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FLU ID F LO W T H R O U G H P A C K E D A N DFLUIDIZED SYSTEMS

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8 1 1 1 n | l l / l r v . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. .P r e s s u r e d ~: op t i m m ~ h p a c k e d t u b e s , v i s c o u s fl ow _G o l i e r a l e . r r e l a l i t l l l . . . . . . . . . . . . . . . . . . . . . . . .D a t a a n d ~ , q ~ li pl tl e lf f . . . . . . . . . . . . . . . . . . . .C . r r e l a l i . u . f r e sl l l l s . . . . . . . . . . . . . . . . . . . .

N o m , , r ~ r a p h . . . . . . . . . . . . . . . . . . . . . . . . . . . .( ~ e l i i q ' a l iz t,t I I a ' ~ '. s u r e - , t r o p e q u a t i o n . . . . . . . . . .T r a n . i t h m a l r a n g e . . . . . . . . . . . . . . . . . . . . .D i t h , r e n l i l l e q u a t i o n . . . . . . . . . . . . . . . . . . . .- N o l n o g r a p h . . . . . . . . . . . . . . . . . . . . . . . . . . . .

P a g e P a g e1 P r e s s u r e d r o p t h r o u g h p a c k e d t u b e s , v i s c o u s2 f l o w - - C o n t i n u e d3 S h a p e - f a c t o r e s t i m a t i o n s . . . . . . . . . . . . . . . . . . . 5 13 F h f i d i z a t i o n o f s o l i d s . . . . . . . . . . . . . . . . . . . . . . . . 5 77 G e n e r a l . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. 57V e s i c u l a r a n d n o n v e s i e u l a r p a r t i c l e s . . . . . . . . . . 5 78 F l u i d i z a t i o n o f n o n p o r o u s p a r t i c l e s . . . . . . . . . . 5 78 D e s c r i p t i o n o f f l u i d i z a ti o n . . . . . . . . . . . . . . . . 5 78 E x p e r i m e n t a l d e t a i l s . . . . . . . . . . . . . . . . . . . . 5 88 D a t a a n d c o r r e l a t i o n s . . . . . . . . . . . . . . . . . . . 5 99 I l l u s t r a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 91 4 M i n i m u m f l u id v o i d a g e . . . . . . . . . . . . . . . . . . 6 01 5 C o r r e l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 11 7 F l u i d i z a t i o n e f f i c i e n c y . . . . . . . . . . . . . . . . . . . 6 31 7 E q u a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 41 9 D i s c u s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 42 0 I l l u s t r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 62 2 F l u i d i z a t i o n o f a n i r o n F i s c h e r - T r o p s c h c a t a -22 l y s t ................................. 6 7

2 2 M a t e r i a l a n d o p e r a t i o n . . . . . . . . . . . . . . . . . . 6 72 2 D a t a a n d c o r r e l a t i o n s . . . . . . . . . . . . . . . . . . . . 6 92 6 A p p l i c a t i o n t o p r o c e s s d e s i g n . . . . . . . . . . . . . 7 12 7 S a m p l e c a l c u l a t i o n s a n d c o m m e n t s . . . . . . . . 7 52 8 A b r i d g e d e q u a t i o n s f o r e s t i m a t i n g o n s e t o f2 8 f i u i d i z a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 62 8 F l u i d i z a t i o u o f m i x e d m a t e r i a l s . . . . . . . . . . . . . . 7 82 9 S t r a t i f i c a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 82 9 C o r r e l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 92 9 S o l i d - l i q u id s y s t e m s . . . . . . . . . . . . . . . . . . . . . . . 7 93 1 E x p e r i m e n t a l . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 93 1 C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 03 2 D a t a i n t e r p r e t a t i o n o n t h e b a s i s o f t h e3 3 f l o c c u l a t i o n t h e o r y . . . . . . . . . . . . . . . . . . . . 8 03 5 F l u i d i z a t i o n o f p o r o u s m a t e r i a l . . . . . . . . . . . . . . 8 337 G e n e r a l . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . 833 7 E x p e r i m e n t a l d a t a . . . . . . . . . . . . . . . . . . . . . . 8 53 7 C o r r e l a t i o n a n d c o m m e n t s . . . . . . . . . . . . . . . . 8 64 2 M i n i m u m f h f id v o i d a g e . . . . . . . . . . . . . . . . . . 8 74 6 C h a n n e l i n g i n f l u i d i z e d b e d s . . . . . . . . . . . . . . . . 8 749 S u m m a r y . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . 904 9 S u m m a r y o f d e s i g n e q u a t i o n s . . . . . . . . . . . . . . . . . 9 25 0 N o m e n e i a t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 351 A p p e n d i x . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. 95

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I . D i a g r a m o f a p p a r a t u s f o r p r e s s u r e - d r o p s t u d i e s . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 92 . I ' r ~ , - ~ u r e d r , q , e o r r e e u , d t o 4 0 p e r c e n t v o i d s v s . m o d i f i e d R e y n o l d s n u m b e r ( 2 - i n c h s t a n d a r d p a c k e d t u b e ) _ 1 03 . P r e .- s ur e d r o p c o r r e c t e d t o 40 p e r c e n t v o i d s vs . m o d i f i e d R e y n o l d s n u m b e r ( / ~- i ne h s t a n d a r d p a c k e d

: l'r e, ~, -u r~ d r o p c o r r i ,e t e d t o 4 0 p e r c e n t v o i d s v s . m o d i f i e d R e y n o l d s n u m b e r ( 1 - i n c h s t a n d a r d p a c k e d l ; u be ) _ 1 2ft. P r , ,s s u re d r o p o f n i t r o g e n a t v a r i o u s t o t a l g a s p r e s s u r e s ( I - i n c h s t . a n d ~ r d p a c k e d t u b e ) . . . . . . . . . . . . . . . 1 27 . P r e ; - u r e d r o p v s . g a s d e n s i t y ( 1 - i n c h s t a n d a r d p a c k e d t u b e , n i t r o g e n d a t a ) . . . . . . . . . . . . . . . . . . . . . . . . . 1 28 . e 2 q ,~ , v s . c a s v i , ~ e o . i t y f o r C O : a n d a i r ( 2 - i n c h s t a n d a r d p a c k e d t u b e ) . .. .. .. .. .. .. .. .. .. ... .. .. .. .. . 1 39 . l : , ' l a ~ i , m , - h i p I . , t w e e u p r e s s u r e d r o p a n d p a r t i c l e d i a m e t e r . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 1 310 . Fr i t ,~ i ,m fa c t o r v s . m od i f ie d t t e y n o ld s n u m b e r . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 141 1 . P r , , ~ - . u r e d r . p f o r ~ t a s e s i n t u r b u l e n t f l o w t h r o u g h p a c k e d b e d s . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1 51 2 . P r e s s u r e , l r n p t h r ~ , u ~ h c o m m e r c i a l p a c k i n g m a t e r i a l s . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1 713. D a ta of O m a n a n d W a t s o n . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. 1714 . Fr ie l i on f . w to rs fo r v a r i o u s m a te r ia l s . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 19

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1 5. V ar ia ti on ,~ o f.. f r i c t i o n , f a c t o r w i t h R e y n o l d s . n u m b e r f o r f l o w t h r o u g h e m p t y p i p e s o f d i f f e r e n t d e g r e e s o f Pr ou ~ hn e .~ .~ ( a c c o r d i n g t o N i k u r a d s e ) . . . . . . . . . . . . . . . "r .~ D ~ ........................................... 16 . ~ , o id ,~ in p ac k ed tu be s vs. -~ , for sm oo th , uu if or m sp he re s . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . D ~17. V oid s in pa ck ed tu be s vs. D- t for sm oo th , m ix ed sp he re s . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . D ~18. V oi ds in pa c k e d t u b e s vs. ~ fo r cl ay ba ll s . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. .Dp19. V oid s in pa ck ed tu be s vs. D-- t for sm o ot h cy l in de rs . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. D ~20. Vo ids in pa c ke d tu be s vs. D- t fo r A lu nd um cy l in de rs . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. D ~21. Vo ids in pa ck ed tu be s vs. ~ for A lox i te gr an ul es . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. D ~2 2. V o i d s i n p a c k e d t u b e s v s . ~ f o r F e 30 ~ ( i ro n F i s c h e r - T r o p s c h c a t a l y s t ) g r a n u l e s . . . . . . . . . . . . . . . . . . . . . D ~2 3. V o i d s i n p a c k e d t u b e s v s . ~ f o r f u s e d A h m d u m g r a n u l e s _ .......................................D ,24. Vo ids in pa ck ed tu be s vs. -~ for R as ch ig r in gs . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . D ~25. Vo ids in pa ck ed tu be s vs. ~ for a va r i e t y of m at er ia ls . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 2

2 6. S h a p e f a c t o r i n r e l a t i o n t o h e i g h t : d i a m e t e r r a t i o f o r c y l i n d r ic a l b o d i e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 7. S u r f a c e a r e a s a n d s o l i d v o l u m e s f o r v a r i o u s t o w e r p a c k i n g s i n p ip e o f D r = 3 i n c h e s _ _2 8 . V o h u n e a n d a r e a c h a r a c t e r i s t i c s f o r v a r i o u s t o w e r p a c k i n g s s u b j e c t t o t u r b u l e n t f l o w _ - [ [ : : : . . . . . . . . . . 3. . . . . . . . . . 329. D o~ ul f lo w of ga se s th ro u g h s a n d b e ds . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .3 0 . D o w u f l ow g a s e s t h r o u g h v a r i o u s m a t e r i a l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1. P r e s s u r e d r o p t h r o u g h r o u n d s a n d ( c o u n t e r - g r a v i t y f lo w ) i n 2 ~ .' -i nc h t u b e . . . . . . . . . . . . . . . . . . . . . . 33 2. * f e s s u re q r o p t h r o u g h s h a r p s a n d s i n 2 ~ - i n c h t u b e ( c o u n t e r -g r a v i t y f l o w ) _ - - - : : : . . . . . . . . . . . . . . . . . . . 33 3 . * r e s s u r e a r o p t h r o u g h r o u n d a n d s h a r p s a n d s i n 4 - i n c h t u b e ( c o u u t e r - g r a v i t v f l o w ) : : : - - - : . . . . . . . . . . . 333 L I r e s s u r e d r o p t h r o u g h m i x t u r e s o f s a n d s ( c o u n t e r - g r a w t v f l o w ) .. .. .. .. .. ... .. .. .. .. ... .. .. .. ..:]5 . M o d i f i e d f r i c t i o n f a c t o r s v s . m o d i f ie d R e y n o l d s n u m b e r _ " . . . . . . . . . . . . . . . . . . . . . . . . . . . - - - 3. . . . . . 4: ]6 . D a t a o n f l o w o f w a t e r t h r o u g h s a n d s , o b s e r v e d b y H a t c h a n d c o r r e l a t e d b y m e a n s o f e q u a t i o n 4-6 _-_ -.-_ -- 43 7, V o l u m e a n d a r e a c h a r a c t e r i s t i c s f or v a r i o u s t o w e r p a c k i n g s s u b j e e ~ t o l a m i n a r f l ow _ . . . . . . . . . . . . . . . . . 43 8. F l o w t h r o u g h m o v i n g b e d s ; d a t a a n d c o r r e la t i o n o f H a p p e l . . . . . . . . . . . . . . . . . . . . . . . . _ . . . . . . . . . . . . . 43 9. } t a p p e l ' s d a t a c o r r e l a t e d a c c o r d i n g t o e q u a t i o n 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 0 . P r e s s u r e d r o p t h r o u g h p a c k e d b e d s f o r f l ui d s i n s t r e a m l i n e f lo w _ _ _ : . . . . . . . . . . . . . . . . . 4............................... 484 1 . . M o d i f i e d f r i c t i o n f a c t o r s v s . m o d i f i ed R e y n o ld s n u m b e r . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 44 2 . l ' r e~ s u r e d r o p f or l a m f i l ar , t r a n s i t i o n a l , a n d t u r b u l e n t f lo w o f a i r ~ h r o u g h p a c k i n g s . . . . . . [ _ : [ : : ~ : -_ - : 5

43 . G ra ph ic al re pr es e nt a t io n of th e vo id fu nc t io n . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 54 4 . ( ' o r r e c t i o n f a c t o r f o r t r a n s i t i o n r a n g e _ _ _ 5.......................................................4 5. U n i f o r m r o u n d s a n d s . . . . . . . . . . . . . . . . . . . . . . . .46. t:,,iform ro u nd sa nd s . . . . . . . . . . . . . . . . . . . . . . . : : :: : :: : :: : :: : :: :: : :: : :: : :: : :: : :: :: : :: : :: : :: : :: : :: 547 . M ix tu re s of ro u n d sa nd s . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . :_ __ -_ :_ :_ __ :_ _ 54 8 . U u i f o r m s h a r p s a n d s . . . . . . . ~49. U ni fo rm s h a rp sa n d s . . . . :::::::::::::::::::::::::::::::::::: . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . . 5550. O p e r a t h ~ st a~ es of fl ui di ze d be ds . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. 551. F lu id iz a ti on a p p a r a tu s . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. 585 2. F l u i d i z a t i o n o f r o u n d s a n d s i n 2 ~ - i n c h u n i t . . . . . . . . . . - 55 3. I ' ]u ! d ! z at ! o n o f s h a r p s a n d s i n 2 a ~- in c h u n i t . . . . . . . . . . . . . . . . . . . . . . . . . . ~.5 4. l ' h u d l z a t m n o f s h a r p s a n d s i n 2 ~'..;-in eh u n i t . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5 . F l u i d i z a t i o n o f m i x t u r e s o f r o u n d a n d s h a r p s a n d s . . . . . . . . . . . . : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : " : - 2 2 5 95 6 . M i ~ , im u m fl u id v o i d a g e , ~ y , f o r r o u n d a n d s h a r p s a n d s i n r e l a t i o n ~ o p a r t i c l e d i a m e t e r . . . . : _ _ _ : _ : . : _ _ 65 7 . F l u i d i z a t i o n o f l a rg e , u n i f o r m , r o u n d s a n d s i n 2 ~ - i n c h u n i t . . . . . . 6 25 8 . F lu ~ d i zaU o n o f sm a l l , u n i f o r m , r o u n d sa n d s i n 2 ~ - i n c h u n i t . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 6 25 9. F l u i d i z a t i o n o f u n i f o r m s h a r p s a n d s i n 2 1 ~- in c h u n i t . . . . . . . : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : . . . . . . . : : 6 26 0. F l u i d i z a t i o n o f u n i f o r m r o u n d a n d s h a r p s a n d s i n 4 - i n c h u n i t . . . . . . - . . . . . . . . . . . 6 2t ;1 . F h f i d i z a t i o n o f m i x t u r e s o f s a n d s i n 2 1f i- in ch a n d 4 - i n c h u n i t s . . . . . - : -_ - . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 36 2 . Va lu e s o f n , i n r e l a t i o n to D , f o r sa n d s . . . . . . . . . . . . . . . . . . . . . . . . : :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: 6 36 3 . F l u id i za t i o n an d ex p a n s io n l i n e s o f a t y p i c a l sm a l l sa n d . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. : : _ _ : . . . . 6 36 4 . S lu ~ in ~ p o in t s i~ , 2 ! ~ . - in eh u n i t . . . . . . _" . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . - . . . . . . . . . . . . . . . . . . . 6 56 5 . F l u i d i za t i o n e f f i e i en c i e s f o r r o u n d an d sh a r p sa n d s . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 6 6~ ;6 . W e i g h t - s i z e d i s t r i b u t i o n o f i r o n F i s c h e r - T r o p s c h c a t a l y s t b e d s i n v e s t ig a t e d _ - . . . . . . : - - - : : _ _ : : : i _ _ _ 6 767 . U ni fo rm azJd nf ix cd ir on ca ta ly st s . . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. . .. 686 8 . M i n i m u m f l u id v o i d a g e ~ - f o r s a n d a n d i r o n F i s c h e r - T r o p s c h c a t a l y s t i n r e l a t i o n t o p a r t i c l e d i a m e t e r _ _ 6 96 9. F r i c t i o n - f a c t o r p l o t f o r v a r i o u s m a t e r i a l s _ _ _ 6 9....................................................7 0 . P r e s s u r e d r o p i n r e l a t i o u t o m a s s v e l o c i t y f o r f l u i d iz a t i o n o f i r o n F i s c h e r - T r o p s e h c a t a l y s t . . . . . . . . . . . . 7 071 . F hf id iz at io n of i ro n F is ch er -T ro ps ch ca ta ly st . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 707 2 . V - d u e s o f n , i n r e l a t i o n t o Dv f o r s a n d s a n 'd i r o n F i s c h e r - T r o p s c h c a t a h ' s t . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 07 3 . F l u i d i z a t i o n e f f ic i e n c ie s i n r e l a t i o n t o p a r t i c l e d i a m e t e r c a l c u l a t e d f o~ : b e d - e x p a n s i o n r a t i o s 1 .0 5 . 1 .1 '5 ,a n d 1 . 25 _ _ _ 7 0- _ _ _ _ _ _ _ _ _

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CONTENTS V: P a g g7476. particle diame ter D~ vs. reac tor .di ame te r Dt for a. space velocity" of 3.00 and ~ ri ou s recycle r a t ! o s : 7 - - - "7~. Fl~idizatiot~ efficiency, E~b, an a oect -expa nsmn far m, t,, vs. rea cto r om met er, D~, ~or a space veloc.]tv oI300 an d va ri ou s ~ec ycl e ra ti os ............................................................... 74

D , . o . r 7577. ~ vs. D~ for the iron Fischer -Tropsch catalyst. (Shape factor >,=1.73) . . . . . . . . . . . . . . . . . . . . . . . .Graphical so lution for expansion of iron Fischer-Tropsch catalyst bed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7678. 7779. Con sta nt C in rel at io n t o p ar ti cl e d ia me te r D . ..................................................80..Mi~Jimum fluidization mass velocities obser ved and c alcul ated by Logwinuk and comp ared w ith equa-tion 56 .................................................................... ~ . . . . . . . . . . 77

81. Fluid iz at ion of mi xe d be ds ................................................................... 7982. Fluidiz at ion of mi xe d be ds ................................................................... 7993. E.~pansion in li qui d me di um s ................................................................. 8084. Cor rel at ion of l it er at ur e da ta ................................................................. 8185. Calculated fluidization efficiencies and fluidization work for various mass velocities . . . . . . . . . . . . . . . . . 81$6. Da ta of Wi lh el m an d I~:wauk and L. P. Ha t ch .................................................. 82$7. Modified friction factor vs. modified Reynolds number for data of Wilhehn and ]~:wauk . . . . . . . . . . . . . . 8388. Close cu ts an d mi xt ur es of ant hr ac i te .......................................................... 8489. Weig ht-s ize di st ri bu ti on s of be ds in ve st ig at ed ................................................... 8590. Anthracite- f lu id ization data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . = . . . . . . . . . . . . . . . . . . . 8591. Eff ec tive vo id ag e in ant hr aci te be ds ........................................................... 86. . . . . 8 792. Corr ela tion of an th ra ci te da ta . .. . . . = .................................................... 8793. Values of m in re la ti on to D~ fo r v ar mu s ma te ri al s ..............................................94. Minimum fluid voidage, ~,~r, for variou s mate rial s in relati on to effective particl e diam ete r D~ .. .. .. .. 8795. Ty pe s of ch an ne li ng in fl ui di ze d be ds .......................................................... 8896. P~e ssu re- dro p cu rv es fo r ch an ne li ng be ds ....................................................... 8997. Typic al pre ssu re dro p vs. ma ss flow re la ti on s in ch ann el in g soli ds ................................. 8908. Ci~anneling facto rs in relat ion to effective parti cle diam eter for a variet y of ~.naterials .. .. .. .. .. .. .. .. 89L 9O99. Cham~elin~ fa ct or :~4 vs. ~ fo r var io us ma te ri al s ...............................................

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F L U ID F L O W T H R O U G H P A C K E D A N D F L U I D I Z E DS Y S T E M S

b yM . L e v a , ~ M . W e i n t r a u b , ~ M . G r u m m e r , e M . P o l l c h i l~ , ~ a n d H . t -I . S t o r c h s

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Introduction

W T H t h e d e v e l o p m e n t o f n e w p r o c e ss e s fo rt h e p r o d u c t i o n o f s } m t h e t ic l i q u i d f u e l s , a ne x t e n s i v e l i te r a t u r e s e a r c h w a s u n d e r t a k e nt o u n c o v e r f u n d a m e n t a l r e l a t i o n s h ip s b e t w e e nf lu id a n d h e a t f l o w s a n d t h e o p e r a t i n g v a r i a b l e so f n e w ty p e s o f c o n v e r t e r s. E x a m i n a t i o n o fp u b l i s h e d c o r r e l a t i o n s r e v e a l e d t h a t c o n s i d e r -a b l e u n c e r t a i n t v e x i s t e d i n t h e c o r r e l a t i o n o fth e o p e r a t i n g v a r i a b le s o f s u c h e q u i p m e n t w i t ht h e p r e s s u r e ~ lr o ps w h i c h c o u l d b e e x p e c t e dt lu 'o u gh p a c k d a n d f l u i d i z e d s y s t e m s ; c o r r e l a -t i o n s p r o p o s e d i l l t h e l i t e r a t u r e d i f f e r e d f r o me ac h o t h e r fr e q u e n t l y b y a s m u c h a s 7 5 t o

~~:ork on m a n u s c r i p t c o m p l e t e d . N o v e m b e r 28, 5 9 5 0 : . . . . .l ' llomi(.:ll engine,ft. R~,search and D e v e l o p m e n ~ ~ r a n e n , u m e e o i~ } ' n t h c | i c L i q u i d F m, l s . U . S . D e p a r t m e n t o f t h e I n t e r io r , B u r e a u o f~l l r los , ~ ru( ' t ' IOl l , I~ l .C i fi ef R e s e r o t a ~ 4 D e v e l o p m e n t B r a n c h , O f f i c e o f S y n e t h e t i oL f q u t 4 F u e l s , U . S . D e p a r t m e n t o f t h e T n t e ri o r , B u r e a u o f 5 f i n e s , B r u c e -t o n , P a .

1 0 0 p e r c e n t, . B e c a u s e n e w p r o c e s s e s , e s p e -c i a ll y m o r e r e c e n t m o d i f i c a ti o n s o f t h e o r ig i n a lF i s c h e r - T r o p s c h p r o c e s s , m u s t c o m p e t e w i t ho l d , f i r m l y e s t a b l i sh e d p r o c e s s e s o n t h e b a s i s o fu n i t , p r o d u c t c o s t , t h e p r e s s u r e - d r o p c o r r e l a t i o n si n t h e l i t e r a t u r e w e r e c o n s i d e r e d t o b e t o o i n -a c c u r a t e f o r u s e in c a l c u l a t in g t h e e n e r g y r e -q u i r e d t o p a s s f l u i d s t l u ' o u g h p a c k e d b e d s .T h e f o l l o w i n g s t u d y w a s b e g u n i n 1 9 4 6 t od e v e l o p c o r r e la t i o n s t h a t ~ o u l d b e s u i t a b l e f o rt h e d e s ig n o f n e w e q u i p m e n t i n w h i c h f l u id sa r e b r o u g h t i n t o c o n t a c t w i t h g r a n u l a r m a -t e r ia l s . T o a r r i v e a t g e n e r a l r e l a t i o n s h i p s ,s y s t e m s w e r e c h o s e n t h a t d i d n o t i n v o l v ec h e m i c a l r e a c t i o n s , a n d a p a r t i c u l a r e f f o r t w a sm a d e t o g i v e t h e c o r r e l a t i o n s o n l y i n t e r m s o fq u a n t i t i e s t h a t a r e o r d i n a r i l y a v a i l a b l e f r o mg e n e r a l p r o c e s s a n d d e s i g n s p e c i f i c a t i o n s .1

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A C K N O W L E D G M E N T S .T h e a u t h o r s a r e g r a t e f u l t o t h e i r a s s o c i a t e si n t h e B u r e a u o f M i n e s f o , " i n d i s p e n s a b l e h e l pd u r i n g t h e i n v e s t i g a t i o n s a n d c o n s t r u c t i o n a n d[ l s s e m b l y o f t h e e q u i p m e n t . . T h e y t a k e D a r t i c u -a r p l e a s u r e i n a c k n o w l e d g i n g t h e i n t e r e s t .c o o p e r a t i o n , a n d c o n s t r u c t i v e s u o '~ e st io n s "M. A. E l l i o t t , E . L . Cla rk , J . I t . Crowe l l , anc~E . I t . A m i c k , J r .E d i t o r i a l a s s i s t a n c e w a s r e n d e r e d b v X o r m aG o l u m b i c a n d R . C. G r a s s .C o n s t r u c t i o n d e t a i l s p e r t a i n i n g t o t h e v a r i o u su n i t s w e r e s u p e r v i s e d b y W . E . M i l l e r , W . H .

n ~ ;~ l ~a ~ s ,~ n d W i L e ~ a u t h , T t} e g r ap h s w e r e. ~ n a o . j . V i d o s h , a n d t h er e p r o d u c t i o n s b y G . L . I - I e n n e m a n o f t h eG r a p h i c b e r v i c e s S e c ti o n .

2

T h e a u t h o r s a r e g r a t e f u l a l s o f o r t h eass i s t an ce g iv en b y W . T . :Rood . , ,, 1 -r ~ge .ne ro t t he Co a l R ese a rc h Sec t ion- ." a~ ]~ ' ,2 r . ~ lcL~lt~aeoGmaeS S~m thes~s Secho n., fo r m ak in g ~.~ dp o w d e r s , c t a t a , o n n o ~ o f o i ls t h r o u g h c a tM y sT h e a u t h o r s w a n t t o t h a n k A . O . 0 m a n a n dK . M . W a t s o n , o f t h e U n i v e r s i t y o f W i s c o n s inf o r h a v i n g s u p p l i e d t y p i c a l p i e c e s o f p a ck in gm a t e r i a l s f o r e x a m i n a t i o n o f s u r f a c e r o ug h n es s ;

C h e m i c a l E n g i n e e r i n g P r o g r e s s f o r p e r m i s s i d nt o c o p y v a r i o u s f i g u r e s a n d p a r t s o f t h e t e x tp u b l i s h e d p r e v i o u s l y ; a n d I n e z G . B O O h eM y r t l e R . L e e , a n d S o p h i e R a d o s e v i c h f o rt y p i n g t h e m a n u s c r i p t.

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LITERATURE SURVEY

F L U I D F L O W T H R O U G H P A C K E D B E D SS t u d i e s o f f l u i d f l o w t h r o u g h b e d s o f s o l i d sh a v e b e e n r t ' l ) o r t e d i n s u c h d i v e r s i f i e d j o u r n a l su s t h o s e i n l h e f i e h l s o f p e t r o l e u m p r o d u c t ! o n ,s : in i t a ry e n g i n e e r i n g , c h e m i c a l e n g i n e e r i n g ,p h y si cs , h y d r o d y n a m i c s , m e c h a n i c a l e n g i n e e r -h i, g, p h y s i / ' a l ( .h ~ , m i s tr y , a n d g e o p h y s i c s . T h ew i d e v a r i e t y o f s c i e n t i f i c i n t e r e s t s i n v o l v e dhas f requen ily ,~ ,~ : . ~ used a n in ve s t i ga to r to s t u d yt h e d t' c ct o f o n e v a r i a b l e w i t h C o m p l e t e d i s-r e g a r d f o r t h e c o n s t a n c y o f a n o t h e r c o n d i t i o nw h i c h a n i n v e s t i g a t o r i n a n o t h e r f i e ld h a ds l t o ~ q l t o t ) e i m p o r t a n t .I n 1 S5 6, D ' A r c y ~ r e p o r t e d t h e p r o p o r t i o n -

a li ty b e t w e e n p r e s s u r e d r o p p e r u n i t l e n g t h o f a~

o r o u s b e d a n d i h e f lo w o f w a t e r t l n ' o u g h it .n 1 8 6 3, D u p u i t ~ s u g g e s t e d t h a t t h e a p p a r e n tl iq u id w l o e i t y b a s e d o n t h e c r o s s s e c ti o n o f t h ee m p t y tu b e n m s t b e J es s t h a n t h e a c t u a lv e l o c i ty i n th e p o r e s . I f t h e p o r e s p a c e in t h eb e d i s c o n s i d e r e d t o b e e v e n l y d i s t r i b u t e d , t h ep o r o s i t y o f a l a y e r o f i n f i n i t e s i m a l t h i c k n e s sn o r m a l t o t h e d i r e c t i o n o f f lo w w i l l b e e q u a l t ot h e p o r o s i ty . & o f t h e b e d . D u p u i t , t h e r e f o re ,r e vi se d t h e D ' A r c y e q u a t i o n t o r e a du = ~ K A P / L .

S u b s e q u e n t i n v e s t i g a t o r s i g n o r e d t h i s p o r o s i t yc o n c ep t f o r a n u m b e r o f y e a r s .V o n E m e r s l e b e n ~ d e r i v e d t h e D ' A r c y e q u a -t io n f r o m f u n d a m e n t a l h y d r o d y n a m i c p r in -c iples .A r n o u l d ' s ; d a t a o n a i r f lo w t h r o u g h b e d s o fr i n g s , s p i r a l s , a n d t r i a n g l e s l e d t o t h e f o l l o w i n gc o r r e l a t i o n :q =O.O2 $ g '~ AP/v ,

w h e re q = a i r f lo w , m ? / s e c .A P = p r e s s u r e d r o p , r a m . of H .,Op = a i r d e n s i t y , k g . / m )p~ .D'Arey, H. P. G. Les Fontai nes Publi que de la Ville de Dijon:. ~uit. A. J.. ~:tu,les Theoretiques et Practiques sur le Mouvemen ttlt~$~ l l l X : Paris. 1S6:L

X?)n Emersl,.ben Otto, Da s Dare.vsehc Filtergesetz: Phys~kal. Ze~t-se~trlfl, vol. 2tl. 192,5. pp. g]1-610.r,~Arll~uld. J., Corps de Remplis sage et de Garnissage et Per te de ,arge Cre~r~ pi r Lt.ur Emld h-e~ " Jo ur Chinfie Ind vol 21 1929,PP. 47,~-4So - , ., . . . . , ,p~ .M.usk~a', ., an d Botset, f. G., Flow of Gas Thr oug h Porous Me dia:ayslcs, vo l. 1, 1931, pp. 27--34.

M u s k a t a n d B o t s e t s o b t a i n e d d a t a o n t h ef lo w o f a i r t h r o u g h g l a s s b e a d s , s a n d s , a n ds a n d s t o n e s w h i c h t h e y c o r r e la t e d a sA P = K ( p u ) a / 4 .

S c h o e n b o rn a n d D o u g h e r t y g a d d e d t o t h el i te r a t u r e b y p r e s e n t i n g i n g r a p h i ca l f o r m t h e i rd a t a o n t h e f l o w o f a i r, w a t e r , a n d o i l t h r o u g hb e d s o f v a r i o u s c o m m e r c i a l r in g a n d s a d d l ep a c k i n g s .W h i t e ~ r e c o g n i z e d t h a t t h e i n c o n s i s t e n te x p o n e n t s in t h e r e la t io n b e t w e e n A P a n d u o rG , e x p r e s s e d i n t h e a b o v e r e f e r e n c e s , w e r e d u et o t h e f a c t t h a t t h e e x p o n e n t v a r i e d w i t hR e y n o l d s n u m b e r , n l u c h a s i t d o e s f o r f l o wt h~ :o u gh e m p t y p ip e s . H e a t t e m p t e d t oc o r r e l a te d a t a o f o t h e r i n v e s t i g a t o r s f o r r i n g -a n d s a d d l e - p a c k e d b e d s b y p l o t t i n g J v s . R e,w h e r e / i s d e f n e d b y th e e q ua t io n

A P 2 f p u 'F ,L g D vF ~ i s a n e m p i r i c a l c o r r e c t i o n f a c t o r d e p e n d e n to n p a r t i c l e s iz e. T h e c u r v e s i n d i c a t e d f a i r l yg o o d c o r r e l a t i o n f o r i n d i v i d u a l p a c k i n g s , b u tt h e v a l u e s o f f f o r s a d d l e s w e r e t w o t o t lu - eet i m e s t h e v a l u e s f o r r i n g s a t t h e s a m e R e y n o l d sn u m b e r s.F a n c h e r a n d L e w i s n a ls o e v a i u a t e d f i T h e i rd a t a f o r f lo w of ai r, w a t e r , a n d c r u d e p e t r o l e u mt h r o u g h b e d s o f s a n d s , s a n d s t o n e s , a n d l e a ds h o t w e r e p r i n c i p a l l y in t h e v i s c o u s ra n g e , a ss h o w n b y t h e l i n e a r i t y o f t h e i r l o g -l o g c u r v e sf o r : f _ _ A P D ~ g ~ = C .-- 2 pL u ~- ReU v a r i e d w i t h t h e n a t u r e o f t h e p a e l d n g . T h ev a l u e o f D ~ , u s e d b y F a n e h e r a n d L e w i s , w a s aw e i g h t - m e a n d i a m e t e r

Dv=[Z w~(D ~)a] ~/~ .A l l e n xo_ o b t a i n e d s i m i l a r r e l a t i o n s h i p s f o r t h ef lo w of a ir , n a p h t h a , a n d m i n e r a l o i l t h r o u g hSchoenborn, E. M., and Doughe rty, W. 3"., Pressure Dr op andFlooding Velocity in Pocked Towers with Viscous Liquid s: Trans . Am.

Inst. Chem. En~.. vol. 40, 1944, pp. 31-77.l0 White, A. M., Pressure Drop an d Lo adin g Velocities in P ackedTowers: Trans. Am. In st. C hem. Eng., vol. 31, 1935, pp. 3~-408.n Fancher, O. H., and Lewis, 5. A., Flow of Simple Fluid s ThroughPorous Materials: Ind. Eng . Chem., vol. 25, 1933, pp. l l~ -i l~ 7.~-"Allen, It. V., Pressure Drop for Flow T hrou gh Beds of Granula rAbsorb ents: P etro h R efiner, vol. 23, 1944, pp. 247-252.3

. ,

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,

I'

t ' ' ",.--

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I!4 F L U I D F L O W T I -I R O U G I- I P A C K E D A N D F L U I D I Z E D S Y S TE , A I Sb ed s o f g r an u / a r ab s o rb en t s (b au x i t e an d fu l l e r' se a r t h ) a l t h o u g h h e u s e d a r e c ip r o c a l -v o l u m em e a n d i a m e t e r :

D -F 1 7 ~~ - L ~ J "

T h e l i m i ts o f A l l en ' s d a t a w ere :0 . 0 5 < R e < 5 0 0

7 < / < 1 0 ~0 . 0 0 0 8 f t . < D ~ ( b a u x i t e ) < 0 . 0 0 9 1 f t .0 . 0 0 1 1 f t . < ~ D ~ ( f a i l e r ' s e a r t h ) < 0 . 0 0 9 6 f t .

b e F : j j i a a n d U c .h id a '~ " p a s se d g a s e s t h r o u g ho r o ~ e n n m e s t o n e , l e a d s h o t , a n d R a s -ch ig r in~s an d expressed theft " resu l t s in the formo f t h e eq u a t i o n :

Fo r cy l i n d e r s ,

& P . / u ~- \ ~ / D x , ,

wh ere 1 and n are fu nct ions of the pack ing a~idA and m are func t ions of bo th Packing a iidR ey n o l d s n u m b er . T h e f t " ex p e r i m en t a l l im i tsan d co n s t an t s a r e g i v en i n t ab l e A . G am s o n , T h o d o s , an d H o u g en ~ p l o t ted t heh,observed value s of / vs . R e for air f low OVer-wean d d t3- spheres a nd cy l inders , w here they decfinedf "~PD~,gp2 L G ~

R e = D ~ ,G / t~ . "

D,=~/doho+ U2d/-. ,T h ey o b t a i n ed s ep a ra t e cu rv es fo r w e t an d d rypackings .

TABLE A. - -C on s ta nt s o f Uchida and F uj i ta ~a 14

i

I,

:b

I :! IF l o w .

1 0 < R e < 3 0 ... . . . .. . . . .. . . .. . . . .. . . . .. . . . .. . . .. . . . .. . . . ..

3 0 < R ~ . < I 0G .............................................

t 0 0 < R e < 1 , 0 O ~ _ .........................................

In 1932 , Chalmers , Tal iafer ro , and Rawl ins ~6i n t ro d u ced t h e p o ro s i t y co n cep t i n t o t h e i r d e f i -n i t io n o f f r i c t i o n f ac t o r f if A P D ~ g o ~ .p l u s

[ 'h i s co n cep t, w h i ch h a d b een d ev e l o p e d b y. D u p u i t Y h ad a l s o b een u s ed b y B o u s s i n es q ~ sm a t h eo re t i ca l d e r i v a t i o n o f fo rm u l as s i m i l a rt o t h o s e o f D 'A rcy .T la U c h i d a , S . : a n d F u j i t a , S . , P r e s s u r e D r o p T h r o u g h D r a -owt , s : ~oc . cne m. l nd ( J apan ) vo l 37 1934 rm vo4I - . o ~ y P ekedT m v , r ~ . t~ , S ; 4 ,: m d U e h l d a , S . , P r e s s u r e D r o p T h r o u g h D r - P a --~ ( , ; - - ~ ,oc . ~ae m. m a . ( J apan) vo l 37 1934 791B - :~ eked. " , -, am s o n . . I t ' . T h o d o s O ' a n d H 'O u ~ e~p p " . t ~ 9 . 4 B . -. ~ t o m o n t u m T r a n s fe r m t h e F l o w o f O a s e s T h r o u g h G r a n u | a r S o li d s:Tr~m~: .~m. I ns t . Ch em . E ng. , vol . 39, 1943, Pl) . 1-35el, " t . n$almers , l . , Tafiaferro, D . B, and Raw lins , E. L. Flo w of. "~ a: ~ T i E q u g h P o r o u s 3 fe d i a : T r i m s A .m I n s t l t { in ' n n a x r ~ + i r a n dre , r rr{!, l ) i v . , vo l . 98 , 1932 , pp . 375--40{i. " . . . . . . . . . . . . . ng . ,;", ~'oOrkienit~'fd rJ fo ot no te 5, p . 3.- s e . I . ,~l . a . . O n t h e T h e o r y o f t h e T r a n s m i s s i o n o f O aAcros s P orou s -XIedla: Co mp t . Rend . , vo l . 159 , 1914, pp . 390 , 519 . s e s

P a c k i n g :

B r o k e n l im e -s t o n e 5 r a m .< D , < 1 0 m m .

A - - - - 1 0 , 6 0 0m = - - 0 . 8 7l - - - -1 . 15n - - -- - 0 . 3 0A - -- - 1 0 , 6 0 0m = - - 0 . 8 7l - - - -1 . 15n = - - 0 . 3 0A = 3 , 6 7 0m = - - 0 . 6 4l = 1 . 1 5n - - - - 0 . 3 0

L e a d s h o t 1 .8 R a s c h i g r in g sm m . < D , < 4 . 4 5 m m . < D p ~ 1 0 ~ .h i m. mm.

A = 2 , 4 0 0m = 0 . 8 6l = 1 . 0 5n = 0 . 0A = 5 2 0m = - - 0 . 4 7l = 1 . 0 5n - - 0 . 0A - - - - 5 2 0m = - - 0 . 4 7l = 1 . 0 5n = 0 . 0

A = 3 5 0m = - - 0 . 6 41 = 0 . 9 4 ,n - - 0 . 0A = 1 4 5m = - - 0 . 3 8l = 0 . 9 4n = 0 . 0A - - - 5 1m = - - 0 . 1 6l -----0.94n = 0 . 0

In 1934 , Oh i l ton a nd Oolbu rn ~9 had corre-.l a t ed t h e i r d a t a fo r g as fl o w t h co u g h p ack edtubes wi th a so-cal l ed "wal l -e f f ec t fac tor , A / ' ,w h i ch , h o w ev er , i m p l i c i t l y co m p en s a t ed t o acer ta in degree for poros i ty as wel l as the ef fec tof the D ~ / D , ra t io ,a P 2 f a 2 A t .L - - g o D ~ p

f i s expressed graphical ly as a funct ion of R e,and A~ i s expressed graphicalh- as a f lmc t ion ofD / D .Bak hm etef f and Feodoro ff ~0 def ined / byt h e ea r l ie r co n v en t i o n

f _ = 2 g ~ P D ~p L u -zg Chik on , T . ] : r. , and Colbu rn , A . P , , P re s s ure Dr op in P acked T ubes :Ind . E ng. Ch em ., vol . 23, 19.31, pp. 913-931.:o Bakhm ete f f , B . A . , and F eodorof f , N . V . F low Th roug h Gramf lar. ' t[edia: .,Tour. Ap pl. ~[ee h., v ol. 4, 1937, pp . A97-A1 04.

7


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L I T E R A T U R E S U R V E Y

b u t , . , - , r r e l a t ed t h e v a l u es o f f t h ey o b t a i n ed f o r~

a s t t o w t l l r o u g h b e d s o f l e a d s h o t b y p l o t t i n gag a i n s t Re a n d ~ . F o r l a m i n a r f lo w , t h e y o b -t a i n ed . f = 7 1 0 / R e ~ ~nan d f o r t u r b u l en t f l o w

f = 2 4 . 2 / ( R e ) o 2 ~3 .F o r v i s co u s f l o w o f g a s e s an d l i q u i d s t h r o u g hp o r o u s ea r b o n , H a t f i e l d ~1 f o u n d t h a t. h i s f r i c t i o nf a c to r s i n t h e i lo w r a n g e 1 0 - ~ < R e < 1 0 ~ c o u l d b el in e a r ly c o r , 'e l a t e d w i t h t h e R e y n o l d s n u m b e rb y d e t i n i n g

f A P D v g ~ ~= f f - d - uI t c an b e s een t h a t t h i s d e f i n i t i o n i s i d en t i ca lw i t h t h a t p r o p o s e d b y C h a l m e r s e t a l ? ~.M ey e r an d W o r k .23 r e l a t e d t h e b ed v o i d ag ef o r a g i v en p ac k i n g t o s o m e v a l u e ~= r ep r e -s en t i n g t h e l o o s es t p ack i n g p o s s i b l e f o r t h es p eci ti ed m a t e r i a l . T h e y d e f i n ed

a n d r e p o r t e dD ~ = Z w i D i

~ P K ~ t ( 6 7 - 8 )

where K- -- --47 .5 fo r cru sh ed roc k an d 33 .3 fo rlead sho t .H ap p e l '~ co r r e l a t e d f v s . Re , w h e r e ~ w a s afunct ion o f t he rda tive ', ,1 so l ids vo lm ne ( i - -~ ) :f = A P D ~ g ep

L G ~ ( 1 - - 8 ) ~D ~ w o~ d e f i n ed a s

1D ~

{ a pp e ! ) r e p o rt e d t h a t f o r t h e l a m i n a r r a n g e- 1 0 3 / / e a n d f or t h e t u r b u le n t r a n g e . I = 2 0 7 /(R e) r).'" ~'


11/52

i , i

1 i

! " o

i iI ~ i

i ,

? ,

F L U I D F L O W T I -I R OU GI - I P A C K E D A _N 'D F L U I D I Z E D S Y S T E 3 I S

- - Z p - - -~ ' ~ l ~ b \ p l ~ / 'w h e r e SI = S+ 4/ D , C-----a c o n s t a n t d e p e n d e n ton pa r t i c l e sha pe .

F o r s o l i d s p h e r e s a n d s a d d l e s , 0 = 0 . 4 .F o r r in g p a c k i n g s C = 1 .0 .H a t c h 37 d e v e l o p e d a d i m e n s i o n a l l y h o m o g e -ne ous e qua t ion f o r p r e s su r e d r op in pa c l


12/52

LITE RA TU RE

FLUIDIZATIOND e s p i t e a n u m l w r o f y e a r s o f c o m m e r c i a l a p -p l i ca ti on o f f l u id iza t i o~( t e ch n iqu es , no q ua n t i -t a t i v e d a t a a p p e a r e d i n t h e l i t e r a t u r e p r i o r t o

1947.A n u ln l w r o f a r ti c le s h a v e a p p e a r e d i n w h i c h.~ , . i ous e lua l i t a t i ve a spec t s o f f l u id i za t i ou a rei'~'~:l~s~ed: pa r t ieu lar ly as ap pl i cab le to ca ta ly t icc-.~t.k in~ so-~,s an d ot he r fu nc t io ns in the pe -

t roh , l nn i nd us t ry .~K i t e a n d R o b e r t s .7 d i s c u s s t h e a p p l i c a t i o n o ff lu it li zl tt ion t o t he p ro cess o f ca l chm t ion o f l ime -stone .A n u m b e r o f a rt ic l e s h a v e a p p e a r e d o n~

roeesse s s imi l a r t o f l u id i za t i on , su ch a s t h ea c k w a s h i n g o f w a t e r f i l t r a t io n s a n d b e d s *sand so li ds e lu t r i a t i on w i th l i qu id s o r ga se s , s9 -93P a r e n t , Y a g o l , a n d S t e i n e r 94 d i s c u s s e dn u m b e r o f q u a l i t a t i v e a s p e c t s o f f l u i d i z a t i o nd es iu n a n d r e p o r t e d t h a t t h e p r e s s u r e d r o p. . )a cr os s a f lu l d lz e d l e d w a s a p p r o x i m a t e l y e q u a lt o t h e w e i g h t o f t h e s o l i d s p e r u n i t c r o s s s e c t i o no f th e b e d .W i l h e h n a n d K w a u k 9~ p r e s e n t e d s o m e f u n -d a n le n ta l d a t a t h a t w e r e s u b s e q u e n t l y d i s c u s s e db y 5 t e r s e ? ~ T h e t w o p a p e r s a r e t r e a t e d i nm o r e d e t a il i n a s u b s e q u e n t s e c t i o n YI n 1 9 48 a n d 1 94 9 , a n u m b e r o f p a p e r s a p -p e a r e d o n v a r i o u s r e s t r i c t e d b u ~ i m p o r t a n ttopics

~ Thc,ma.% C. L. , Aud erson, N. K., Beeker, ~l'. A., an d 5I cAfee, I. ,Crack ~ ~ with C lt: lvs ts Proe Am. Petr~)l I ns t. vol. 24, see. 3 1943t " P ; : . ' , - ~ , 2 .Wk.kham. It. P...Xteehanism of Flow in Fluid-Catalyst Cracking:Pert,1. Rvfin, r v,d. 24. July 19t5, pp. 2:3-2;tLtt Carlemith ' L E an 1 :[huson, F. B, Pilot-Pl ant Devel opmen t ofFluid C~uahl ic Cra(,k-ing: Ind . Eng. Chenl., eel. 37. 1945, pp. 451-455.t~ .Murphr~,e E.V.. ,.t al.. Improved Fluid Process for Catalytic Crack-Ing:Tr;in ~m In~t Chem. En% v,,l. 41, 1945, pp. ]9-33.a Tht,ni;~.~. C: I.J. :.n 1 Itr,ekst~a', J., Flui d zcd Fixed Bed: Ind Eng.CIlt,~t,. "col. ~7. 1:~3. lq*. 3;42-:-:34.~t Murphre,,. E. V.. G,dir. E . ft., and ]Caulakis. A. F., Th e Fl uids-.olids Technique- - ~,l,l,]ieat~on~ in the Petroleum In,austry: Jo ur.. tns LPet r,l ., vol . 33, 1:,47. l, '. v~,:;-~:21). . .t~ E~Io L G.. Le 6 "uek uff Catalyti que: Chimi e et Ind ust rm, e el. 09,194S,I ) P . 121-127.t' Kiw, R. P.. an d R(,bt,rts, E. ft.: Chem. Eng. , vol. 54, .-'X'o.12, Dee.1947, pp. 112-115.~Slh~tch, L. P.. Fh,w Tlmmgh Granular 51:edia: Trans. Am. ~oc.Xfech. [.:n~:.. vul. c2. lOl,. pp.. kil lS-A ll2 . . .t~.M:aHn, I'L, I{v~varehes ,)I1 the The ory of Free Grind ing: T ran s.Cera~iiie Foe.. eel. 2,;. lq2d-7, pp. 21-33.v Cr~mtl,. W., Pn,.mn;div Transp ort of Plants: Chem. Ind. (Londo n),eel. tt, 1,~25. pp. 2~ff'l'-xl3T.*! B t' k ~. S. P . an 1 Plum nwr . "iX'. B, Susp ensi on of-AIae~ooseopomPar-tides i*t a Tur bulen t (.las ,~tl'eam: In,t. En g. Chem., e el .. 0, 19_8, pp.

I "-O0-12~]4. ' ~ ~ 1 1934~Wadell, lI., Se,linwntatmn Formu la.: Ph.vsic., re . 5, , pp.~I-2,1..~ C:~nq~. T. R. , S,~,linwntation and Design of Settling Ta nks : Pr ec.. , t l n . . % e . Civil Fng. . vol. 71, 1':45, pp. 445-45tL~l l'~,,,llt, .T. D.. Ya~: .l. N., a nd S~einer, C. S., Flu ldlzul g Process:Ch,.h~. Eu~. Pl,v..q',.~!: eel . t3, 1947 I 'P. 429-43tL

~s Wilh,.in~. R~ tI., :rod ICwauk. hi.. The Fluidiz~t on of Solid Par-tleh.s: C h , , m , Ettg. Pr-u .. v~l. 44, 194~. pp. 201-218.~ .M,,r~o. R 11.. Fluidizadon of Granu lar Solids: In d. E ng. Chem.,~'o~. !1. I!,I!L I' ~. 1117-1121.

SU RV EY 7L o g w i n u k ~s c a r r ie d o u t a n e x i e n s l v e s t u d yo f fl u i d a n d h e a t f l o w i n w h i c h a i r , c a r b o nd i o x i d e , a n d h e l i u m w e r e u s e d t o fl u i d iz e av a r i e t y o f s o li ds T h e b a s i c s im i l a r i t y b e -t w e e n f l o w t h r o u g h f ix e d a n d f lu i d iz e d b e d s w a ss t r e s s e d b y E r g u n a n d O r n in g , ~9 a n d ~ 2 - t e r md a t ~ c o r r e l a ti o n w a s p r o p o s e d . L e w i s e t a l. 1i n v e s t i g a t e d b o t h b a t c h a n d c o n t i n u o u s f l u i d -

i z a t i o n o f g l a s s s p h e r e s o f v a r i o u s s iz e s T h eS t o r m e r v i s c o s it y o f a e r a te d b e d s w a s m e a s u r e da n d a n a l y z e d b y 5 [ a t h e s o n . o et a l. , a n d B e c k 3r e p o r t e d o n t h e u s e o f s t i r r e r s a n d b a f f l e s a sa i d s t o f l u i d i z a t i o n .B y m e a n s o f t e m p e r a t u r e l n e a s u r e m e n t s a n dt r a c e r g a s , G i l l il a u d a n d 5 [ a s o n ~ s t u d i e d t h em i x i n u a n d b a c k m i x i n g o f b o t h t h e s o l i d s a n dg a s e s ~ n s m a l l - d i a m e t e l : f l u i d iz e d b e d s . 5 [ e i s s -n e r a n d h [ i c l d e y ~ r e v e a l e d t h a t f l u i d i z ed b e d sp o s s e s s ~ d e f i n i t e c a p ~ c i t y f o r f i l t e r i n g f i n em i s t s a n d d u s t s .A n u m b e r o f a d d i t i o n a l p a p e r s ~ -1 ~ h a v ea p p e a r e d d e s c r i b in g t h e a p p l i c at i o n o f f i u id i z a -t i o n t o m o r e p r o c e s s e s, a n d ~ f e w o t h e r r e c en ~p a p e r s 1~-1~ h a v e a d d e d t o t h e l i t e r a t u r e o n t h ea s s o c i a t e d s u b j e c t s o f ~ t t r it i o n , e r o s io n , a n ds o l i d s f l o w .

9BLogwi nuk, A. I~., Ph. ]9. Thesis: Case Insti tute of Teehnolo.~',August 1945.~SErgun, S., and Orning, k. A., Fluid Flow Through RandomlyPacked Columns and Fluidized Beds: Ind. Eng. Chem., eel. il, 1949,pp . 1179-1184.1 Lewis, \V. K., Ginil and, E. R., and Bauer, W. C., Characteristics of:Fluidized Parti cles: I nd . Eng . Chem ., eel. 41, 1949, pp. 1104-1117.2 5fatheson, G. L.. Herbst W. A., and Holt, P. H., Charaete'istics of:Fluid-Solid Sys tems Ind En g. Ch em., eel. 41, 1949, pp. 1099-1104.Beck. R. A.. Evaluati on of Fluid Catalyst. Laboratory Scale: Ind.:Eng. Che m., eel. 41, 1949. pp. 1242-1243.Gilliland, E. R., and .Alison, E. A ., Gas and Solid .AIixing in Fluid -ized Beds: Ind. Eng. Chem., eel. 41, 1949, pp. 1191-1196..AIeissner, H . P., and .-Xfwkley, H S., Remo val of .-XIists and Dus tsfrom Air b.v Beds of Fluidized Solids: Ind. Eng. Chem., eel. 41. 19-19,pp. 1238-1242.Nieholson E. VV., .Afoise, Y. E., and t tar dv , R. L., Fluidized-SolidsPilot Plants: 'Ind. Eng. Chem., eel. 40, 194~, liP. 2033-.'2039Lewis W. If., Gilliland, E. R., and Reed, W. A., Reaction of 5[eth -ane with 'Cop per Oxide in a Fluidized Bed: Ind. Eng. Chem., eel. 41,1949, pp 1227-1~7.Lewis W K., Gilliland, E. R., and McBride, O. T., J'r., Gasificationof Carbon by Carbon Dioxide in a Fluidized Bed Ind. Eng. c ncm. ,eel . 41, 1949, pp. 1213-1226.Singh &. D. and I.:ane, L. $., Fluid Devolatilization of Coal forPowe r-Pi 'ant Pr:aetiee: Tra ns. Am . Soc..Xfech. Eng ., eel . 70, 1948, pp.957-964.~o Par ry, V. F.,*Oood man, I. B., and Wa-.ner, E. 0., i)ry iug Low-Rank Coals in the Entrained and Fluidized State: .Alining Eng., eel. 1,see. 3, Ap ril 1949,~)p. 95-95.u Dimitri 5[ S..Tongedyk, R. P. md Low s H. C., Distillation ofFlu idi zed Hftrd `iVo,d: Chem . Eu,.'., ee l. 55, No. 12, 1948, pp. 124-125.~o Wall, C..1., and Ash, `iV. J., Fluid-Solid Air Sizer and Dryer: In d.En g. Che m., eel. 41, 1949. pp. 1247-1249.~ Canad ian Cl~cmieal Process Industries, Oil Recovery by Fluidi~a-tion: Vol. 33, No. 2. Febru ary 1919, p. 123.~ Stoker, R. L., Erosion Due to Dust Particles in a Gas Stream: Ind.En g. Che m., eel. 41, 1949, pp. 1196-1199.~ Forsv the, W. L., Jr., and Hertwig, W. R., Attrition of Fluid Crack-ing C atalyst s: Ind . Eng . Chem., eel 41, 1949, pp. 1200-1206.~ ~lbri;,ht, C. W., Holden, J. H., Simons, H. P., and Sehmid t, D. L.,Pne uma tic Feeder for Finely Divid ed Solids: Chem . Eng., eel. 56, No.6, 1949, PI). 10S-l ll.n SchnaekY, .1. F., New Wa.v to Pressure-Seal Solids Flowing T hro ugha Conti nuous Process: Chem. E ng., eel. 55. No. S, 1948, pp. 124-126.

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PRESSURE DRO P TH RO UG H PACK ED TU BES, TURBULENT FLO WGENERAL CORRELATION

VARIABLESO r i e n t i n g e x p e r im e n t a l r u n s a n d a s u r v e y o fth e l i t e r a tu r e in d ica ted th a t t h e n a tu r e o f th ep r essu r e d r o p o b ta in ed in a p ack ed tu b e i sr a th e r co mp lex . Th e v a r i ab le s u p o n wh ichth e p r e ssu re d r o p d ep en d s m ay b e co n s id e r edunder two genera l c lass i f ica t ions, as fo l lows:

A . V a r i a b l e s r e l a t e d t o t h e f l u i d f l o w i n g t h r o u g ht h e b e d :1 . W e i g h t r a t e o f fl o w .2 . D e n s i t y o f f l u i d .3 . V i s c o s i t y o f f l u i d .B . V a r i a b l e s r e l a t e d t o t h e n a t u r e o f t h e b e d :1 . D i a m e t e r o f t u b e .2 . D i a m e t e r o f p a c k i n g .3 . F r a c t i o n o f e f f e c ti v e v o i d s .4 . S h a p e o f p a r t i c l e .5 . S u r f a c e r o u g h n e s s o f p a r t i c l e .6 . O r i e n t a t i o n o f p a r t i c l e s .

Th is s tu d y i s co n ce r n ed wi th th e e f fec t o f al lo f th e ab o v e v a r i ab le s wi th th e ex cep t io n o f th eo r i en ta t io n o f th e p a r t ic l e s . B ecau se , i n m o s tin d u s t r i a l ap p l i ca t io n s , t h e b ed s a r e p r ep a r eds i m p l y b y d u m p i n g t h e p a c k i n g m a t e r i a l i n t oth e tu b es , l i t t l e o r n o co n t r o l can b e ex e r c i sedo v e r a r r an g emen t o f th e p a r t i c l e s ; h o wev er , i ti s b e l i ev ed th a t t h e co n f ig u ra t io n s th a t a r i sef r o m d u m p in g a r e n o t su f f l c ien t lv d if f e r en t f l ' o mea('h o th er to af fec t resu l ts s ign if ican t ly .Th e g en e r a l p l an f o llo wed in o r d e r " to a r r iv ea t a wo r k ab le co r r e l a tio n was :a . D e r i v a t i o n o f a w o r k i n g e q u a t i o n .b . P r o c u r e m e n t o r e x p e r im e n t a l d a t a w i t h s m o o t hp a r t i c l e s .e . C o r r e l a t i o n o f d a t a .d . C o m p a r i s o n o f c o r r e la t i o n w i t h t h e w o r k i n ge q u a t i o n .e . I n v e s t i g a t i o n o f t h e e f f e c t o f p a r t i c l e r o u g h n e s su p o n p r e s s u r e d r o p .

D E R I V A T I O N O F A W O R K I N G E Q U A T I O NTo a r r iv e a t a su i t ab le eq u a t io n d esc r ib in gf lo w th r o u g h p a ck ed co h m ms, i t m u y b e co n -v en ie n t to h eg in wi th th e g en e r a l f lo w eq u a t io n sp e r t a in in g to emp ty p ip es :

A k_" ,u2- ~P - - g ~ u " D t " - 3" (1 )Ear l i e r ex p e r imen ta l o r i en t in g o b se r v a t io n sma d e in co n n ec t io n wi th p r e ssu r e d r o p th r o u g h8

p ack e d co lu m n s an d f lu id iza t io n o f s o ;p a r ti c le s s u g g es t e d t h a t e q u a t i o n ( 1 ) b e m o d i ~acco rch a.g to th e a ssu m p t io n o f Fa i r an d H a tc l ~ ;~ tnus, t i le veloci ty th rough the voids can i ) !expressed by" t~ . .

wh ere u is the avera ge ve loci ty of the f lu idiappro achin g the be d; k~, th e "propor t ion o f ; 'voids in the be d th at are ef fec t ive as far as!~f lu id flo w th r o u g h th e m i s co n ce r n ed ; an d 8, t h ep o r o s i ty r a t io ex p r essed a s v o id v o lu me p 6 r "u n i t o f p a c k e d t u b e v o l u m e .Fu r th e r mo r e , a ssu min g th a t t h e d imen s io n s !o f th e v o id s a re o f th e same o r d e r o f ma g n i tu d e ! ,a s th e p a r t i c l e d i ame te r , t h en D~-~4r,where ~.~is a mod if ied hyd raul ic rad iu s of the in terst ieesl.B y d e f ini t io n , l e t

r ~e _ _f fe ct iv e v o l u m e o f t h e p a c k i n g i n t e r s t i c e s ":e f f e c t iv e s u r f a c e' ~ f f p a r t i e l e s h a p e ' S - ' ,o f p a r t i c l e s ] k f a c t o r )o r

- ~ - ~) koxA' (3i::. : c .wh ere A is the sur face; I~ , the volum e of one . /p ack in g p a r t i c l e ; .~, t h e p r o p o r t io n o f th e :ef fec t ive area of th e pac king ; and X, an area: 'v o lu me sh ap e f ac to r to b e d e f in ed l a t e r .By sub st i tu t in g (2) and (3) in to (1) , one '. :o b ta in s

\ p ~ - . / ( 4 )AX/ ' iSu b s t i tu t in g : . .

D ~

( the expression for spheres) forAV~

an d G f o r p u an d r ea r r an g in g , eq u a t io n (4 )b eco mes .

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14/52

i t l o n s , n , - - - - - ' 2 ." . SHAPE F~CTO RI n o r d e r t o d e f i n e t h e s h ap e f ac t o r , X , i nequation (5) let

D ~ a v e r a g e d i a m e t e r o f a p a r t i c l e o f a n y a r b i t r a r y~hape;2. D r = d i a m e t e r o f a s p h e r e o f e q u i v a l e n t; v o l u m e ;A=surface area of a particle of arbitrary shape; andA ~s urf ac e area of a sphere of equivalent volume.

'~ Then, A=~D , 2 ' , w h e r e ~ i s a n a r e a s h a p e~. factor , an d A ~ = ~-D~~.! * ~ " ' t C ~ P ~ ' ~ "~' for the sphere of equivalent v o hm e .~ B y earlier definition, T wa s de signate d asK ;, ; t h e v o l u m e o f t h e p a r t i c l e . T h en ,

i' P R E S S U R E D R O P T I- -I RO U GI -- I P A C K E D T U B E S , T U R B U L E N T : FL O Wm pi r iC a ] b ' , ! t f ound f r om e xp e r i m e n t s~ - ]t h e m p t y t ub e s m a t e x p o n e n t n c a n n a v ea n y v a lu e b e t w e e n 1 a n d 2 , d e p e n d i n g o n t h estate of flow. For comp. le t .e ly lan . f inar mo t ion ,n ~ 1 , w h e r e as , m r c ' o m p l e t e ly t u r b u l e n t e o n d i -

w h e r e 7 i s a v o l u m e s h ap e f ac t o r . . , ~ ' p = ~

(o )

f o r t h e s p h e r e o f eq u i v a l en t v o l u m e .By de f in i t ion le tA ~ D , :x = ~ =---D-

Sincev ~ ~' D , . s = ~ D . s ,

solution for Dv y i ek l s :D r = 1 . 24 1 7 ~ /~ D ~ . ( 7 )

Subs t i tu t ing (7 ) in to (0 ) y ie ldsx 0.642~D,~ a' = ~ ' : : a D , , ? =0"2057~/-'q" (8)

F o r an y p a r t i c l e ,A a 1

s u b s t i t u t i n g t h i s i n t o ( 8 ) an d r eca l l i n g t h a t D =7 ta = ~" t, '~, yie ldsAX= 0.205 ~ . (9)

EXP ERIMENTAL WORKI n o r d e r to ev a l u a t e k an d n i n eq u a t i o n ( 5 ),e x p e r hn e n t a l d a t a a r e n e e d e d . P r e l i m i n a r ye x p e ri m e n ts r e v e a l e d t h e e x t r a o r d i n a r y e f f e c t

t h a t t h e v o i d s i n t h e b e d a n d t h e d e g r e e o fs u r f a c e r o u g h n e s s o f t h e p a c l d n g e x e r t u p o n t h ep r e s su r e d r op . B e c a u s e l i t e r a t u r e d a t a o n l yi n f r e q u e n t l y a c c o u n t f o r t h e v o i d e f f e c t , a n db e c a u s e s u r f a c e r o u g h n e s s h a d s o f a r n o t b e e nc o n s i d e re d , t h e w o r k o f o t h e r i n v e s t i g a t o r sc o u l d n o t b e u s e d i n t h i s c o r r e l a t i o n ; f o r t h i sr e a s o n , a n e n t i r e l y n e w s e t o f e x p e r i m e n t a ld a t a w a s o b t a i n e d i n a n e f f o r t t o s u p p o r te q u a t i o n ( 5 ). T h e e x p e r i m e n t a l w o r k is r e -p o r t e d i n t a b l e I o f t h e a p p e n d i x o f t h i s p a p e r ,a n d a d e s c r i p t i o n o f t h e e x p e r i m e n t a l u n i t i sg i v en i n f i g u r e 1 . Y ~q ~e r ev e r n ec es s a r y , co r -r e c t i o n s w e r e m a d e f o r th e p r e s s u r e d r o p a c r o s st h e s c r e e n a n d t h e f i r st la y e r o f p a c k i n g m a t e r i a lo n t o p o f t h e s c r een .

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bo - P r e s s u r e d r o p tube (I -3 inches dig.I n t e r c h a n g e a b l e u n i o n s )b - A i r b l o w e r .c- Gas manifold ( c r o s s )d - R o t n m e t e r s.e - M a n o m e t e r .f - Charge and discharge unions.g - C o n l r o l ( s i le n c i n g ) v a l v e .Fz~u~, 1 .- -DIAGRAM

h - S e c o n d a r y c o n t ro l ( s i l e n c i n g )valve.I -Un ion.J - P r i m a r y c o n t r o l v a l v e .k - P r e s s u r e g n g e f o r t o t a l p r e s s u r e .I - R o t o m e t e r p r e s s u re g ag e .

m - R o f o m e t e r t h e r m o m e t e r .n - S u p p o r t i n g s c r e e n ,O F A P P A R A T U S F O RPRESSURE-DROP STUDIES.

S y s t e m a t i c e x p e r i m e n t s w e r e p e r f o r m e d u s i n g0 .7 5 - i n ch , 1 - i n ch , 2 - i n ch , an d 3 - i n ch s t an d a r dp i p es . U s in ., l o g a r i t h m i c co o r d i n a t e s , a p r e -l i m i n a r y p: o f p r e s s u r e d r o p v e r s u s m a s sv e l o c i t y w a s m a d e . T h e a v e r a g e s l o p e (n )o f t h e l in e s w a s 1.9 0. B e c a u s e f r o m e q u a t i o n(5 ) i t a p p e a r s t h a t A p i s p r o p o r t i o n a l t o

( l - a P - -8s

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]0 F L UID F L OW T HR O UGH P AC K E D AND F L UIDIZ E D S YS T E MSS i n c e f o r p r a c t i c a l p u r p o s e s ( 1 - 6 ) ~ -' i s a p p r o x i -m a t e l y e q u a l t o ( 1 - ~ ), o n e m a y w r i t e :

~p o c ( l - -~ ) .~ s . o ( I 0 )T a b l e 1 , t h e k e y t o f i g ' m ' e s 2 t o 6, i n d i c a t e st h e w i d e r a n g e o f t e s t c o n d i t i o n s . I n t h eI07 0

5 ,0

: a - , o , 7 ~ " G , o ~ - 37 . 2 % o r ig ina l vo ids _ [0 - 4 0 . 0 % ,, .

b - I 0 . 2 2 8 " G l a s s spheres0 - - 38 . 8 % oHg lno l vo ids

- 0 - 4 0 . 0 % , , , ,(p-41 9 % . , ,

c - I 0 . 3 8 8 " G l o s s s p h e re s? - 42 . 5 % o r |g ]no [ vo ids - 4 4 . 7 % " .

I,0(,9,.%>~20O

o 1.0'.' 0.7to 0.5n~00o~ 0 3":3o 0 .2c l

0JLtJn."n 0 . 0 7

0 . 0 5o030.0 2 ~ / _ _ _ = III 0 0 2 0 0 3 0 0 6 0 0 1 0 00 3 0 0 0 6 0 0 0M O D I F I E D R E Y N O L D S N U M B E R O pG

F I , - m R E 2 . ~ P R E S S U R E D R O P C O R R E C T E D T O 4 0P E R C E N T V O I D S V S . M O D I F I E D R E Y N O L D SN U M B E R ( 2 - 1 N C H S T A N D A R D P A C K E DT U B E ) g r a p h s , p r e s s u r e d r o p s r e f e r t o 1 f o o t o f p a c k e dh e i g h t . a n d w e r e c o r r e c t e d t o 4 0 p e r c e n t v o i d sby using relation (I0). The choice o f 40percent as a reference state was arbitrary,and any other value except, near 0 and 100percent cou ld have been chosen. Usinglogarithmic coordinates, AP40was plotted againstthe respective modified Reynolds number,D_~G The averao.e slope of the lines is 1.90,#just as was found earlie,, for the preliminaryplots of AI' versus G. Data pertaining to runs

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F ~ Q V R E 8 . -- P RE S SU R E D R O P C O R R E C T E D T O 40P E R C E N T V O I D S VS. M O D I F I E D R E Y N O L D SN U M B E R ( ~ - I N C I t S T A N D A R D P A C K E DT U B E ) .

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PFIC ~-R E 4 . - - P R E S S U R E D R O PC O R R E C T E D T O 40 P E R C E N TV O I D S VS . M O D I F I E D R E Y -N O L D S N U M B E R ( S - IN C HS T A N D A I % D P A C K E D T U B E ) .


16/52

P R E S S U R E D R O P T H R O U G H P A C K E D T U B E S ~ T U R B U L E . N T F L O W

T A I ~ L E 1 . - - K % y t o . f i g u r e s 2 to 6

l l U l i ~ 0 . [ l l ' h i ' s/ - -

b - - 1 . . . .e - 1 . . . . .

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i - 1 . . . . .i - 1 . . . . .k - 1 . . . .

a - 2 . . . . .b - 2 . . . .c - - 2 . . . .d - 2 . . . .c - -- 2 . . . .

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h h - 2 . . . .i [ ! i i - 2 . . . .

a - 3 . . . . .b - 3 . . . .i ll e - 3 . . . . .d - 3 . . . .e - - 3 . . . .

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C on s ide r a t io n o f e qu a t ion s ( 13 ) a nd ( 14 )r e v e a ls t h a t a l l q u a n t i t i e s w i t h t h e e x c e p t i o n o fX a n d 8 a r e r e a d i l y a v a i l a b l e f r o m p r o c e s sspe c i f ic a t i ons . I t a ppe a r s , t he r e f o r e , t ha t t heu s c f u ! n e s s o f t h e e q u a t i o n s c a n b e g r e a t l y i n -crea~c~l b y d Q ' e l o p i n g c o r r e l a t i o n s w h i c h p ~ r m i tp r e a w u o n o ~ ~ a n d 6 . S u c h d e v e l o p m e n t s h a v eb e e n a t t e m p t e d a n d a r e r e p o r t e d i n a l a t e rse c t ion .I n t h e d e r i v a t i o n o f X , n o r e s t r i c t i o n s w e r ei m p o s e d o n t h e s h a p e o f t h e p a r t i c l e s o f d i a m -e t e r D , ~ . T h i s w o u l d p o s s i b l y s u g g es t , t h a t t h e

f a c t o r sh o u l d a p p l y t o a c o n s i d e r a b l e v a r i e t y o fp a r t ic l e s , h o w e v e r: c o m p l e x . F a i r s u b s t a n t i a -t i on o f t h i s i s f ound in f i gu r e 10 , w h ic h show sm o d i f i e d f r i c t i on f a c to r s f o r r i ngs , c y l inde r s ,a n d s p h e r e s t o b e i n e s s e n t i a l a g r e e m e n t w i t he ac h o t h er . L a t e r w o r k w il l d e m o n s t r a t e t h a td a t a o b s e r v e d w i t h B e r l s a d d l e s , s h a p e s t h a ta r e c o n s i d e r a b l y m o r e c o m p l e x t h a n r i n g s , a l sofall in l ine.F o r p a r t i c l e s o f s i m p l e g e o m e t r i c s h a p e , t h es h a p e f a c t o r m a y r e a d i h - b e c a l c u l a t e d f r o m t h ep a r t ic l e d i m e n s i (m s . F o r m o r e c o m p l e x s h a p e s ,k i s b e s t f o u n d b y a c t u a l e x p e r i m e n t . U s u a l l yt h e t o t a l v o i d s , 8, c a n b e d e t e r m i n e d b y i m -m e r s i o n . I f t h e a r e p o r o u s , t h e c r e v -f i l ledpa r t i c l e s

i ce s m a y b e w i t h p a r a ff i n , a n d t h e w a t e r -d i s p la c e m e n t m e t h o d m a y t h e n b e u s e d . A f t e rt h e v o i d s h a v e b e e n d e t e r m i n e d , a p r e s s u r e -d r o p e x p e r i n l e n t i s b e s t . p e r f o r m e d u n d e r c o n -t r o l le d f low c ond i t i ons . S o lu t ion f o r X i s t he ni m m e d i a t e l y p o s s ib l e b v s u b s t i t u t i n g r e sp e c -t i ve va lue s~ in to e qua t ion ( 12 ) .F o r s p h e r e s , X = I ; b u t f o r a l l o t h e r p a r t i c l e s ,X > l . T h i s i s i n a g r e e m e n t w i t h t h e f u n d a -m e n t a l o b s e r v a t i o n t h a t a s p h e r e i s t h a t s h a p et h a t p r o v id e s a g i v e n v o l u m e w i t h t h e l e a s tsur face a rea .

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Tw o f a c to r s s e e m p r im a r i ly r e spons ib l e f or :." t he l o s s o f p r e s su r e t ha t a c om pr e s s ib l e f lu id [',~ ]l ffe rs w h e n p a s s ing th r o ug h pa c ke d c o lum ns ..e v a r e ( 1) e xpa ns ion a nd c on t r a c t io n c a use d . b y t h e s h a p e o f t h e v o i d s i n t o a n d t h r o u g h w h i c h ~ hue flu! d m us t f l ow a nd (2 ) f l i e t i o n be tw e e n the ', ' m s t r e a m a nd the pa r t i c l e su r fa c e . I f be ds '.o f e q u a l v o i d c o n t e n t w e r e m a d e u p o f s p h e re s , c y l i n d e r s , a n d r i n g s , t h e r i n g s , h a v i n g t h e : :s t r ea m . I t a p p ea rs , t h er e fo r e, t h a t t h e s h a p e f a c t o r m e r e h - a c c o u n t s f o r t h e a d d i t i o n a l e f f e c tw h ic h the i nc r e a se d su r f a c e o f nonsp he r i c a l p a c k i n g s e x e r ts u p o n t h e p r e s s u r e d r o p .T h e v a l i d i t y o f t h e e q u a t i o n w a s t e s t e d O v er D p a r a nge o f ~ e x t e n d ing f r om 0 . 074 to 0 .615. ' I n sp i t e o f t h i s c ons ide r a b le va r i a t i on , no c o r- r e c t ion f a c to r f o r w a l l e f f ec t w a s r e qu i r e d in e qu a t ion ( 14 ). Th e r e a son fo r t h i s om is s ion i s~ p p r e n t f r o m a n e x a m i n a t i o n o f t h e m e t h o d ,y w h i c h ~ w a s d e t e r m i n e d . H 8 i s f o u n d b y :im m e r s ion , t he w a l l e f f e c t i s a c c ou n te d f o r i nt h e m e a s u r e m e n t s . T h i s h a s a l r e a d y b e e n o b -se r ve d b y C a rm a n ,~ 9 a nd s im p le p r oo f w i l l be " :g i v e n l a t e r. T h e f a c t t h a t t h e e q u a t i o n a p pl ie sD ~

to h igh r a t i o s o f ~ s e e m s to i nd i c a t e a f unda - : ,m e n t a l s i m i l a r i t y b e t w e e n f l o w t h r o u g h e m p t ya nd ve r y loose ly pa c ke d c on du i t s . F o r m kxed : i sphe r e s , a s a t i s f a c to r y c o r r e l a t i on r e su l t s w he nt h e a r i t h m e t i c a v er a g e d i a m e t e r o n ~ w e i g h t "bas is i s chos en for D~. .E x a m i n a t i o n o f f i g u re 10 i n d i c a t e s t h a t t h es c a t t e r o f t h e d a t a i s a p p r o x i m a t e l y 4 - 8 p e r -c e n t. E x p e r i m e n t a l m e a s u r e m e n t s n l a v b e i n : ' e r r o r b y a s m u c h a s 4 -5 p e r c e n t , o w i n g t o a n ii~ Work cited in footnote36, p. 8. Y ,"


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~Iost common gases have viscosities w i t h i nt h e r a n g e 0 . 0 1 9 t o 0 . 0 7 7 l b . h r . ~ f t. ] . T h e s ev a l u es , w h e n r a i s ed t o t h e 0 . 1 p o w e r a s r e q u i r e db y e q u a t i o n ( 1 2 ), e c o m e 0 . 7 3 - I- 7 e r c e n t . A st h i s v a r i a t i o n i s ~ i t h i n t h e l i m i t s o f e r r o r o ft h e p r e s s u r e - d r o p c o r r e l a t io n , t h e v a l u e o f 0 . 7 3f or /~ o. ~ a y b e a c c e p t e d a s c o n s t a n t f o r t h e p u r -p o s e s o f t h e n o m o g r a p h . W i t h A p e x p r e s s e d i np o u n d s p e r s q u a r e i n c h , t h e c o n s t a n t 3 . 5 0 b e -c o m e s 0 . 0 2 4 3 . C o m b i n i n g t h i s w i t h g a n d ~ o. zt r a n s f o r m s e q u a t i o n ( 1 2 ) t o e q u a t i o n ( 1 5) .

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16 F L U I D F L O W T H R O U G H P A C K E D A N D F L U I D I Z E D S Y S T E h l SI t m a y b e n o t e d t h a t f o r r e g u l a r g e o m e t r i cs h ap es t l ~e r a t i o Dp/x c a n b e e v a l u a t e d b y t h ed e f i n i n g eq u a t i o n ( 9) .

DpD ,= (6V~/rr)l/s and -~-=6VT,/A..205A-- ~ p 2 3T h e h o m o g r a p h ( f i g . 1 1 ) w a s c o n s t r u c t e df l 'o m eq u a t i o n ( 15 ) w i t h an ax i s f o r each o f t h ef o u r g r o u p s o f v a r ia b l e s .

I L L U S T R A T I O N

F i g u r e 11 m a y b e u s e d t o s o lv e s e v e r a l t y p e so f p r o b l e m s .P R O B L E M i

O n e t h o u s a n d p o u n d s o f a ir p e r h o u r i s to b eb l o w n t h r o u g h a r e a c t o r c o n s i s t i n g o f t e n 2 . 5 -i n c h - d i a m e t e r b y 1 0 - fo o t -l o n g p i p e s i n p a r a l l e l .T h e p i p e s a r e p a c k e d w i t h m o d e r a t e l y s m o o t hc y l i n d e r s 0 .7 4 0 i n c h i n d i a m e t e r a n d 0 .7 4 0 i n c hl o ng . I t h a s b e e n d e t e r m i n e d t h a t 1 91 c y l i n -d e r s j u s t f il l 2 f ee t , o f 2 .5 - i n c h - d i am e t e r p i p e .T h e a v e r a g e a i r t e m p e r a t u r e i s to b e 1 97 F .In le t . p r e ssu re i s 5 p s i o.W h a t , p r e s s u r e d r o p " ~an b e ex p ec t ed ?S o l u t i o n

T h e m o d i f ie d R e y n o l d s n u m b e r is DpG/t,, a p -p r o x i m a t e l y 4 ,4 0 0, a n d h e n c e w e ll i n t h e t u r b u -l e n t r a n g e f o r w h i c h t h e n o m o g r a p h h o l d s .T h e v o l u m e o f e a c h p a c k i n g p a r t i c l e i s :(0.740) Or) (0.740)~ / 4 = 0 . 3 1 8 i n . 3 .

T h e p a r t i c l e - s u r f a c e a r e a is :(~) (0.740)2/2+ Or) (0.740) (0.740) =2 .58 in3.

T h e v o l u n l e o f 2 f e e t o f ' ~ '2 z . _ , - m c h - d i a m e t e rpip e is 114.8 in . S.T h e v o l u m e o f 1 9 1 p e l l e t s i s 6 0 .7 i n 2 .1 1 4 . 8 - - 60.7Z=-- 114.8 - -=0.470 .

D , ,6 I ~ 6 X 0 .31 8 ^X ~ - - - - - - ~ = 0 . 7 4 o i n.I n l e t a i r d en s i t y i s c a l cu l a t ed t o b e 0 ,0 8 1l b . / f t . 3. . k s a f i r s t ' ap p r o x i m a t i o n , a s s u m e t h a t

t h e eh . an g e i n g a s d en s i t y a s a r e s u l t o f p r e s s u r ed r o p i s n eg l i g i b l e an d t h a t 0 .0 81 l b . f l t 2 is t h ea v e r a g e d e n s i t y o f t h e g a s .B ec au s e t h e~ t u b e

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