e d a t a , i t i s f i r s t e x p r e s s e d in terms of the o p e r a t i n g v a r i a b l e s and p a r t i c l e s i z e s . T h i s approach f a c i l i t a t e s in s o l v i n g t h e r a t e c o n s t a n t i n t e g r a l e q u a t i o n s . The a g g l o m e r a t i o n r a t e c o n s t a n t KI,J c a n be

178

r e p r e s e n t e d by t h e p r o d u c t of two f u n c t i o n s ; t h e f i r s t f u n c t i o n , kop, is d e p e n d e n t upon t h e o p e r a t i n g c o n d i t i o n s , and t h e o t h e r , k ( d I , d J ) , is s i z e - d e p e n d e n t , a s :

It i s d i f f i c u l t t o o b t a i n a n e x p r e s s i o n f o r k ( d I , d J ) from a t h e o r e t i c a l s t a n d p o i n t . Based on t h e b e h a v i o r of p a r t i c l e s , one r e s t r i c t i o n t h a t c a n be imposed on t h e f u n c t i o n a l form of k ( d I , d J ) is t h a t i t s h o u l d be symmetric w i t h r e s p e c t to dI a n d dJ. The u l t i m a t e f u n c t i o n a l form of k ( d I , d J ) must be d e t e r m i n e d w i t h t h e a i d of experimental data.

i l

Even w i t h t h e a s s u m p t i o n s of E q u a t i o n 4, t h e r e a r e s t i l l t o o many p o s s i b l e t o be t e s t e d , and f u r t h e r s i m p l i f i c a t i o n of t h e c o m b i n a t i o n s of ko and k ( d I , d t e s t i n g p r o c e d u r e fs needed. achieve t h i s , t h e p a r t i c l e population balance E q u a t i o n 3 , f o r a s p e c i f i c o p e r a t i n g c o n d i t i o n , i s r e a r r a n g e d as f o l l o w s :

40

I k

OP

= [MN(I)/Mtl/[i 6

1

-

k(d,_,,d,)N(J)N(I-J)dJ

L 5)

k(dI,dJ)N(I)N(J)dJl

6

1

Thus, if t h e c o r r e c t f u n c t i o n a l form of k ( d I , d J ) i s used i n E q u a t i o n 5 , the calculated k s h o u l d have t h e same v a l u e f o r a l l of t h e p a r t i c l e s i z e s under T h i s p r o v i d e s a means t o t e s t t h e f u n c t i o n a l form of s p e c i f i c opeygting conditions. k(dI,dJ). To f i n d t h e c o r r e c t f u n c t i o n a l form of k ( d , d J ) , s e v e r a l symmetric f u n c t i o n s w i t h r e s p e c t t o d and dJ were s u b s t i t u t e d i n t o E q u a t i o n 5. Our s t u d i e s showed t h a t t h e f u n c t i o n a l form of

o v e r the whole p a r t i c l e s i z e range a t r e s u l t s i n a n e a r l y c o n s t a n t v a l u e of k specific operating conditions. T h e r e f o % , K I , J can be e x p r e s s e d a s :

The e:?perimental d a t a was used t o c a l c u l a t e MN(I)/Mt; then t h e a g g l o m e r a t i o n r a t e constant k w a s c a l c u l a t e d u s i n g E q u a t i o n s 5 and 6 . These values a t d i f f e r e n t j e t t e m p e r a t u r z g a r e shown i n T a b l e 1. T a b l e 1. THE CALCULATED VALUES OF k BY PARTICLE POPULATION BALANCE USING E X P E R I ~ ~ T A DATA L J e t Temp, 'C koP

144.4 1.78

x

10-9

143.3

1.20

x

10-9

142.8 -___ 0.9

x

10-9

142.2 -__ 0.45

x

The value of k i n c r e a s e s s i g n i f i c a n t l y with a s l i g h t i n c r e a s e i n j e t temperature (Table 1 and F&re 2). AGGLOMERATION MODEL As t h e h o t j e t g a s stream i s f e d i n t o t h e f l u i d i z e d bed through t h e n o z z l e a t a t e m p e r a t u r e s u b s t a n t i a l l y h i g h e r than t h e f l u i d i z i n g gas t e m p e r a t u r e , a hot j e t z o n e i n the c e n t r a l p o r t i o n of t h e bed i s c r e a t e d . The c o n c e n t r a t i o n of s o l i d s i n t h e j e t zone i s much l o w e r t h a n t h e s o l i d s c o n c e n t r a t i o n i n t h e bulk of t h e bed. The s o l i d p a r t i c l e s e n t e r t h e j e t zone and exchange heat w i t h t h e h o t j e t gas. The t e m p e r a t u r e of t h e p a r t i c l e s i n the j e t zone i n c r e a s e s ; f o r some p a r t i c l e s , t h i s

179

I

r e s u l t s i n p a r t i a l m e l t i n g . Upon t h e c o l l i s i o n of two s t i c k y p a r t i c l e s , a g g l o m e r a t i o n may occur. Whether a g g l o m e r a t i o n t a k e s p l a c e o r n o t depends on s e v e r a l p a r t i c l e c h a r a c t e r i s t i c s , i n c l u d i n g t h e r e l a t i v e v e l o c i t y of t h e c o l l i d i n g p a r t i c l e s , t h e t h i c k n e s s of t h e molten l a y e r , and t h e v i s c o s i t y of t h e molten material.

In t h e a r e a n e a r t h e j e t , the p a r t i c l e s a r e assumed t o t r a v e l h o r i z o n t a l l y a s t h e y a r e e n t r a i n e d i n t o t h e j e t u n t i l t h e y r e a c h t h e j e t boundary where p a r t i c l e s e n t e r i n t o t h e j e t zone and t r a v e l upward and f i n a l l y e x i t from t h e t o p of t h e j e t . The e n t r a i n m e n t of g a s i n t o a f r e e j e t h a s been g i v e n by Ricou and S p a l d i n g ( 7 )

as:

where Mgo Mg

-

= mass flow r a t e of i n i t i a l j e t g a s , kg/h =

mass flow r a t e of i n i t i a l and e n t r a i n e d g a s , kg/h

x = d i s t a n c e from n o z z l e e x i t , m dn = n o z z l e d i a m e t e r , m pgi = d e n s i t y of e n t r a i n e d g a s , kg/m3 pgo = d e n s i t y of g a s e x i t i n g n o z z l e , kg/m3 The p r e s e n c e of p a r t i c l e s may a f f e c t t h e e n t r a i n m e n t of g a s into t h e j e t s t r e a m . However, t h i s e f f e c t was found t o be n e g l i g i b l e f o r t h e p a r t i c l e - s i z e range (mean p a r t i c l e d i a m e t e r = 350 urn) u s e d in t h i s s t u d y (8). The p a r t i c l e s a r e e n t r a i n e d near t h e j e t by t h e e n t r a i n e d g a s ; then t h e y change d i r e c t i o n and move upward due t o momentum exchange w i t h t h e j e t gas. In t h i s s t u d y , t h e flow of g a s e n t r a i n e d t o t h e j e t i s n e g l i g i b l e in comparison w i t h t h e j e t g a s f l o w r a t e . However, t h e rate of g a s e n t r a i n m e n t h a s been used t o e s t i m a t e t h e p a r t i c l e e n t r a i n m e n t i n t o t h e j e t . As t h e p a r t i c l e s e n t e r i n t o t h e j e t , t h e y t r a v e l upward due t o t h e j e t g a s momentum. The f o l l o w i n g momentum b a l a n c e was used t o c a l c u l a t e t h e p a r t i c l e v e l o c i t y in t h e j e t zone.

where x = o d e f i n e s t h e l o c a t i o n where t h e p a r t i c l e s e n t e r t h e j e t zone. v and v a r e p a r t i c l e and g a s v e l o c i t i e s , r e s p e c t i v e l y , eP is t h e p a r t i c l e s v o i d f r a g t i o n , and CD is t h e d r a g c o e f f i c i e n t . With t h e assumption t h a t h e a t t r a n s f e r t o a p a r t i c l e is v i a h e a t exchange w i t h i t s s u r r o u n d i n g g a s stream, t h e h e a t b a l a n c e on a s i n g l e p a r t i c l e in t h e r e g i o n n e a r and in t h e j e t is e x p r e s s e d a s :

where a is t h e p a r t i c l e t h e r m a l d i f f u s i v i t y . a t t = O , T

P

where TB i s t h e bed t e m p e r a t u r e 180

= T B

10)

aT = o a t r = 0, -2

ar

and

-+= aT

at r = R, K~

h(Tv

-

(

h(T,

-

T ) near the j e t P

12)

T ) a t t h e j e t zone P

where KS i s t h e t h e r m a l c o n d u c t i v i t y of p a r t i c l e s , T is j e t t e m p e r a t u r e , and Tv is 3 t h e t e m p e r a t u r e i n t h e r e g i o n n e a r t h e j e t . (Both t e m p e r a t u r e s a r e measured experimentally.) The h e a t t r a n s f e r c o e f f i c i e n t h is computed u s i n g t h e f o l l o w i n g expression ( 9 ) : hd -2

= 2.0

+

g

d p (V 0.6 ( a v ' g

-

v ) 1/2

1

c

IJ

(+-%

1/3 13)

g

where k is t h e g a s t h e r m a l c o n d u c t i v i t y , v i s t h e g a s s t r e a m v e l o c i t y , v p a r t i c l g v e l o c i t y , d is t h e d i a m e t e r of t h g p a r t i c l e , pg is gas viscosity! is the s p e c i f i c heat!

is t h e and c

P

Using t h e above h e a t and momentum e q u a t i o n s , t h e t e m p e r a t u r e of a s i n g l e p a r t i c l e Tp a t any l o c a t i o n n e a r and i n t h e j e t can be c a l c u l a t e d . I f t h e c a l c u l a t e d t e m p e r a t u r e of t h e p a r t i c l e s , T , i n t h e j e t zone r e a c h e s t h e m e l t i n g t e m p e r a t u r e , t h e o u t e r l a y e r of t h e p a r t i c l e s i e l t , and t h e p a r t i c l e s may agglomerate upon c o l l i s i o n . For e a c h c o l l i s i o n , there is only a f i n i t e p r o b a b i l i t y of P* l e a d i n g t o s u c c e s s f u l agglomeration. The p r o b a b i l i t y P* is t h e f r a c t i o n of a l l t h e c o l l i s i o n s , which meet t h e f o l l o w i n g agglomeration criteria: R e l a t i v e K i n e t i c Energy of C o l l i d i n g P a r t i c l e s


ET TiGnPERATiikES AND A F L U I D I Z I N G A I R TE8ERATURE OF 115.7"C

144.4

kop From Model

1.78 X lo-'

From kg&perimen t

1.78

x

10-9

143.3 1.20 X IO-'

1.20

x

10-9

142.8

142.2

0.89

X lo-'

0.63 X lo-'

0.90

x

0.45

x

10-9

T a b l e 3. THE PREDICTED VALUES OF ko AT DIFFERENT FLUIDIZING AIR TEMPERATURES AND A JET T E M ~ R A T U R EOF 144.4"C Fluidizing A i r Temp, OC-

_____ 115.7

kop From Model

1.78 X IO-'

kop From Experiment

1.78

x

10-9

93.5

104.6 1.15 X lo-'

1.05

x

0.68 X

0.84

x

-

82.3

-

0.54 X IO-'

0.66

x

10-9

REFERENCES -

I.

A r a s t o o p o u r , H . , Huang, C. S and W e i l , S. A., " F l u i d i z a t i o n Behavior of S t i c k y P a r t i c l e s , " J o u r n a l of F i n e ! r t i c l e S o c i e t y (1986).

2.

A r a s t o o p o u r , H., Gu, A. Z. and W e i l , S. A., "The E f f e c t of Gas D i s t r i b u t o r s on t h e Agglomeration P r o c e s s i n F l u i d i z e d Beds," i n t h e Proceeding! of t h e 4 t h I n t e r n a t i o n a l Symposium on A g g l o m e r a t i o n , 443-450, 1985. 183

I

l

3.

A r a s t o o p o u r , H . , W e i l , S. A., Huang, C. S. and Gu, A. Z., "A Fundamental Study i n Support of t h e U n d e r s t a n d i n g of t h e Agglomeration of Coal i n C o a l G a s i f i e r s , " i n t h e P r o c e e d i n g s of t h e 2 0 t h I n t e r s o c i e t y Energy C o n v e r s i o n E n g i n e e r i n g C o n f e r e n c e , Vol. 1,1625-1630, 1985.

4.

Gluckman, M. J.. Y e r u s h a l m i , J. and S q u i r e , A. M . , " D e f l u i d i z a t i o n C h a r a c t e r i s t i c s of S t i c k y o r Agglomerating Beds," F l u i d i z a t i o n Technology, K e a i r n s , D., Ed., 395 (1976).

1,

5.

Vora, M. K., Sandstrom, W. A. and Rehmat, A. G . , "Ash Agglomeration i n t h e F l u i d i z e d Bed." Paper p r e s e n t e d a t t h e S i x t h N a t i o n a l C o n f e r e n c e on Energy and t h e Environment, P i t t s b u r g h , May 21-24, 1979.

6.

H a r i r i , H., Rehmat, A. and A r a s t o o p o u r , H . , "Temperature D i s t r i b u t i o n i n a F l u i d i z e d Bed With a C e n t r a l J e t . " Paper p r e s e n t e d a t t h e A.1.Ch.E. Annual Meeting, New York, November 15-20, 1987.

7.

Ricou, F. P. and S p a l d i n g , D. B., "Measurement of E n t r a i n m e n t by A x i s y m m e t r i c a l T u r b u l e n t J e t s , " J o u r n a l of F l u i d Mechanics 11, 21-32 (1961).

8.

T a t t e r s o n , D. C., Marker, T. L. and F o r g a c , J . M., " P a r t i c l e E f f e c t s on F r e e J e t E n t r a i n m e n t , " The C a n a d i a n J o u r n a l of Chemical E n g i n e e r i n g , =:361-365 (1987).

9.

Bird, R. B., S t e w a r t , W. E. and L i g h t f o o t , E. N . , York: John Wiley h S o n s , 1960.

T r a n s p o r t Phenomena. New

APPENDIX R e l a t i v e K i n e t i c Energy of C o l l i d i n g P a r t i c l e s The compression a c t i o n between t h e two c o l l i n e a r - c o l l i d i n g p a r t i c l e s w i l l keep on u n t i l t h e r e l a t i v e v e l o c i t y between t h e s e two p a r t i c l e s is zero. A t t h i s p o i n t , t h e d e f o r m a t i o n i s a t t h e maximum, a s i s t h e c o n t a c t a r e a between t h e two particles. However, t h e sum of t h e k i n e t i c e n e r g i e s of t h e two p a r t i c l e s r e a c h e s a minimum. T h i s can be proved u s i n g t h e momentum b a l a n c e s f o r t h e c o l l i n e a r - c o l l i d i n g particles. The d i f f e r e n c e between t h e sum of t h e k i n e t i c e n e r g i e s of t h e two p a r t i c l e s b e f o r e c o l l i s i o n and t h a t of t h e two p a r t i c l e s a t maximum d e f o r m a t i o n can be d e r i v e d u s i n g t h e f o l l o w i n g a s s u m p t i o n s . Assume t h a t t h e v e l o c i t i e s of two ( v l and p a r t i c l e s b e f o r e c o l l i s i o n w i t h mas8 m l and m2 a r e v1 and v2, r e s p e c t i v e l y . v2 a r e c o l l i n e a r . ) I f t h e maximum d e f o r m a t i o n i s a c h i e v e d , t h e s e two p a r t i c l e s w i l l have t h e same v e l o c i t y , v ' . The momentum b a l a n c e may be w r i t t e n as: m l vl

+

m 2 v2 = ( m l

+

m2) v '

The d i f f e r e n c e of t h e k i n e t i c e n e r g i e s i n t h e s e two s t a t e s i s :

P o t e n t i a l F o r Energy D i s s i p a t i o n i n P a r t i c l e s The p o t e n t i a l d i s s i p a t i o n c a p a b i l i t y of molten m a t e r i a l on t h e s u r f a c e s of t h e i s caused t o flow r e l a t i v e t o t h e s u r f a c e change and t h e compression a c t i o n between

is associated with the viscous d i s s i p a t i o n colliding particles. The m o l t e n m a t e r i a l mainly by t h e sudden p a r t i c l e v e l o c i t y p a r t i c l e s d u r i n g c o l l i s i o n and, t o a much

184

s m a l l e r d e g r e e , by t h e a c t i o f l of s u r f a c e t e n s i o n . A s a f i r s t e s t i m a t e , t h e flow Of t h e molten l a y e r is approximated by t h e v i s c o u s f l u i d ( t h e c r e e p i n g f l o w ) over t h e spherical particles. T h u s , t h e d r a g f o r c e e x e r t e d on t h e p a r t i c l e s is c a l c u l a t e d from t h e f o l l o w i n g e q u a t i o n s (9).

where Fn and Ft are t h e summations of t h e p r o j e c t i o n s of normal and t a n g e n t i a l f o r c e s e x e r t i n g on hard-core s u r f a c e in t h e d i r e c t i o n o p p o s i t e t o t h e p a r t i c l e f l o w d i r e c t i o n . V is t h e c h a r a c t e r i s t i c v e l o c i t y of t h e m e l t e d l a y e r r e l a t i v e t o t h e p a r t i c l e hard c o r e . p L is t h e v i s c o s i t y of t h e melted m a t e r i a l .

I f t h e t h i c k n e s s e s of t h e melted l a y e r s a r e 61 and €5, r e s p e c t i v e l y , t h e energy d i s s i p a t e d due t o v i s c o u s f l o w can be approximated as t h e p r o d u c t of f o r c e e x e r t e d on t h e p a r t i c l e h a r d c o r e and t h e r e l a t i v e d i s t a n c e t r a v e l e d between them.

P o t e n t i a l Dissipation Capability

= (Fn

+

F t ) x (61

It is f u r t h e r assumed t h a t v is e q u a l t o t h e h a l f vl v2 beEore p a r t i c l e c o l l i s i o n ; t h u s :

I

-

1

P o t e n t i a l Dissipation Capability = 3 n p Q

I

vl

-

+ 6,)

61

=

6ap v 9.

(--I

+

62 2

2

of t h e r e l a t i v e v e l o c i t y

vp

61

+

62 2

I ( 7 )

ACKNOWLEDGMENT T h i s work was s p o n s o r e d by t h e U.S. AC21-87MC23283.

Department of Energy under C o n t r a c t No. DE-

185

- - - - - - - -j ( ( L K *nn

"-3.

J

F i g u r e 1.

SCHEMATIC DIAGRAM OF THE EXPERIMENTAL SETUP

RESIDENCE TIME, h

F i g u r e 2. COMPARISON OF WEIGHT PERCENTAGES OF PARTICLES LARGER THAN 850 pm CALCULATED FROM THE PARTICLES' POPULATION BALANCE EQUATION AND EXPERIMENTAL DATA AT POUR D I F F E R E m J E T AIR TEMPERATURES

186

'

0

2

4

6

8

RESIDENCE TIME, h ACSO4OZ8Yi

F i g u r e 3.

COMPARISON OF WEIGHT PERCENTAGES OF AGGLOMERATES WITH FOUR DIFFERENT CONE ANGLE GAS DISTRIBUTORS

RADIAL DlSTAWCE c, m

Figure 4 .

..7,,a..

J E T ZONE ISOTHERMS IN A FLUIDIZED BED AT A J E T A I R TEMPERATURE OF 149°C AND A F L U I D I Z I N G A I R TEMPERATURE OF 115OC

187