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Pergamon Chemical Engineering Sc ience , Vol. 52, No. 10, pp. 1609-1622, 1997 1997 Elsevier Science Ltd. All rights reservedPrinted in Great BritainPII: $ 1 1 1 1 O 9 - 2 5 1 1 9 ( 9 1 ~ ) 1 1 @ 5 1 1 - 8 0 0 09 - 25 0 9/ 9 7 $ 1 7. 00 + 0 .0 0

The f lu id ized-bed membrane reactor fors team methane reforming: modelverif ication and parametric s tudy

A. M. Adr i s ,* C. J . L im and J . R. GracCD e p a r t m e n t o f C h e m i c a l E n g i n e e ri n g , U n i v e r s it y o f B r it is h C o l u m b i a , V a n c o u v e r , B C ,

C a n a d a V 6 T 1 Z 4( R e c e i v e d 1 9 A p r i l 1 9 9 6 ; i n r e v i s e d f o r m 2 5 N o v e m b e r 1 9 9 6 ; a c c e p t e d 2 7 N o v e m b e r 1 9 9 6 )

A b s t r a e t - - A n e w a p p r o a c h is p r e s e n te d f o r t h e m o d e l l in g o f a fl u id i ze d - b e d m e m b r a n e r e a c t o r( F B M R ) . T h e m o d e l c o n s i d e r s th e t w o - p h a s e n a t u r e o f t h e f l u id i ze d - b e d r e a c t o r s y s te m a n d t h ep a r a l l e l r e a c t i o n s t a k i n g p l a c e i n s t r e a m m e t h a n e r e f o r m i n g , a s w e l l a s s e l e c t i v e p e r m e a t i o nt h r o u g h t h e w a ll s o f m e m b r a n e t u b e s i m m e r s e d i n t he b e d . T h e m o d e l is b a s e d o n t h et w o - p h a s e b u b b l i n g b e d m o d e l w i t h a l l o w a n c e f o r s o m e g a s f l o w i n th e d e n s e p h a s e . P l u g f l o wis a s s u m e d f o r th e c o m b i n e d s w e e p g a s a n d p e r m e a t i n g h y d r o g e n f lo w i n g t h r o u g h t h e m e m -b r a n e t u b e s . F r e e b o a r d n o n - i s o t h e r m a l e f f e c t s a n d r e a c t i o n s a r e a l s o t a k e n i n t o a c c o u n t . T h ec o u p l e d d i f fe r e n ti a l e q u a t i o n s f o r t h e f lu i d iz e d b e d a n d m e m b r a n e t u b e s a r e s o l v e d n u m e r i c a l ly .T h e m o d e l i s i n v e r y g o o d a g r e e m e n t w i t h e x p e r im e n t a l d a t a , b o t h w i t h a n d w i t h o u t p e r -m e a t i o n , o b t a i n e d i n a p i l o t - s c a l e r e a c t o r s y s t e m . P a r a m e t r i c i n v e s t i g a t i o n s d e m o n s t r a t e t h ee ff ec t o f k e y o p e r a t i n g v a r i a b l e s a n d d e s i g n p a r a m e t e r s o v e r a w i d e r a n g e , T h e m o d e l i s a ls ot e s t e d f o r i t s s e n s i t i v i t y t o c h a n g e s i n h y d r o d y n a m i c p a r a m e t e r s . I n c r e a s i n g t h e p e r m e a t i o n o fh y d r o g e n t h r o u g h t h e m e m b r a n e t u b e s is o f k e y i m p o r t a n c e i n a c h i e v in g h ig h m e t h a n ec o n v e r s i o n s a n d i n m i n i m i z in g a d v e r s e r e a c t io n s i n t h e f r e e b o a r d r e g io n . H y d r o d y n a m i c a n dk i n e t i c p r o p e r t ie s h a v e l i m i t e d i n f lu e n c e f o r t h e c o n d i t i o n s s t u d i e d . 1 9 97 E l s e v i e r S c i e n c eL t d . A l l r i g h t s r e s e r v e dK e y w o r d s : F l u i d i z a t i o n ; m e m b r a n e s ; p e r m e a t i o n ; r e f o r m i n g ; h y d r o g e n ; r e a c t o r m o d e l l i n g .

1. INTRODUCTIONS t e a m r e f o r m i n g o f l i g h t h y d r o c a r b o n s , e s p e c i a l l yn a t u r a l g a s , i s a n i n d u s t r i a l l y i m p o r t a n t c h e m i c a l r e -a c t i o n a n d a k e y s t e p f o r p r o d u c i n g h y d r o g e n a n ds y n g a s f o r a m m o n i a a n d m e t h a n o l p r o d u c t i o n , h y -d r o c r a c k i n g a n d h y d r o t r e a t i n g , o x o - a l c o h o l a n dF i s c h e r - T r o p s c h s y n t h e s i s a n d o t h e r i m p o r t a n t p r o -c e ss es i n t h e p e t r o l e u m a n d p e t r o c h e m i c a l i n d u s t r ie s .H o w e v e r , i n d u s t r i a l f i x e d - b e d s t e a m r e f o r m e r s s u f f e rf r o m s e v e r a l p r o b l e m s w h i c h s e r i o u s l y a f f e c t t h e i ro p e r a t i o n a n d p e r f o r m a n c e . T h e s e i n c lu d e l o w c a t a -l ys t e f fec t i veness due t o i n t e rna l mass t r ans fer r es i s t -a n c e i n t h e l a r g e c a t a l y s t p a r t i c l e s , l o w h e a t t r a n s f e rr a t e s , l a r g e t e m p e r a t u r e g r a d i e n t s a n d t h e r m o d y n -a m i c e q u i l i b r i u m c o n s t r a i n t s . T h e s e p r o b l e m s w i t hc o n v e n t i o n a l r e f o r m e r s c a n b e a l l e v i a t e d b y u s i n ga f lu i d iz e d - b e d m e m b r a n e r e a c t o r ( F B M R ) s y s t e m f o rs t e a m m e t h a n e r e f o r m i n g (S M R ) ( A d r is e t a l . , 1994).T h i s n e w r e a c t o r s y s t e m c o m b i n e s s e v e r al a d v a n t a g e s

* Present address: Department of Research and Te chno-logy Support , SA BIC R&D, P.O . Box 42503, Riyadh 11551Saudi Arabia., Corresponding author.

o f fl u id i z e d b e d s a s c h e m i c a l r e a c t o r s , i n p a r t i c u l a rc a t a l y s t b e d t e m p e r a t u r e u n i f o r m i t y , i m p r o v e dh e a t t r a n s f e r a n d v i r t u a l e l im i n a t i o n o f i n t r a c a t a l y s td i f f u s i o n a l l i m i t a t i o n s , w i t h a d v a n t a g e s o f f e r e d b yp e r m s e l e c t i v e m e m b r a n e t e c h n o l o g y , i n p a r t i c u l a rs h if ti n g t h e c o n v e n t i o n a l t h e r m o d y n a m i c e q u i li b r iu ma n d i n s i t u s e p a r a t i o n a n d r e m o v a l o f a d e s i ra b l er e a c t i o n p r o d u c t i n a v e r y p u r e s t a t e .In a r e l a t ed s t udy (Adr i s, 1994), a p i l o t - sca l e r e fo rm -i n g p l a n t o f i n t e r n a l d i a m e t e r 1 0 2 m m w i t h a h y d r o -g e n c a p a c i t y o f 6 m 3 [ S T P ] / h , a b l e t o o p e r a t e a t t e m -p e r a t u r e s u p t o 7 5 0 C a n d p r e s s u r e s u p t o 1 .5 M P a ,w a s c o m m i s s i o n e d t o e x a m i n e t h e c o n c e p t o f t h e n e wf l ui d iz e d - b ed m e m b r a n e r e a c t o r s y s t e m f o r s t e a m r e -f o r m i n g o f n a t u r a l g a s a n d t o s t u d y i t s p r o p e r t i e s . T h ep r e s e n t p a p e r c o n s i d e r s t h e m o d e l l in g o f th e F B M R -S M R r e a c t o r .

T h e f i r s t a t t e m p t t o m o d e l t h e F B M R s y s t e m w a sc o n d u c t e d b y A d r i s e t a l . (1991) , who s i mul a t ed ani n d u s t r i a l - s c a l e f l u i d i z e d - b e d m e m b r a n e r e f o r m e r i no r d e r t o e x p l o r e t h e p o t e n t i a l o f t h i s n e w r e a c t o rs y s t e m a n d c o m p a r e i t w i t h c o n v e n t i o n a l r e f o r m i n gu n i t s . T h i s e a r l i e r m o d e l w a s b a s e d o n t h e O r c u t tm o d e l w i t h p e r f e c t m i x i n g o f th e d e n s e p h a s e g a s( O r c u t t e t a l . , 1 9 62 ) a n d w i t h a n u m b e r o f si m p l i fy i n g1609

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1610 A.M . Adr i s et al.a s s u m p t i o n s w h i c h m a d e t h e s y s te m o f e q u a t io n s s im -i l ar t o t h o s e f o r a C S T R . T h o s e s i m p l i f i c at i o n s w e r ea d e q u a t e f o r 'g r o s s ' p r e d i c t i o n o f th e o v e r a l l r e a c t o rp e r f o r m a n c e .

I n o r d e r t o r e p r e s e n t t h e h y d r o d y n a m i c s b e t te r , t h es i m u l a t i o n w o r k i n t h e p r e s e n t p a p e r i s b a s e d o n t h et w o - p h a s e b u b b l i n g b e d r e a c t o r m o d e l ( G r a c e , 1 9 84 ) ( 7)w i t h a l l o w a n c e f o r s o m e g a s f l o w ( a s s u m e d t o b e i np l u g f lo w ) i n t h e d e n s e p h a s e . T h i s a s s u m p t i o n w a s ( 8)a l s o u s e d in a s e c o n d v e r s i o n o f t h e O r c u t t m o d e l( O r c u t t et a l . , 1 9 62 ). B o t h v e r s i o n s o f th e m o d e l c o n -s i d e r s e le c ti ve r e m o v a l o f h y d r o g e n b y p e r m e a t i o nt h r o u g h m e m b r a n e t u b e s i m m e r s e d i n b o t h t h e d e ns eb e d a n d t h e d i l u t e p h a s e . R e a c t i o n t a k i n g p l a c e o v e re n t r a i n e d c a t a l y s t p a r t i c l e s i n t h e f r e e b o a r d z o n e i sa l s o t a k e n i n t o a c c o u n t i n t h e p r e s e n t m o d e l .

2 . MODELDEVELOPMENT2.1. M o d e l a s s u m p t i o n s

T h e p h a s e s c o n s i d e r e d i n t h e p r e s e n t m o d e l a r ei l l us t r a t ed schemat i ca l l y i n F i g . 1 . The model i s basedo n t h e f o l l o w i n g a s s u m p t i o n s :( 1 ) S t e a d y - s t a t e c o n d i t i o n s a r e a s s u m e d .( 2) T h e d e n s e c a t a l y s t b e d i s c o n s i d e r e d t o b ec o m p o s e d o f t w o p h a s e s, a b u b b l e p h a s e a n da dense phase .( 3) A x i a l d i s p e r s io n o f g a s i s i g n o r e d i n b o t hphases .( 4 ) R e a c t i o n o c c u r s m o s t l y i n t h e d e n s e p h a s e .H o w e v e r , t h e b u b b l e s c o n t a i n s o m e s o l i d s

w h i c h c o n t r i b u t e t o t h e o v e r a l l r e a c t i o n .(5) In view of thei r smal l s ize, the di ffusional resis t -ance inside the catalyst par t icles i s neglected.( 6) T h e i n t e r i o r o f t h e m e m b r a n e t u b e i s ta k e n a sa s e p a r a t e r e g i o n w h i c h e x c h a n g e s h y d r o g e n

9 )10)1 1 )1 2 )

w i t h b o t h t h e b u b b l e p h a s e a n d t h e d e n s ep h a s e . A ' s w e e p g a s ' s u c h a s s t e a m i s u s e di n s i d e t h e m e m b r a n e t u b e s t o m a i n t a i n a l o wp a r t i a l p r e s s u r e o f h y d r o g e n t h e r e , h e l p in g t op r o m o t e p e r m e a ti o n o f h y d ro g e n t h r o u g h t h ewal l s o f the t ubes .S w e e p a n d p e r m e a t i n g g a s e s a r e i n p l u g f l o wi n s i d e t h e m e m b r a n e t u b e s .G a s e s l e a v i n g t h e b e d s u r f a c e t r a v e l i n p l u gf l o w a n d u n d e r g o c h e m i c a l r e a c t i o n i n t h ef r e e b o a r d r e g i o n o v e r t h e s u r f a c e o f e n t r a i n e dca t a l ys t pa r t i c l es .T h e c o n c e n t r a t i o n o f s o li d s i n t h e d i l u t e f re e -b o a r d p h a s e d e c a y s e x p o n e n t i a l l y w i t h h e i g h t.H y d r o g e n i s th e o n l y s pe c ie s w h i c h p e r m e a t e st h r o u g h t h e m e m b r a n e t u b e w a l l s .I d e a l g a s b e h a v i o u r i s a s s u m e d .T h e t e m p e r a t u r e i s a s s u m e d t o b e c o n s t a n t i nt h e d e n s e b e d r e g i o n , b u t i t m a y v a r y i n t h ef r e e b o a r d r e g i o n .

2 .2 . M o d e l f o r m u l a t io n2.2.1. D e n s e c a t a l y s t b e d e q u a t io n s . A m o l e b a l a n c eo n c o m p o n e n t i (w h e r e i e q u a l s 1 f o r m e t h a n e , 2 f o r

s t ea m , 3 f o r c a r b o n m o n o x i d e a n d 4 f o r c a r b o n d i o x -i de ) i n t h e b u b b l e p h a s e g i v e sdnibd h = k i q a b e b A ( C i d - - C i b ) + ~ b P s A R i b . (1)

F o r i = 5 (h y d r o g e n) , t h e c o m p o n e n t m a s s b a l a n c e i nt h e b u b b l e p h a s e i s g i v e n b ydnibdh = klqabg 'bA(Cia - - Cib )

P n o s _+ ( ~ b P s A R i b - - ~ e ( - - ~ H ) C e v lg ,b ( P r l ~ po~s)2 )

_ _ [ _ h y d r o g e n a n dPermbates w e e p asoo z=op h ~ s e l D IPermeate.~.F_~ . ~ . ~ ~ h=H

i g a sM e m b r a n etubes

o t h e r~L_ product. ~ stream= L r - - - - J F r e e b o a r d

z o n e

~ h=Oreactants I ~ l l S eb e dz o n eFig. 1. Sch ematic showing phases considered in the fluidized-bed mem brane reactor mod el.

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Mo del l ing of a f lu idized-bed membrane reac torw h e r e C ~pz i s t h e e q u i v a l e n t p e r m e a t i o n c a p a c i t y p e r f r e e b o a r d r e g i o n g iv e su n i t l e n g t h o f t h e m e m b r a n e t u b e , d e f in e d a s th ee x t e r n a l s u rf a ce a r e a o f th e m e m b r a n e t u b e s d i v i d e db y t h e t u b e w a l l t h i c k n e s s p e r u n i t l e n g t h .

S i m i l a r l y , a m o l e b a l a n c e o n c o m p o n e n t i ( i = 1 - 4 )i n t h e d e n s e p h a s e g i v e s

dn iad h = ki q a b ~ 'b A ( C i b - - C i d ) q- O a p , A R i a . (3)

F o r h y d r o g e n , t h e c o r r e s p o n d i n g e q u a t i o n i sdn idd h - k i q a b e b A ( C i b - - C i d )

, { p H ' ~+ ~ t p s A R i d - e \ M H / ]x C , t , , l - - e b ) P a s - - p O ; S ) . 4 )

F i n a l l y , a m o l e b a l an c e o n h y d r o g e n ( c o m p o n e n ti = 5 ) i n t h e s e p a r a t i o n p h a s e ( i .e . i n s i d e t h e m e m -b r a n e t u b e s ) g iv e s

d h MHH {(1 - - e b ) P d - - pO~5)+ eb(pO.b5 _ pO;5)}. (5)

B o u n d a r y c o n d i t i o n s a t h = 0 a r e n~b = n ~ ,( U o - U m i ) / U o , n ld = n i i U ~ f / U o a n d ni~ = 0 , wh e re i ti s a s s u m e d t h a t t h e g a s f l o w t h r o u g h t h e d e n s e p h a s ei s t h a t n e e d e d f o r m i n i m u m f l u i d i z a t i o n .

I t i s c o m m o n p r a c t ic e in m o d e l l i n g st e a m r e f o r m i n gr e a c t o r s t o c o n s i d e r t h e c o n v e r s i o n o f tw o k e y c o m -p o n e n t s a n d t h e n t o o b t a i n t h e c o n c e n t r a t i o n s o ft h e o t h e r c o m p o n e n t s b y a p p l y i n g s to i c h i o m e t r icr e l a t i o n s ( X u a n d F r o m e n t , 1 98 9; A d r i s e t a l . , 1991;S o l i m a n e t a l . , 1 9 9 2 ) . T h e p r e s e n t m o d e l , h o w e v e r ,c o n s i d e rs t h e c h a n g e i n t h e m o l a r f lo w o f e ac h c o m p o -n e n t s e p a r a t e l y s o t h a t d i f f e r e n c e s i n d i f f u s iv i t i e s c a nb e a c c o u n t e d f o r r i g o r o u s l y .

T h e r e a c t i o n r a t e t e r m s , R i b a n d R i d i n e q s ( 1 ) - ( 4 ) ,r e p r e s e n t t h e r a t e s o f f o r m a t i o n o f c o m p o n e n t i i n t h eb u b b l e o r d e n s e p h a s e , e s s e n t i a l ly e q u a l t o t h e i n t r i n -s i c r a t e s s i n c e t h e e x t e r n a l m a s s t r a n s f e r r e s i s t a n c e i sn e g l i g i b le fo r t h e s i ze o f c a t a l y s t p a r t i c l e s c o n s i d e r e d .E a c h R~ i s t h e c o m b i n a t i o n o f t h e r a t e s o f f o r m a t i o na n d d i s a p p e a r a n c e o f t h is c o m p o n e n t t h r o u g h t h et h r e e p r i n c i p a l p a r a l l e l r e a c t i o n s t a k i n g p l a c e i n s t e a mr e f o r m i n g g i v e n in A p p e n d i x A . R e a c t i o n r a t e e x p r e s -s i o n s a n d c o n s t a n t s , e q u i l i b r i u m c o n s t a n t s a n d a d -s o r p t i o n c o n s t a n t s a r e a l s o g iv e n in A p p e n d i x A . T h eX u a n d F r o m e n t ( 19 89 ) r a t e e x p r e s s i o n h a s b e e n u t i l -i z e d d u e t o i t s g e n e r a l n a t u r e a n d i t s a b i l i t y t o d e -s c r i b e t h e k i n e t i c s o f t h e r e f o r m i n g r e a c t i o n o v e ra w i d e r a n g e o f o p e r a t i n g c o n d i t i o n s ( E l n a s h a i e e t a l . ,1990).T h e h y d r o d y n a m i c p a r a m e t e r s r e q u i r e d to s o l v ee q s ( 1 ) - (5 ) a r e o b t a i n e d u s i n g s t a n d a r d r e l a t i o n s f r o mt h e l i t e r a t u r e a s s u m m a r i z e d i n A p p e n d i x B .

1611

2.2.2. D i l u t e p h a s e ( i. e. f r e e b o a r d r e g i o n ) e q u a -t i o n s . A m o l e b a la n c e o n c o m p o n e n t i ( i = 1 - 4 ) i n t h e

d n i , = q J ~ A R i z . (6)d zF o r i = 5 ( h y d r o g e n ) t h e d i l u t e - p h a s e e q u a t i o n i s

dn,~dz Vz AR ,z - *e ~ Cep,(P.z -- e~; 5) (7)w h e r e z i s t h e d i s t a n c e a b o v e t h e b e d s u r f a c e . T h eb o u n d a r y c o n d i t i o n a t z = 0 i s n~ = n~d + n ~ b, e v a l u -a t e d a t h = / - / . u?z i s t h e s o l i d s m a s s c o n c e n t r a t i o n i nt h e f r e e b o a r d z o n e g i v e n a s : u ? z = E z / U o , whi le E~ i st h e e n t r a i n m e n t f l u x o f so l i d s a t a d i s t a n c e z a b o v e t h eb e d s u r fa c e , g i v e n b y W e n a n d C h e n ( 19 82 ) a s

Ez = E ~ + (Eo - - Eo~)e - c z (8 )w h e r e E o i s t h e e n t r a i n m e n t f l u x o f s o l i d s a t t h e b e ds u r f a c e , E o~ i s t h e e n t r a i n m e n t f l u x o f s o l i d s a b o v e t h et r a n s p o r t d i s e n g a g e m e n t h e i g h t ( T D H ) a n d a~ i s a no v e r a l l d e c a y c o n s t a n t , t a k e n h e r e a s 4 m - 1 a s s u g -g e s t e d b y G e l d a r t ( 1 9 8 6 ) . E 0 a n d E ~ w e r e a l s o c a l -c u l a t e d a c c o r d in g t o t h e p r o c e d u r e g i v e n b y G e l d a r t(1986).T h e s e le c ti v e s e p a r a t i o n o f h y d r o g e n b y t h e m e m -b r a n e t u b e s i n t h e f r e e b o a r d z o n e i s d e s c r i b e d b ya m o d i f i e d f o r m o f eq . ( 5) :

d n , ~ _ , ( p , ~d zz e \ M H ] C e p t ( P ~ - - pO~5). (9)

2.3. S o l u t i o n a l g o r i t h mT h e s o l u t io n a l g o r i t h m i s c o m p o s e d o f t h r e e m o d -ules :

( 1 ) T h e f i r s t m o d u l e s o l v e s f o r r e a c t i o n a n d p e r -m e a t i o n i n t h e c a t a l y s t b e d z o n e .

( 2) T h e s e c o n d m o d u l e s o l v e s f o r r e a c t i o n a n d p e r -m e a t i o n i n t h e p a r t o f t h e f r e e b o a r d z o n e w h i c hi n c l u d e s m e m b r a n e t u b e s .

( 3) T h e t h i r d m o d u l e s o l v e s f o r th e r e a c t i o n i n a n yp a r t o f t h e f r e e b o a r d z o n e t h a t d o e s n o t i n c l u d ep e r m e a b l e m e m b r a n e t u be s .

E a c h m o d u l e f i r st c a l c u l a t e s t h e p a r a m e t e r s n e e d e db y t h e d i f fe r e n t i a l e q u a t i o n s d e s c r i b i n g t h e p h e -n o m e n a t a k i n g p l a c e i n t h a t p a r t o f th e r e a c t o r a n dt h e n s o l v e s t h e m o d e l d i f f er e n t i a l e q u a t i o n s b y c a l l i n ga n u m e r i c al r o u t i n e N L D E Q D w h i c h us es t h eR u n g e - K u t t a m e t h o d , w i t h v a r i a b l e s t e p si ze to e n -s u r e s o l u t i o n a c c u r a c y . A l l v a r i a b l e s a r e d e f i n e d a sd o u b l e p r e c i s i o n v a r i a b l e s t o i m p r o v e t h e a c c u r a c yw h e n d e p e n d e n t v a r i a b l e s a r e v a r y i n g s t e e p l y. D u e t oa d e l i c a t e b a l a n c e b e t w e e n t h e t h r e e t e r m s i n v o l v e d i nt h e d i f f e r e n t ia l e q u a t i o n s d e s c r i b i n g t h e c h a n g e i nm o l a r r a t e s i n t h e b u b b l e a n d d e n s e p h a s e s , i n t e g r a -t i o n h a d t o b e s t a r t e d w i t h a v e r y s m a l l s t e p s i z e ,t y p i c a l l y 1 0 - 1 m . T e m p e r a t u r e p r o f i l e s w e r e b a s e do n e x p e r i m e n t a l m e a s u r e m e n t s i n t h e d e n s e b e d a n di n t h e f r e e b o a r d ( A d r i s , 1 9 9 4 ) , w i t h t h e t e m p e r a t u r e

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1612a s s u m e d t o b e u n i f o r m b e l o w t h e b e d s u rf a ce . A ne x p e r i m e n t a l v a l u e o f t h e e x p a n d e d b e d h e i g h t w a sa l s o u s ed , w h i le t h e p e r m e a t i o n c a p a c i t y w a s b a s e d o nm e a s u r e m e n t s c a r r i e d o u t o n p a l l a d i u m t u b e s ina s e p a r a t e p e r m e a t i o n r i g ( A d r is , 1 9 9 4) . T h e l i m i t i n gc a s e o f a f l u i d i z e d - b e d r e a c t o r w i t h o u t m e m b r a n es e p a r a t i o n c a n b e s o l v e d b y s e tt i n g Cept = O.

3. MODELVALIDATION3.1. M o d e l p r e d ic t io n s v s e x p e r i m e n t a l d a t a

E x p e r i m e n t a l re s u l ts f or t h e p i l o t - s c a l e F B M R -S M R i n v e s t i g a t i o n h a v e b ee n r e p o r t e d e l s e w h e r e( A d r i s , 1 9 94 ; A d r i s e t a l . , 1 9 9 4 b ) f o r s t e a m - t o - c a r b o nr a t i o s f r o m 2 .3 t o 4 .2 , r e a c t i o n t e m p e r a t u r e s f r o m 7 2 0t o 9 3 0 K a n d p r e s s u r e s f r o m 0 . 69 t o 0 .9 8 M P a . T h em o d e l d e v e l o p e d a b o v e c a n b e t e s t e d u s i n g t h e see x p e r i m e n t a l d a t a b o t h w i t h a n d w i t h o u t s e l e c ti v ep e r m e a t i o n . T h e v o l u m e f r a c t i o n o f t h e b e d o c c u p i e db y s o l i d s d i s p e r s e d i n t h e b u b b l e p h a s e i s t a k e n a s0 . 5 % o f t h e v o l u m e f r a c t io n o f t h e b e d o c c u p i e d b yb u b b le s , i .e . ~b = 0 .005 e b ( s e e Gr ac e , 1986 ; Ku n i i an dL e v e n s p i e l , 1 99 1) . A v e r y g o o d m a t c h b e t w e e n e x p e r i -m e n t a l r e s u l t s a n d m o d e l p r e d i c t i o n s w a s o b t a i n e da s s h o w n b y F i g . 2 . D e v i a t i o n s b e t w e e n t h e m o d e lp r e d i c t io n s a n d t h e e x p e r i m e n t a l d a t a a r e s o m e w h a tl a r g e r fo r t h e r e a c t i o n r u n s w i t h o u t p e r m e a t i o n ,w h e r e p r e d i c t i o n s a r e m o r e s e n s i t i v e t o a n y e r r o r i nt e m p e r a t u r e , b e c a u s e t e m p e r a t u r e i s t h e m a j o r f a c t o rd e t e r m i n i n g c o n v e r s i o n w h e n t h e r e i s n o s e l e c t i v es e p a r a t i o n .

F o r r e a c t i o n - p e r m e a t i o n r u ns , a n y e r r o r in t h et e m p e r a t u r e r e a d i n g a f f e ct s t h e p r e d i c t i o n s t o a l e s s e re x t e n t b e c a u s e t h e r e a c t i n g m i x t u r e i s s h i f t e d f r o me q u i l i b r i u m d u e t o t h e i r r e v e r s i b le i n s i t u h y d r o g e ns e p a r a ti o n . T h e c o n t r i b u t io n o f p e r m e a t i o n t o t h eo v e r a l l c o n v e r s i o n , t o g e t h e r w i t h t h e u s e o f e f f ec t i v ep e r m e a b i l i t y c o n s t a n t s m e a s u r e d a n d f i tt e d in t h ee x p e r i m e n t a l s t u d y ( A d r i s e t a l . , 1994 b ) , e x p la in theb e t t e r m a t c h b e t w e e n m o d e l p r e d i c t i o n s a n d e x p e r i -m e n t a l d a t a f o r t h e r e a c t i o n - p e r m e a t i o n r u n s. T h e

0.80.7- No permeation

>~ 0 . 6 -0 0 . 5 -~1~ 0 . 4 -

~ 0.2-~ 0.113. 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Experimental methane c o n v e r s i o nFig. 2. Experimental vs predicted methane conversion. Forexperimental details , see Ad ris (1994) and Adris e t a l . (1994b).

A. M. Adris et a l .m e a n a b s o l u t e v a lu e o f t h e d e v i a t i o n o f t he p r e d i c t e dm e t h a n e c o n v e r s i o n f ro m t h e e x p e r i m e n t a l c o n v e r -s i o n w a s 2 . 4 % f o r r e a c t i o n - p e r m e a t i o n e x p e r i m e n t sa n d 4 . 2 % f o r ru n s w i t h o u t p e r m e a t i o n .

T y p i c a l c o m p a r i s o n s b e t w e e n s i m u l a t i o n p r e d i c -t i o n s a n d e x p e r i m e n t a l d a t a a r e g i v e n i n T a b l e 1 f o ra r u n w i t h o u t p e r m e a t i o n a n d f o r a r e a c t i o n - p e r -m e a t i o n e x p e r i m e n t . I t i s c l e a r fr o m t h i s t a b l e t h a t t h em o d e l p r o v i d e s g o o d p r e d i c t io n s f o r t he r e a c t io n c o n -v e r s i o n s, t h e t o t a l h y d r o g e n y i e l d a n d t h e p e r m e a t i n gh y d r o g e n f l o w . T h e r e a r e , h o w e v e r , d i f f e re n c e s i n t h eo u t l e t g a s c o m p o s i t i o n , e s p e c i a l l y i n t h e r a t i o b e t w e e nc a r b o n o x i d e s p r o d u c e d b y t h e re a c t i o n . T h i s m a y b ed u e t o t h e d i f f e r e n c e b e t w e e n t h e c a t a l y s t u s e d h e r ea n d t h a t u s e d b y X u a n d F r o m e n t ( 1 98 9) t o d e v e l o pt h e k i n e t i c r a t e e x p r e s s i o n s e m p l o y e d i n t h e s i m u l a -t i o n . D i f f e r e n t r e f o r m i n g c a t a l y s t s h a v e d i f f e r e n t a b i l -i t ie s t o c a t a l y s e t h e w a t e r - g a s s h i ft r e a c t i o n ( R o s t r u p -N i e l s e n , 1 9 8 4 ) . T h e r e f o r e , t h e f r a c t i o n o f t h e c a r b o nm o n o x i d e c o n v e r t e d t o c a r b o n d i o x i d e b y th i s re a c -t i o n m a y v a r y d e p e n d i n g o n t h e c a t a l y s t . H o w e v e r ,t h i s v a r i a t i o n s h o u l d n o t h a v e a m a j o r i n f l u en c e o nt h e p r e d i c t e d o v e r a l l m e t h a n e c o n v e r s i o n , w h e t h e r t oc a r b o n m o n o x i d e o r c a r b o n d i o x i d e .

T h e r e s u l ts p r e s e n t e d i n T a b l e I a l s o i n d i c a t e ( b yd i ff e re n c e ) t h e c o n t r i b u t i o n m a d e b y t h e e n t r a i n e dc a t a l y s t p a r t i c l e s i n t h e s p l a s h z o n e ( i. e. r e g i o n i m -m e d i a t e l y a b o v e t h e d e n s e b e d u p p e r s u rf a c e) to t h er e a c t i o n c o n v e r s i o n . B e c a u s e o f t h e h e a t e r d e s i g n i no u r e x p e r i m e n t a l r e a c to r , th e s p l a s h z o n e t e m p e r a t u r ei s h i g h e r t h a n t h e b e d t e m p e r a t u r e , a n d t h e r e f o r e t h ec a t a l y s t p a r t ic l e s i n t h e f r e e b o a r d c o n t r i b u t e d p o s i t -i v e ly t o t h e r e a c t i o n b y a b o u t 7 % o f t h e o v e r a l lc o n v e r s i o n . I n a n i n d u s t r i a l r e f o r m e r , h o w e v e r , t h ee f fe c t o f t h e e n t r a i n e d c a t a l y s t p a r t i c l e s is l i k e l y t o b en e g a t i v e d u e t o l o w e r t e m p e r a t u r e s i n th e f r e e b o a r dz o n e , u n l e s s a n e q u i l i b r i u m s h i f t i s a f f e c t e d b y m e a n so f p e r m s e l e c t i v e m e m b r a n e s a s d i s c u s s e d b e l o w o ru n l e ss t h e f r e e b o a r d r e g i o n i s s p e c i a l l y h e a t e d .

T h e m o d e l d e v e l o p e d a n d v a l i d a t e d a b o v e i n cl u d e ss t a n d a r d h y d r o d y n a m i c e q u a ti o n s a n d c o r r e l a t i o n sf o r b u b b l i n g f l u i d i z e d b e d s a n d u t i l i z e s k i n e t i c r a t ee x p r e s s i o n s f r o m t h e l i t e r a t u r e a n d e x p e r i m e n t a l l ym e a s u r e d t e m p e r a t u r e s , b e d h e i g h t s a n d C e p t v a l u e s .O t h e r w i s e t h e r e a r e n o f i t t e d p a r a m e t e r s . N o t e t h a tw i t h t h e a b u n d a n c e o f c a t a l y s t i n t h is r e a c t o r s y s te m ,t h e r e a c t i o n c o n v e r s i o n i s h i g h l y i n f l u e n c e d b y t h et h e r m o d y n a m i c e q u i l ib r i a , a s w e ll a s b y h y d r o g e np e r m e a t i o n r a t e s .3.2. S e n s i t i v i t y a n a l y s i s

T h e m o d e l i s e x a m i n e d h e r e f o r i ts s e n s i t i v it y t of o u r e s t i m a t e d p a r a m e t e r s : s o l id s c o n c e n t r a t i o n i n t h eb u b b l e p h a s e , d i s t r i b u t i o n o f f e ed g a s b e t w e e n t h eb u b b l e a n d d e n s e p h a s e s , c a t a l y s t a c t i v i t y a n d b u b b l es iz e . P e r m e a t i o n w a s o m i t t e d a t t h i s s t a g e to a v o i d i t sc o n t r i b u t i o n w h i c h m a y o b s c u r e t h e e f fe c t o f t h e sep a r a m e t e r s . S e n s i t i v i ty t e s ts w e r e r e s t r i c t e d t ot h e c a t a l y s t b e d c o n v e r s i o n , e x c l u d i n g t h e f r e e b o a r de ff ec ts w h i c h v a r y f r o m o n e r e a c t o r t o a n o t h e rd e p e n d i n g o n t h e r e a c t o r c o n f i g u ra t i o n a n d c a t a l ys t

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Mo d e l l in g o f a f lu id ize d -be d m e m bran e r e ac to rT ab le 1 . C o m p ar i s o n o f m o d e l p re d ic tio n s w i th e xp e r im e n ta l d a ta f o r tw o typ ica l run s. O p e ra t in gcon ditio ns: T = 541C, P = 0.64 M Pa , @b = 0.005eb, U a = U m f

1613

E x p e r i m e n ta l M o d e l E x p e r i m e n ta l M o d e ld a ta p re d ic t io n s d a ta p re d ic t io n s(w/o penn .) (w/o perm.) (with perm.) (with perm.)

Exi t me than e conve rs ion 0 .400 0 .391 0 .419 0 .421Exit s team conv ers ion 0 .182 0 .177 0 .200 0 .183M etha ne conv ers ion a t bed surface NA 0 .363 N A 0 .382To tal hyd rog en yield 1.421 1.471 1.515 1.550Perm eate hydr ogen f low, mo l/h 0 0 2 .31 2 .39O ut l e t g a s c o m p o s i t io n ,vo lume % (dry bas is ) :CH 4 24.0 24.8 22.4 22.7C O 0.8 1.0 0.8 1.2CO 2 16.5 14.9 16.8 15.3He 58.7 59.3 60.0 60.8

N A : n o t av a i lab le .

T ab le 2 . E f f e c t s o f s o l id s c o n c e n t ra t io n in th e bubb le p h as e o n th e m e th an e c o n v e r s io n :T = 700C, P = 1.5 M Pa , F c = 60 mo l/h , S / C = 3.5V o lum e f rac t io n o f be do c c up ie d by bubb le p h as esolids, qbb 0.0 0.0001 0.0005 0.001 0.005M ethan e conv ers ion 0 .569 0 .570 0 .573 0 .575 0 .579

Table 3 . M ode l sensi tiv ity to gas f low th ro ugh the dense phase : T = 700C,P = 1 .5 M Pa, F c = 60 mo l/h , S / C = 3.5Frac t io n o f g as f lo w in gth ro ug h d e n s e p h as e ,Ga /A U,, , 0.01 O. 1 0.5 1.0 5.0Me than e conv ers ion 0 .554 0 .555 0 .562 0 .568 0 .579

p a r t i c l e - s iz e d i s t r i b u t i o n . T h e b e d t e m p e r a t u r e w a sa s s u m e d t o b e u n i f o r m i n t h e s e te s t s, a n d a l l v a r i a b l e s ,e x c e p t th e o n e u n d e r i n v e s t ig a t i o n , w e r e m a i n t a i n e dc o n s t a n t i n e a c h c a s e .

3.2.1. M o d e l s e n s i t i v i ty t o s o li d s c o n c e n t r a t i o n i n t h eb u b b l e p h a s e . T h e v o l u m e f r a ct i o n o f t h e b e d o c c u -p i e d b y b u b b l e p h a s e s o l i d s , ~ b , w a s v a r i e d f r o m 0 t o0 .0 0 5. M e t h a n e c o n v e r s i o n w a s p r e d i c t e d f o r f i v e d i f -f e r e n t c a s e s a s p r e s e n t e d i n T a b l e 2 . T h e i n c r e a s e i nr e a c t i o n c o n v e r s i o n w i t h i n c r e a s i n g s o l id s c o n c e n t r a -t i o n i n t h e b u b b l e p h a s e m a y b e a t t r i b u t e d t o a r e d u c -t i o n i n b u b b l e b y - p a s s i n g , i . e . t o c o n v e r s i o n i n t h eb u b b l e p h a s e o v e r t h e s u r f a c e o f t h e d i s p e r s e d c a t a l y s tp a r t i cl e s . T h e i n s e n s i t i v i ty o f t h e r e s u l t s t o ~ ba r i s e s b e c a u s e t h e c o n v e r s i o n r a p i d l y a p p r o a c h e sa n e q u i l i b r i u m v a l u e , w i t h l i m i t e d i n f l u e n c e o f h y d r o -d y n a m i c s .

3.2.2. M o d e l s e n s i t iv i t y to g a s d i s t ri b u t i o n b e t w e e nb u b b l e a n d d e n s e p h a s e s . S i m u l a t i o n r e s ul t s p r e s e n t e d

a b o v e c o n s i d e r e d t h e g a s f l ow t h r o u g h t h e d e n s ep h a s e t o b e t h a t n e e d e d f o r m i n i m u m f l u id i z a ti o n ,w h i c h i s t h e r e f e r e n c e c a s e c o n s i d e r e d i n t h i s s t u d y .T h e s e n si t iv i t y o f t h e m o d e l t o t h i s a s s u m p t i o n w a se x a m i n e d b y v a r y i n g t h e g a s f l o w t h o u g h t h e d e n s ep h a s e a t h = 0 fr o m f i ve ti m e s t o 1 % o f t h e f lo wn e e d e d f o r m i n i m u m f l u id i z a ti o n . T h e s i m u l a t i o n r e -s u i ts s u m m a r i z e d i n T a b l e 3 i n d i c a t e t h a t t h e m o d e l isn o t v e r y s e n s i t iv e t o t h i s p a r a m e t e r . W h e n t h e fl o wt h r o u g h t h e d e n se p h a s e i s t a k e n a s 1 % o f t h a t n e e d e df o r m i n i m u m f l u id i z a ti o n , a p p r o x i m a t i n g t h e s ta g -n a n t b e d a s s u m p t i o n a d o p t e d b y K u n i i a n d L e v e n -s p i el ( 1 96 9 ) a n d G r a c e ( 1 9 84 ) , t h e m e t h a n e c o n v e r s i o ni s p r e d i c t e d t o b e r e d u c e d , b u t b y v e r y l i t t l e .

A g a i n , b u b b l e b y - p a s s i n g a c c o u n t s f o r t h is c h a n g ei n m e t h a n e c o n v e r s i o n u p o n c h a n g i n g t h e g a s d is t ri -b u t i o n b e t w e e n t h e b u b b l e a n d d e n s e p h as e s. T h es i m u l a t e d r u n s i n t h i s s t u d y a r e c h a r a c t e r i z e d b y l o ws u p e r f i c ia l g a s v e l o c i t ie s , o n l y a b o u t s i x t i m e s t h em i n i m u m f l u i d i z a t i o n v e lo c i t y . I t is a n t i c i p a t e d t h a tt h e s e n si t iv i t y o f t h e m o d e l t o t h i s p a r a m e t e r w o u l d b e

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1614even less at higher superficial gas velocities moretypical of i ndustri al fluidized-bed reactors.

A. M. Adris et a l .

3.2.3. M o d e l s e n s i t i v i ty t o c a t a l y s t a c t i v i t y . Thekinetic rate expressions used to estimate the rates ofreaction were developed (Xu and Frome nt, 1989) fora different catalyst with a different nickel content. Thecatalyst used in our work might have a differentactivity. While the difference in catalyst act ivity be-tween two commercial catalysts is unlikely to affectthe reaction rate estimation by more than 50% (E1-nashaie e t a l . , 1990), the activity was changed hereover a wide range to examine its effect on the modelpredictions. Table 4 compares five cases where thereaction rate coefficients, kl to k3, were varied from0.025 to 5.0 times the values predicted by the equa-tions given in Appendix A.

The predicted methane conversion for these fivecases indicates that the catalyst activity has a limitedeffect on the model predictions, within the range ofactivity of commercial catalysts for the catalyst inv en-tory investigated. When the catalyst activity was re-duced by 50%, the conversion decreased only from0.808 to 0.804. Larger changes were predicted whenthe activity was varied over a wider range. Thechanges in methane conversion shown in Table 4 aredue to the interaction between the chemical reactionand the mass exchange between the two phases (Adris,1994), i.e. both thermo dynamics and interphase masstransfer play important roles.

3.2.4. M o d e l s e n s i t i v i t y t o b u b b l e s i ze e s ti m a -t i o n . The Mori and Wen (1975) equation (see Appen-dix B) for estimating the bubble diameter, like otherwidely used relations for bubble diameter estimation,was developed for beds without internals. In the ex-perimental reactor system (Adris e t a l . , 1994b), how-ever, membrane tubes are placed vertically in thereactor and the bubble diameters could well differfrom the estimated ones. In this section the bubblediameter predicted by the Mori and Wen equationwas multiplied by factors of 0.4, 0.6, 0.8, 1.0 and 1.2 tostudy the impact of bubble size on the conversion

predictions. Table 5 gives the predicted values formethan e conversion in each case. The bubbl e size isseen to have little influence on the reaction conver sionfor the co nditio ns investigated.

3.3. G a s d i s t r i b u t i o n b e t w e e n p h a s e sAccount ing for a change in the num ber of moles of

gas due to chemical reaction complicates fluidized-bed reactor modeling (Irani e t a l . , 1980; Kai andFurusaki, 1987). This is an important considerationfor steam me thane reforming where, as seen from eqs(A1) and (A3) in Appendix A, the reactions causea significant increase in molar gas flow. A hy-drodynamic investigation of the distribution of addi-tional gas flow resulting from the increase in the to talnumber of moles due to reaction (Adris e t a l . , 1993)showed that at least some of the addit ional flow endsup in the bubble phase. It is not clear, however,whether the additional moles generated stay in thedense phase for some distance or transfer quickly tothe bu bble phase.

The model outlined in the present study assumesthat the gas flows through both the bubbl e phase andthe dense phase change with height due to the increasein the total molar flow rate caused by the reformingreactions. Since the reactions occur mostly in thedense phase, most of the additional gas volume isgenerated there. The extra moles are distributed be-tween the two phases by interph ase mass transfer and,possibly also, by bulk transfer of excess moles gener-ated to the bub ble phase, with some of the extra molesalso removed due to permeation.The change in the gas flow throu gh the bubble anddense phases along the bed height is plotted in Fig. 3for three different situations, calculated based on themodel presented in this work. The plot shows that thegas flow through both phases increases with heightwhen there is no permeation, with the dense phaseshare of the excess gas being about 6 50 . An increasefollowed by a slight decrease is exhibited for reac-tion -per meati on with a limited permeation capacity( C e p = 1.0 km); in this case the dense phase accom-modates about 500 of the excess gas, the bubble

Table 4. Model sensitivity to catalyst activity level: T = 800C, P = 1.5MPa,F c = 60 mol/h, S / C = 3.5

Rate coefficients, kt to k3,multiplied by 0.025 0.1 0.5 1.0 5.0Methane conversion 0.731 0.786 0.804 0.808 0.817

Table 5. Model sensitivity to est imated bubble size: T = 700C, P = 1.5 MPa,F c = 60 mol/h, S / C = 3.5

Bubble diameter factor 0.4 0.6 0.8 1.0 1.2Methane conversion 0.579 0.579 0.577 0.570 0.559

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Modelling of a fluidized-bed membrane reactor0.01 . 0

0 . 9 -

~ 0 . 8 ~etJ~ 0.7-.( / )- 0.6-1o

0.5-2'- '~ 0 . 4 -

~ 0 . 3 -

0 .20 . 0

0.1 0.2 0.3 0.4zx a4

2 .O E

No permeation- - -W- - Cep=1 .0 km ~ 1.4

Cep=l 0 km0 '1 0 '2 0 '3 0.4

Ri-a .

1.8 ~J~--IJ='-I

1 . 6 .oii=

0

H eight coordinate, mFig. 3. Change of gas flow through bubble and dense phases along the reactor for no permeation and fortwo different permeation capacities: T = 800C, P = 1.5 MPa, Fc = 80 mol/h, S / C = 3.5, P s = 0.4 MPa,Fs = 80 mol/h.

1615

Table 6. Model predictions for reforming reaction with and without permeation considering variable gasflow in both phases and constant dense-phase gas flow assumptions:F c = 80 mol/h, S / C = 3.5, T = 800C,P = 1.5 MPa, P s = 0.4 MPa, Fs = 80 mol/h (freeboard reaction ignored)Permeation capacity, km 0 0 10 1.0

Variable gas Constant Variable gas Constantflow in both dense phase flow in both de nsephaseModel assumption phases gas flow phases gas flowMethane conversion 0.774 0.752 0.803 0.781Steam conversion 0.323 0.314 0.337 0.328

phase about 35%, with the balance being removed ashydrogen by the membrane tubes. When the per-meat ion capacity is increased to 10 km, the gas flowsteeply decreases after an initial increase, with mo st ofthe excess gas removed by hydrogen permeationthrough the membra ne tubes.

In a variant of the model presented above, the gasflow through the dense phase was maintained con-stant, i.e. Ud was maintained constant, so that allthe excess gas generated in the dense phase andnot removed by the permeable membrane tubes wasaccommodated by the bubble phase. An adjustmentwas carried out between each step in the integration.Table 6 gives the model predictions for two casesconsidering this 'constant dense phase gas flow'assumption compared with the predictions of theoriginal model.It is clear from Tab le 6 that the divi sion of excessgas distributi on between the bubbl e and dense phasescan affect the model predictions to a small but ap-preciable extent. Given the available experimental

results which are dominate d by reaction equilibriumand permeability, it would be difficult, if not imposs-ible, to dis criminate between the two models based o nreaction experiments. Separate experiment s designedto determine the gas flow in the separate phases arerequired to discriminate between these two rival as-sumptions, i.e. to determine how extra moles of gasgenerated by the reactions are distribu ted between thetwo phases.

4 . PA R A M E T R I C I N V E ST I G A T I O NA parametri c investiga tion was conducted to ob-

tain better insights into the effect of major operatingvariables and design parameters influencing the per-formance of the reactor. In addition , the performanceof the FBMR system was explored beyond the rangeof parameters which could be studied experimentallydue to limitations imposed by economic and safetyconsiderations.

The react ion-pe rmeati on option has been used forthe predictions in this section, with the con tri buti on of

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1616 A .M . Adr i s et al .t h e f r e e b o a r d i g n o r e d a n d t h e t e m p e r a t u r e a s s u m e d 1.00 -t o b e u n i f o r m , e x c e p t w h e r e e x p l i c i t l y s p e c i f i e d o t h e r -w i s e . T h e m o d e l w i t h v a r i a b l e g a s f l o w i n b o t h p h a s e s e - 0 . 9 5-i s u s e d . V a r i a b l e s a n d p a r a m e t e r s s t u d i e d a n d t h e i r .o,r a n g e s a r e a s f o l l o w s : t e m p e r a t u r e : 4 0 0 - 8 0 0 C ; p r e s - ~ 0 .9 0 -s u re : 0 . 3 - 2 . 7 M P a ; s t e a m - t o - c a r b o n m o l a r f e e d r a t i o : ~>1 . 5 - 5 .5 ; m e t h a n e m o l a r f e e d r a t e : 2 0 - 1 0 0 m o l / h ; p e r - oo 0 .a 5 -m e a t i o n c a p a c i t y , C e p : 0 . 4 - 7 . 0 k m ; s w e e p g a s f l o w 0 .a 0 .t -r a t e : 4 0 - 1 2 0 m o l / h ; s e p a r a t i o n s id e p r e s s u r e : t ~t - -0 . 1 - 0 . 9 M P a . . , 0 .7 5.

T h e i n v e s t i g a t i o n f o c u s e d o n t h e e f fe c t o f c h a n g i n g ~ 0 .7 0-t h e s e p a r a m e t e r s a n d v a r i a b l e s o n t h e c o n v e r s i o n o fm e t h a n e . A n o t h e r p a r a m e t e r , t h e f r a c t i o n o f h y d r o - 0.0g e n s e p a r a te d f ro m t h e r e a c t io n d o m a i n t h r o u g h t h em e m b r a n e t u b e s , i s a l s o u s e fu l h e r e i n i n d i c a t i n g t h ee x t e n t o f t h e e q u i l i b r i u m s h i ft . T h i s p a r a m e t e r i s re -s p o n s i b l e fo r a l t e r in g t h e c o m p o s i t i o n o f t h e r e a c t i n gm i x t u r e b y c h a n g i n g i t s h y d r o g e n c o n t e n t . T h e e x t e n to f t h is c h a n g e d e p e n d s o n t h e p o r t i o n o f t h e h y d r o g e np r o d u c e d w h i c h i s r e m o v e d f r o m t h e r e a c t i o n s y s t e m 1.0b y p e r m e a t i o n . I t i s r e f e rr e d t o h e r e a s t h e ' h y d r o g e nf r a c t i o n s e p a r a t e d ' .4.1. E f f e c t o f o p e r a t i n g v a r i a b l e s

4.1.1. O p e r a t i n g p r e s s u r e . I n c o n v e n t i o n a l r e -f o r m e r s , h i g h e r r e f o r m i n g r e a c t i o n c o n v e r s i o n s a r ef a v o u r e d b y l o w e r r e a c t o r p r e s s ur e s , a n o b v i o u s c o n -s e q u e n c e o f L e C h a t e l i e r ' s p r i n c i p l e . I n a n F B M Rs y s te m , t h e S M R r e a c t i o n i s a c c o m p a n i e d b y a s e p a r -a t i o n p r o c e s s w h i c h i s f a v o u r e d b y h i g h e r p r e s s u r e s .T h e r e f o r e , t h e n e t e f fe c t o f i n c r e a s i n g t h e r e a c t o r p r e s -s u r e d e p e n d s o n t h e b a l a n c e b e t w e e n t h e r e a c t i o n a n dp e r m e a t i o n p r o ce s se s . F a c t o r s l ik e t h e p e r m e a t i o nc a p a c i ty , te m p e r a t u r e a n d s t e a m - t o - c a r b o n r a t i o a l lh a v e s i g n i f i c a n t i m p a c t s o n t h i s b a l a n c e ; t h e n e t e f fe c tc o u l d b e a d e c r e a s e , n o c h a n g e o r a n i n c r e a s e i nm e t h a n e c o n v e r s i o n .

F i f t e e n c a s e s w e r e s i m u l a t e d h e r e t o p r e d i c t t h ee f fe c t o f p r e s s u r e o v e r t h e r a n g e 0 . 3 t o 2 . 7 M P a a tt h r e e d i f f e r e n t m e m b r a n e e q u i v a l e n t p e r m e a t i o n c a -p a c i t i e s , 0 .4 , 3 .0 a n d 7 .0 k m . S i m u l a t i o n r e s u l t s t o -g e t h e r w i t h t h e c o r r e s p o n d i n g e q u i l i b r i u m c o n v e r -s i o n s a t t h e r e a c t o r - b e d c o n d i t i o n s f o r e a c h o p e r a t i n gp r e s s u r e a r e p l o t t e d i n F i g . 4. T h e c o n v e r s i o n s i n F i g .4 i n d i c a t e t h e t w o o p p o s i n g e f fe c ts w h i c h t h e r e a c t o rp r e s s u r e h a s o n t h e o v e r a l l c o n v e r s i o n . A t l o w p r e s -s u re , th e m e t h a n e c o n v e r s i o n i s l o w e r t h a n i t s e q u i l i b -r i u m v a l u e d u e t o t h e i n s i g n i f i c a n t e x t e n t o f h y d r o g e ns e p a r a t i o n , a s w e l l a s d u e t o s t r o n g b u b b l e b y - p a s s i n gc a u s e d b y t h e h i g h s u p e r f i c i a l g a s v e l o c i t y . A s t h ep r e s s u r e i n c re a s e s, t h e i m p a c t o f th e p e r m e a t i o n c a p a -c i ty b e co m e s m o r e i m p o r t a n t a n d t h e e x t en t o f th ee q u i l i b r i u m s h i f t i s d e t e r m i n e d b y t h e m e m b r a n e c a -p a c i t y . T h e c a s e s s h o w n i n F i g . 4 w i t h h i g h p e r -m e a t i o n c a p a c i t y ( C e p = 7 . 0 k m ) e x h i b i t t h e s t r o n gp o t e n t i a l o f t h e F B M R f o r S M R r e a c t io n s . T h e 0 .9 6m e t h a n e c o n v e r s i o n o b t a i n e d h e r e a t 8 0 0 C a n d2 .7 M P a e x c e e d s t h e e q u i l i b r i u m c o n v e r s i o n b y a b o u t2 5 % . S u c h a h i g h c o n v e r s i o n c o u l d o n l y b e o b t a i n e da t a m u c h h i g h e r o p e r a t i n g t e m p e r a t u r e , a b o u t 1 30 Ch i g h e r , i n a c o n v e n t i o n a l r e f o r m i n g r e a c t o r .

~Q

0 Equ i l i b r ium~7 Cep=0 .4 km Cep=3 .0 km Ce p=7 .0 m

o . 5 1 . o 1 . 5 2 1 o 2 . 5R e a c t o r p r e s s u r e , M P a

~7O3 . 0

Fig. 4. Effect of reacto r pressure on th e methane conversionfor different pe rm eatio n capacities: T = 800C, F c =60 mol/h, S / C = 3.5, P s = 0.4 MPa, F s = 80 mol/h.

C 0.8-._op ->~ 0.5-C8~ 0.4. -g~ 0.2.

0.0

O Equi l ibr ium c o nv e rs i o n F B M R c o n v e rs i on Hy drogen raction s e p a r a t e d

O

O

4 ~ o 5 ~ o 0 ~ o r~0R e a c t o r t e m p e r a t u r e , C

0.50 ~

0 . 4 5 ~C.2

o . , ~e.-

0.351-

800 0 .3 0

Fig. 5 . Effect of reac tor temp erature on the methane conver-s ion and separa t ion by permeat ion: P = 1 .5 M Pa, F c =60 mol/h S / C = 3. 5 , Ps = 0 .3 MPa, F s = 80 mol/h, Cep = 7.0 km.

4.1.2. O p e r a t i n g t e m p e r a t u r e . I n c r e a s i n g t h e o p e r -a t i n g t e m p e r a t u r e h a s a p o s i t i v e e ff e ct o n b o t h t h er e a c t i o n a n d t h e p e r m e a t i o n p r o c e s s e s , s i n c e b o t hd e p e n d o n t e m p e r a t u r e i n a n A r r h e n i u s f as h io n . B o t ht h e m e t h a n e c o n v e r s i o n a n d t h e h y d r o g e n f r a c t i o ns e p a r a t e d b y p e r m e a t i o n a l w a y s i n c re a s e w i th t e m -p e r a t u r e a s s h o w n i n F i g . 5 . T h e i n c r e a s e i n m e m -b r a n e p e r m e a b i l i t y w i t h i n c r e a s in g t e m p e r a t u r e d o e sn o t n e c e s s a r i l y m a t c h t h e c o r r e s p o n d i n g i n c r e a s e i nr e a c t i o n r a t e a n d e q u i l i b r i u m c o n s t a n t . T h e r e f o r e , t h ee x t e n t o f t h e e q u i l i b r i u m s h i f t v a r i e s w i t h t e m p e r a t u r ea c c o r d i n g t o t h e t e m p e r a t u r e d e p e n d e n c e o f t h e p e r -m e a b i l i t y r a t e c o n s t an t . T h e m e m b r a n e c a p a c i t ya g a i n c o n t r i b u t e s t o t h e e x t e n t t o w h i c h t h e r e a c t i o n i ss h i ft e d f r o m t h e t h e r m o d y n a m i c e q u i l ib r i u m . T h e r e -a c t o r o p e r a t i n g t e m p e r a t u r e i s l i m i t e d i n p r a c t i c e b yt h e m e m b r a n e t u b e l if e ti m e a n d d e p e n d s o n t h e e x i tg a s c o m p o s i t i o n r e q u ir e m e n t s fo r d o w n s t r e a m p r o -c e s s ing .

4.1.3. S t e a m - t o -c a r b o n m o l a r f e e d r a t io ( S / C ) . T h es t e a m - t o - c a r b o n m o l a r f e e d r a t i o i s a n o t h e r v a r i a b l ew i t h t w o o p p o s i n g e ff ec ts o n t h e F B M R . I n c r e a s i n g

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0.8-

0 . 5 -2

0.4-|0.3-

0.2

Modelling of a fluidized-bed membrane reactor0.62 3 4 5i t

Q

0 ~ , ~ , ;

S t e a m - t o -c a r b o n m o l a r f e e d rat io

0.4

0.3

0.2

Fig. 6. Effect of steam-to-carbon molar feed ratio at con-stant methane flow on the reaction conversion and hydrogenseparation: T = 600C, P = 1.5 MPa, F c = 60 mol/h, P s =0.3 MPa, F s = 80 mol/h, Cep = 3.0 km.

t .oo 0 . 9 5 -

~ 0 . 9 0 -O~

0 . 8 5 -o m0 . 8 0 -t -o.7s-0 . 7 0 2 0

1617

l 0

0 Equilibrium With permeation No permeation

0 0

4 o 6 0 8 0 1 ~ oM e t h a n e f l ow , m o l / h

Fig. 7. Effect of reactor throughput on methane conversion:T = 800C, P = 1.5 MPa, P s = 0.4 MPa, F s = 80 mol/h,S / C = 3.5, Cep = 3.0 km.

the S / C ratio increases the reaction conversion ther-modynamically. However, a higher steam concentra- 04stion in the reacting mixture reduces the hydrogenconcen trat ion, thereby diminishin g the drivin g force .~ 0.44-for permeation. The choice of S / C is constr ained at itslower and upper limits by carbon formation and cata- 043lyst re-oxidation, respectively. In addition, pall adium ..has a tend ency to form oxides in an oxidizing atmo- ~ 0.42-sphere (Tsotsis e t a l . , 1993), and high steam- to-car bon ,~rat ios may affect the tube life. 0.41-

In the simulati on, the steam-to-carbon molar feedratio was chang ed from 1.5 to 5.5 by increasing the 0.40flow of steam at a con stan t metha ne flow. The result-ing methane conversion and hydrogen fraction separ-ated for these two cases are presented in Fig. 6. Thenet effect is an overall increase in metha ne conversion.However, a strong negative effect on the selectiveseparation process is exhibited in Fig. 6 by the steepdecrease in the hydrog en fraction separated, from 0.52at S / C = 1.5 to 0.27 at S / C = 5.5, indica ting a reduc-tion in the extent of the eq uilibrium shift.

40 60 80

00

100 120ioo

M e t h a n e c o n v e r s io n0 H y d r o g e n s e p a r a t io n

4'0 ;o 8'0 1~o 1~oSw eep gas flow ra te mol /h

0.38 00.36

a .0.34

e-.o_0.32 ~m0.30 4::r-

0.28 L~10

0.26 '30.24

Fig. 8. Effect of sweep gas flow on the reaction conversionand hydrogen separation: T = 600C, P = 1.5 MPa, F c =60 mol/h, S / C = 3.5, Ps = 0.3 MPa, Cep = 3.0 km.

indicating that the m embrane separation is insuffi-cient to compensate for bubble by-passing.

4.1.4. R e a c t o r t h r o u g h p u t . Increasing the reactorthrough put (i.e. overall gas flow rate) affects the per-formance of the F BMR negatively: (a) by increasin gbubble by-passing and (b) by reducing the ma gnitudeof the equilibr ium shift due to a red uction in thefraction of hydrogen separated by permeation at thesame membrane capacity. The effect of this variablewas examined by performing five simulations wherethe methane feed rate was increased from 20 to100 mol/h at a con stan t steam- to-ca rbon ratio. Re-sults are shown in Fig. 7 confirming the anti cipatednegative effect. The predicted methane conversionwithout me mbrane separation is plotted on the samegraph for comparison. The gap between the conver-sion with and without permeati on is diminished as themeth ane flow rate increases, due to the decline in therole played by membrane separation in shifting theequilibr ium. At the highest methane flow the FBMRgives a lower conversion tha n the equil ibri um value,

4.2. E f f e c t o f m e m b r a n e - s i d e de si gn p a r a m e t e r sThe effect of the sweep gas flow rate was studied by

changing its value from 40 to 120 mol/h. The pre-dicted methane conversions and hydrogen fractionsseparated are plotted against sweep gas flow in Fig. 8.The increase in sweep gas flow reduces the hydrogenpartial pressure on the separation side, thereby in-creasing the permeation driving force and leading tohigher rates of hydrogen removal from the reactiondomain. The extent of the increase in conversion is,however, relatively small, with a tripling of the sweepgas flow only increasing the conversion from about0.415 to 0.434.

The s eparat ion side pressure was varied from 0.1 to0.9 MPa to explore its influence. The pred ictions areplotted in Fig. 9 showing that an increase in theseparati on side pressure causes a decrease in conver-sion. This is because an increase in the hydrogenpartial pressure on the separation side reduces the

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16180.91

0.9) 0.89

o . ~I 0 . 8 7

0 86

0 85

o

D []

0

o 1 2 o 1 4 o 1 8 o i .Separa tion side p r e s s u r e M P a

A . M .0.8

0 5 ~0.4

r - I~ 0 .3 }

0.2

Fig. 9. Effect of separation side pressure on the reactionconversion and hydrogen separation: T = 800C, P =1.5 MPa, F c = 60 mol/h, S I C = 3.5, F s = 80 mol/h, Cev =3.0 km.

2 4 6i i i

O o

0

O Methane convers ion0 H ydrogen sepamlJon0

1.0O.S ~0 . 6 e-.

0.4 ~0.2 ~

r

1.11110.95.t-O'~ 0 . 8 0 .0.85-O.SO.t -

~ o .rs -

070 ~ ; o oEq uivalent perm eation capacity, C op, km

Fig. 10. Effect ofmembranecapacity on the reaction conver-sion and hydrogen separation: T = 800C, P = 1.5 MPa,F c = 60 mol/h, S I C = 3.5, P s = 0.3 MPa, F s = 80 mol/h.

permeat ion driving force. The extent of this negativeeffect is again limi ted, with the ninefold increase in theseparation side pressure only reducing the methaneconversion by about 4% . It should be remembered,however, that higher membra ne side pressures enablethe use of thinner membrane tube walls, thereby en-hancing permeation.

The effect of the capacity of the membrane tubes,expressed as the equivalent permeation capacity, Cep,

Adris et a l .was also examined. As expected, the overall conver-sion increases significantly as the memb rane capacityincreases. The effect is not limited by other factors inthe model. Results are plotted in Fig. 10. However, inpractice tubes must be separated by a distance of atleast 20 dp to 30 dp to mainta in good fluidization(Grace, 1982), and this puts an upper limit on thenumber of tubes. Also the wall thickness must besufficient to allow the tubes to withstand mechanicalforces and erosion in the bed. Like the other twoseparation side parameters discussed above, Ce~ mustbe optimized on an economic basis, considering thecost of the membrane material together with the costof generating and recovering the sweep gas, mostlikely steam.

4.3. E f f e c t o f m e m b r a n e s e p a r a ti o n o n f r e e b o a r d r e a c -t i o n s

One of the important advantages of the FBMRsystem for reversible reactions is its ability to suppressundesirable reactions in the freeboard region by shift-ing the ther modynamic equilibrium by product re-moval mainly in the dense bed. This property of theFBMR is demonstrated here by four simulation runswhere, for illustration purposes, the freeboard wasassumed to be cooler than the average bed temper-ature by 75C, while the mass of entrained catalystwas assumed to be 4 times that estimated for ourreactio n-permeat ion experiments. The first ru n wasperformed without hydrogen separation; in the sec-ond and third, hydrogen was selectively removed us-ing two different membrane capacities, while thefourth had membrane tubes extending into the free-board region. Table 7 gives the conditions and pre-dicted results.

Table 7 shows that freeboard reactions reduce themethane conversion in the first case by about 4%,with the resulting exit conversion falling between theequilibrium conversion at bed conditions and thatcorresponding to the freeboard conditions. In thesecond case, methan e conversion at the bed surfaceapproaches equi librium by virtue of membr ane separ-ation, with freeboard reactions affecting the conver-sion in a negative way, but to a lesser extent than forthe first case. When the membrane capacity is in-creased in the third column, the reaction conversionexceeds the equil ibriu m limits in the bed a nd very

Table 7. Predicted effect of membrane separation on limiting reaction reversal in the freeboard:P = 1.5 MPa, TR = 800C, T1b = 725C, Fc = 80 mol/h, S / C = 3.5, Fs = 80 mol/h, P s = 0.4 MPa,mass of catalyst entrained in the freeboard = 0.03 kgPermeation capacity in dense bed, km 0 2.80 6.73 2.80Permeation capacity in dilute phase, km 0 0 0 1.2Methane conversion a t bed surface 0.774 0.822 0.857 0.822Equilibrium conversion at bed conditions 0.831 0.831 0.831 0.831Methane conversion at reactor exit 0.735 0.798 0.848 0.819Equilibrium conversion at freeboard 0.647 0.647 0.647 0.647conditions

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Mo delling of a fluidized-bed mem brane reac torl i t t l e r e v e r s e r e a c t i o n i s p r e d i c t e d i n t h e f r e e b o a r dr e g i o n . I n d e e d , t h e o v e r a l l c o n v e r s i o n r e m a i n e dh i g h e r t h a n t h e e q u i l i b r i u m c o n v e r s i o n f o r t h e b e dc o n d i t i o n s a n d m u c h h i g h e r t h a n t h e e q u i l i b r i u mc o n v e r s i o n a t t h e f r e e b o a r d c o n d i t i o n s .I t is c l e ar t h a t r e m o v a l o f p r o d u c t h y d r o g e n f r o mt h e d e n s e b e d b y m e a n s o f p e r m e a b l e m e m b r a n e s c a ns i g n i fi c a n t ly r e d u c e a d v e r s e f r e e b o a r d e ff ec ts . F u r t h e rm e m b r a n e s e p a r a t i o n i n t h e f r e e b o a r d r e g i o n c o u l da l s o b e h e l p fu l . I n t h e f i n al c a se , t h e m e m b r a n e c a p a -c i t y i n t h e d e n s e c a t a l y s t b e d i s t h e s a m e a s i n t h es e c o n d c a s e , b u t C ep i s a u g m e n t e d b y a f u r t h e r 1 .2 k mo f m e m b r a n e i n t h e f re e b o a r d . T h i s a d d i t io n l e ad s t oa l m o s t n o r e d u c t i o n i n m e t h a n e c o n v e r s i o n i n t h ef r e e b o a r d , d e s p i t e t h e r e d u c e d t e m p e r a t u r e t h e r e . F o rt h e c o n d i t i o n s e x p l o r e d h e r e , m e m b r a n e s u r f a c e s i nt h e f r e e b o a r d z o n e d o n o t c o n t r i b u t e t o t h e n e t t h e r -m o d y n a m i c e q u il i b ri u m s h if t a n d t h e re f o r e c a n n o tl e a d t o m e t h a n e c o n v e r s i o n s h i g h e r t h a n a t t h e b e ds u r f a c e . T h e y d o , h o w e v e r , c a u s e a r e d u c t i o n i n t h er e v er s e r e ac t io n . T h e d i s tr i b u ti o n o f m e m b r a n e c a p a -c i ty b e t w e e n t h e b e d a n d t h e f r e e b o a r d is i m p o r t a n t i nd e s i g n i n g a f l u i d i z e d - b e d m e m b r a n e r e a c t o r , w i t h t h eo p t i m u m d i s t r i b u ti o n d e p e n d i n g o n o p e r a t i n g c o n d i -t i o n s a n d c a t a l y s t p r o p e r t i e s , a s w e l l a s o n w h a t i sd o w n s t r e a m o f th e r e f o r m i n g p ro c e s s .

5. CONCLUSIONSA c o m p r e h e n s i v e m a t h e m a t i c a l m o d e l h a s b e e nd e v e l o p e d f o r t h e f l u i d i z e d - b e d m e m b r a n e r e a c t o r

( F B M R ) s y s t e m a n d s u c c e s s fu l ly v a l i d a t e d a g a i n s tp i l o t- p l a n t d a t a f o r s te a m m e t h a n e r e f o r m i n g (S M R ) .T h e m o d e l i s u t il i ze d t o e x a m i n e t h e e f fe c t o f o p e r a t -i n g v a r i a b l e s b e y o n d t h o s e w h i c h c o u l d b e r e a l i z e de x p e r i m e n t a l l y . T h e p r e d i c t i o n s d e m o n s t r a t e t h e r o l ep l a y e d b y m e m b r a n e s e p a r a t io n i n e x c e e d in g e q u il ib -r i u m c o n v e r s i o n s a n d i n s u p p r e s s in g f r e e b o a r d r e a c -t io n s . T h e m e m b r a n e c a p a c i t y a n d t h e ir d i s t ri b u t io nb e t w e e n t h e d e n s e c a t a l y s t b e d a n d t h e f r e e b o a r dr e g i o n a r e i m p o r t a n t d e s i g n p a r a m e t e r s i n F B M Rs y s t e m s .H y d r o d y n a m i c p a ra m e t e r s h a v e o n l y a l im i t e d ef -f e c t o n t h e m o d e l p r e d i c t i o n s f o r t h e c o n d i t i o n s e x -p l o r e d b e c a u s e o f t h e d o m i n a n c e o f r e a c t io n t h e r m o -d y n a m i c s a n d s e l e ct iv e p e r m e a t i o n a s t h e t w o m a j o rp h e n o m e n a i n f lu e n c i n g c o n v e r s i o n w it h in t h e F B M Rs y s t e m . M o r e e x p e r i m e n t a l m e a s u r e m e n t s a r e r e -q u i r e d t o d i s c r i m i n a t e b e t w e e n t w o r i v a l a s s u m p t i o n se x p l o r e d i n t h i s w o r k r e g a r d i n g t h e d i s t r i b u t io n o f g a sf lo w g e n e r a t e d b y t h e i n c r e as e i n t h e n u m b e r o f m o l e sd u e t o r e a c t i o n , p ~

NOTATION P iab spec i f i c sur face a rea o f gas bub bl es , Rm2 / m 3 RR1 , RR2 , RR3a c o v e r a l l e n t r a i n m e n t d e c a y c o n s t a n t ,m - 1 R iA r e a c t o r c r o s s - s e c t i o n a l a r e a , m 2C i c o n c e n t r a t i o n o f c o m p o n e n t i, m o l / S / Cm 3

epCepldbdb,,,dbodpDDeNDieE oE zF B M RFcFs#GhHH oAH298k l , k ak 2K 1 , K 3K 2kcH,, k co , kH2k m oklqM nniNorPPl-lb,P n a , P m

1619e q u i v a l e n t p e r m e a t i o n c a p a c i t y : m e m -brane sur face / wal l t h i ckness , m2 / me q u i v a l e n t p e r m e a t i o n c a p a c i t y p e ru n i t l e n g t h , m 2 / m 2b u b b l e s i z e , a f u n c t i o n o f h e i g h t d e -f i ned b y eq . (B1) , mm a x i m u m b u b b l e d i a m e t e r , mi n it ia l b u b b l e s i z e p r o d u c e d a t t h e d i s -t r i but o r l eve l , mm e a n p a r t i c l e d i a m e t e r , mr e a c t o r d i a m e t e r , md e n o m i n a t o r o f th e k i n e ti c r a t e e x -p ress i on def i ned by eq . (A8)ef fec ti ve m ol ec ul a r d i f fus i v i t y o f com -p o n e n t i , m 2 / se n t r a i n m e n t f lu x o f s o l id s a t t h e b e ds u r fa c e , k g / m 2 se n t r a i n m e n t f lu x o f s o li d s a t d i s t a n c ez a b o v e t h e b e d s u r f ac e , k g / m 2 sf lu i d iz e d - b ed m e m b r a n e r e a c t o rm o l a r f ee d r a t e o f m e t h a n e e q u i v a -l en t , mo l / sm o l a r f l o w r a t e o f s w e e p g a s , m o l / sa c c e l e r a t i o n o f g r a v i t y , m / s 2vo l umet r i c f l ow, m3/ sv e r t i c a l c o o r d i n a t e m e a s u r e d f r o md i s t r i b u t o r p l a t e , me x p a n d e d b e d h e i g h t , ms t a t i c bed he i gh t , mh e a t o f r e a c t i o n a t 2 9 8 K , J / m o lra t e coef f i c i en t s o f r eac t i ons (A1) and( A 3 ), r e sp e c t iv e l y , m o l M P a S / k g c , t sr a t e coef f i c i en t o f r eac t i on (A2) ,m o l / k g c, t s M P ae q u i l i b r i u m c o n s t a n t f o r r e a c t i o n s( A 1 ) a n d ( A 3 ), M P a 2e q u i l i b r iu m c o n s t a n t f o r r e a c t i o n ( A 2 )d i m e n s i o n l e s sa d s o r p t i o n c o n s t a n t s f o r C H 4 , C Oa n d H 2 , r e s p e c t i v e l y , M P a - 1d i s s o c i a t i v e a d s o r p t i o n c o n s t a n t f o rH 2 0 , d i m e n s i o n l e s si n t e r p h a s e m a s s e x c h a n g e c o e f f i c i e n tf o r c o m p o n e n t i, m / sm o l e c u l a r w e i g h t o f h y d r o g e n , k g / m o lm o l a r f lo w r a t e o f c o m p o n e n t i , m o l / sn u m b e r o f or i fi c e s i n t h e g r i dr e a c t o r t o t a l p r e s s u r e , M P ap a r t i a l p r e s s u r e o f h y d r o g e n i n t h eb u b b l e , d e n s e a n d s e p a r a t i o n p h a s e ,r e s p e c t i v e l y , M P at o t a l p r e s s u r e o n t h e s e p a r a t i o n s i d e ,M P ap a r ti a l p r e s su r e o f c o m p o n e n t i , M P ai d e a l g a s c o n s t a n t , 8 . 31 4 J /m o l Kra t es o f r eac t i ons (A1) , (A2) and (A3)respec t i ve l y , mo l / kgca sr a t e o f f o r m a t i o n o f c o m p o n e n t i,mo l / kg~ , t ss t e a m - t o - c a r b o n m o l a r f e e d r a t i o , d i -m e n s i o n l e s s

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1620S M RTT D HUbUduoU~s

s t e a m m e t h a n e r e f o r m i n gt e m p e r a t u r e , Ct r a n s p o r t d i s e n g a g i n g h e i g h t , mbubbl e r i s i ng ve l oc i t y , m/ ss u p e r f i c i a l g a s v e l o c i t y t h r o u g h t h ed e n s e p h a s e , m / ssuper f i c i a l gas ve l oc i t y , m/ ss u p e r f i c i a l g a s v e l o c i t y a t m i n i m u mfl ui d i za t i on , m/ sf r e e b o a r d z o n e v e r t ic a l c o o r d i n a t e , m

Gr e e k l e t t e r s~ m f~b~)b, ~)d

I ) e

PnP s

b e d v o i d a g e a t m i n i m u m f l u i d i z a t i o nv o l u m e f r a c t io n o f b e d o c c u p i e d b yb u b b l e sv o l u m e f ra c t i o n o f b e d o c c u p i e d b ys o l id s i n b u b b l e a n d d e n s e p h a s e s , r e-spec t i ve l ye f f e c t i v e p e r m e a t i o n r a t e c o n s t a n t ,m 2 / s M P a -5h y d r o g e n d e n s it y , k g / m 3p a r t ic l e d e n s i ty , k g / m 3s o l i d s c o n c e n t r a t i o n i n t h e f r e e b o a r dz o n e , k g / m 3

S u b s c r i p t sb b u b b l e p h a s ed d e n s e p h a s ef feedf b f r e e b o a r di i n te g e r ( 1 - 5 ) d e n o t i n g g a s e o u s c o m -

p o n e n t sm m a x i m u mm f m i n i m u m f l u i d i z a t i o no a t d i s t r i b u t o r p l a t eR reac t i on s ides sepa ra t i on s i dez a t h e i g h t z i n f r e e b o a r d z o n e

R E F E R E N C E SA d r i s , A . M . ( 19 9 4) A f lu i d iz e d b e d m e m b r a n e r e a c t o rf o r s t e a m m e t h a n e r e f o r m i n g : e x p e r i m e n t a l v e r i f i -c a t i o n a n d m o d e l v a l i d a t i o n . P h . D . d i s s e r t a t i o n ,

U n i v . o f B r i ti s h C o l u m b i a , V a n c o u v e r , C a n a d a .Adr i s , A . M. , E l nasha i e , S . S . E . H . and Hughes , R .( 1 9 9 1 ) A f l u i d i z e d b e d m e m b r a n e r e a c t o r f o r t h es t e a m r e f o rm i n g o f m e t h a n e . C a n a d . J . C h e m .E n g n g 69 , 1061-1070 .Adr i s , A . M. , L i m, C . J . and Grace , J . R . (1993) . Thee ff ec t a n d i m p l i c a t io n s o f g a s v o l u m e i n c r e a s ed u e t o r e a c t i o n o n b e d e x p a n s i o n , b u b b l i n g a n do v e r a l l c o n v e r s i o n i n a f l u i d i z e d b e d r e a c t o r .A . I . C h . E . A n n u a l M e e t i n g , S t . L o u i s , N o v e m -ber 7 -12 , 1993.Adr i s , A . M. , Grace , J . R . , L i m, C . J . and El nasha i e ,S . S . E . H . (1994a) F l u i d i zed be d r e ac t i on s ys t em fo rs t e a m / h y d r o c a r b o n g a s r e f o r m i n g t o p r o d u c e h y -d rogen . U .S . Pa t en t No . 5 ,326 ,550 .Adr i s , A . M. , L i m, C . J . and Grace , J . R . (1994b) Thef l u i d i z e d b e d m e m b r a n e r e a c t o r ( F B M R ) s y s t e m :a p i l o t s c a le e x p e r i m e n t a l s t u d y . C h e m . E n g n g S c i .49 , 5833-5843.

A. M. Adris et a l .D a v i d s o n , J . F . a n d H a r r i s o n , D . ( 1 9 6 3 ) Fl u i d i se dPa r t i c l e s . C a m b r i d g e U n i v e r s i t y P r e s s , C a m b r i d g e ,U . K .Elnashaie, S. S. E. H. , Adris , A. M. , A1-Ubaid, A. S.a n d S o l im a n , M . A . (1 99 0) O n t h e n o n - m o n o t o n i cb e h a v i o u r o f m e t h a n e s t e a m r e f o r m i n g k i n e ti c s .C h e m . E n g n g S c i . 45 , 491-501 .G e l d a r t , D . ( 1 9 8 6 ) P a r t i c l e e n t r a i n m e n t a n d c a r r y -o v e r . I n Ga s Fl u i d i z a t io n Te c h n o l o g y , ed . D . Gel -da r t , Chap . 6 , pp . 123-153. Wi l ey , Ch i ches t e r , U .K.G r a c e , J . R . ( 19 8 2) F l u i d i z e d b e d h y d r o d y n a m i c s . S e c -t ion 8 .1 in H a n d b o o k o f M u l ti p h a s e S y s te m s , ed . G .H e t s r o n i , p p . 8 - 5 t o 8 - 6 4 . H e m i s p h e r e , W a s h i n g t o n .G r a c e , J . R . ( 19 8 4) G e n e r a l i z e d m o d e l s f o r i s o t h e r m a lf l u i d i zed bed r eac t o r s . In R e c e n t A d v a n c e s i n t h eE n g i n e e r in g A n a l y si s o f C h e m i c a ll y R e a c t in g S y s -t e m , e d . L . K . D o r a i s w a m y , p p . 2 3 7 - 2 5 5 . W i l e yE a s t e r n , N e w D e l h i , I n d i a .Grace , J . R . (1986) F l u i d beds as chemi ca l r eac t o r s . InGa s Fl u i d i z a t io n Te c h n o l o g y , ed . D . Gel dar t , pp .2 8 5 - 3 3 9 . W i l e y , C h i c h e s t e r , U . K .I r a n i , R . K . , K u l k a r n i , B . D . a n d D o r a i s w a m y , L . K .

( 19 8 0) A n a l y s i s o f f lu i d b e d r e a c t o r s f o r r e a c t i o ni n v o l v i n g c h a n g e i n v o l u m e . I n d . E n g n g C h e m . F u n -d a m . 1 9 , 4 2 4 - 4 2 8 .K a i , T . a n d F u r u s a k i , S . ( 19 8 7) M e t h a n a t i o n o f c a r -b o n d i o x i d e a n d f i u i d iz a t i o n q u a l i ty i n a f l u id b e dr e a c t o r - - t h e i n f lu e n c e o f d e c r e a s e i n g a s v o l u m e .C h e m . E n g n g S c i . 42 , 335-339 .Ka t su t a , H . , Fa r ra ro , R . J . an d Mc LeU an , R . B . (1979)T h e d i ff u s iv i ty o f h y d r o g e n i n p a l l a d i u m . A c t a M e -ta l l u r g i c a 27 , 1111-1114.Kun i i , D . and Levensp i e l , O . (1969) Fl u i d i z a t i o n En -g i n e e r i n g , W i l e y , N e w Y o r k , U . S. A .Kun i i , D . and Levensp i e l , O . (1991) Fl u i d i z a t i o n En -g i n e e r i n g , 2 n d E d . B u t t e r w o r t h - H e i n m a n n , M A ,U.S.A.M i wa, K . , Mor i , S . , Ka t o , T . and M uch i , I . ( 1972)B e h a v i o u r o f b u b b l e s i n g a s e o u s f l u i d iz e d b e d s . I n t .C h e m . E n g n g 12 , 187-194.M o r i , S . a n d W e n , C . Y . ( 19 7 5) E s t i m a t i o n o f b u b b l ed i amet er i n gaseous f l u i d i zed beds . A . 1 . C h . E . J . 21,1 0 9 - 1 1 5 .O rcut t , J . C . , Da v i ds on , J . F . and P i g fo rd , R . L . (1962)React i on t i me d i s t r i but i ons i n f l u i d i zed ca t a l y t i cr eac t o r s . C h e m . E n g n g P r o g . S y r u p . S e r . 85 , 1 -15 .Ros t rup -Ni e l sen , J . R . (1984) Ca t a l y t i c s t eam refo rm-ing. In C a t a l y s i s S c i e n c e a n d T e c h n o l o g y , eds. J. R.Ander son and M. Boudar t , Vo l . 4 . Sp r i nger , Ber l i n ,G e r m a n y .S i t, S . P . and Grac e , J . R . (1981) Ef fec t o f bubb l ei n t e r a c t i o n o n i n t e r p h a s e m a s s t r a n s f e r i n g a s -f l u i d ized beds . C h e m . E n g n g S c i . 36 , 327-335 .So l i m an , M . A. , Adr i s , A . M. , E l nash i e , S . S. E . H andA1-Ubai d , A . S . (1992) In t r i n s i c k i ne t i cs o fn i c k e l / c a l c i u m a l u m i n a t e c a t a l y s t f o r m e t h a n es t e a m r e f o r m i n g . J . C h e m . T e c h n o l . B i o t e c h n o l . 55,1 3 1 - 1 3 8 .T s o t s is , T . T ., C h a m p a g n i e m , A . M . , M i n e t , R . G . a n dL i u , P . K . T . ( 1 9 9 3 ) C a t a l y t i c m e m b r a n e r e a c t o r s .I n C o m p u t e r A i d e d D e s i g n o f C a t a l ys ts , C h e m i ca lI n d u s t r i e s , Vol . 51 , eds . E . Rober Becker andC a r u s o , J . P e r i r a , p p . 4 7 1 - 5 5 1 . M a r c e l D e k k e r ,N e w Y o r k , U . S . A .W e n , C . Y . a n d C h e n , L . H . ( 1 9 8 2 ) F l u i d i z e d b e df re e b o a rd p h e n o m e n a - - E n t r a i n m e n t a n d e lu tr i-a t i on . A . I . C h . E . J . 28 , 117-128 .

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Modelling of a fluidized-bed membrane reactorWilke, C. R. and Lee, C. Y. (1995) Estimation of

diffusion coefficients for gases and vapors. I n d .E n g n # C h e m . 47, 1253-1257.

Xu, J. and Froment, G. F. (1989) Methane steamreforming, methan ation and wate r-gas shift : I. In-trinsic kinetics. A . I . C h . E . J . 35, 88-96.

A P P E N D IX A : R E A C T I O N R A T E E Q U A T I O N S A N DP A R A M E T E R S

The three main reactions taking place in steam reformingare as follows:

CH4 + H20 = CO + 3H2;-AH298 = - 206.0 kJ/mol CH4 (A1)

CO +H 20 =C O 2 + H2;- AH298 = 41.0 kJ/mol CO (A2)

CH4 + 2H20 = CO2 + 4H2;--AH298 = -- 164.9 kJ/mol CH 4. (A3)

The net rate of formation of the various components areR c H , = - (RR1 + Ra3)Rn2o = -- (RR1 + RR2 + 2RR3)Rco = RR1 -- RR2

Rco2 = RR2 + RR3Rn: = 3RR1 + RR2 + 4 R R 3 (A4)

where RR1, RR2 and RR3 are the int rinsic rates for reactions(AI), (A2) and (A3), respectively. The reaction rate expres-sions developed by Xu and Froment (1989) are used toestimate the individual reaction rates. The functional formsof these expressions are

{~ocH.PHzo pO . S p \ /R R I = k l l p 2. 5 H - ~ l C O ) / D 2 N (AS)\ H( P c o P H 2 o Pco2 \ / 2R R 2 = k 2 \ P n 2 ~ ' ) / D E N (A6)I [PcuP22 p O .S p \ /H2 CO2 2R R 3 : k 3 ~ . - ~ 2 K 1 K - - - - - - 2 - ) / D E N (i7)

where[ P n ~ o \DEu = 1 + kcoPco + kn2Pu2 + ken, Pert, + kn2o - z -- -| .[ r H ~ (A8)

1621Values of the various cons tants are given in Table A1.Equilibrium constants:

K1 = exp (-2 6,830/T + 30.114)K2 = exp (4,400/T -- 4.036)K 3 = K 1 K 2

A P P E N D I X B: H Y D R O D Y N A M I C P A R A M E T E R SThe model uses the Mori and Wen (1975) correlation

which accounts for bubble growth due to coalescence toestimate bubble size as a function of height, i.e.

d b = d bm - - (d b , , - - d bo )e - '3 h / (B1)where db,, is the maximum bubble diameter at the given gasflow rate given by

d b , , = 1.64[A(Uo -- U,,I)] '4 (B2)and dbo is the initial bubble size produced a t the distributorlevel which can be estimated (Miwa et al. , 1972) as

1.38 F A ( U o - - U,s)l'4d b o = ~ L ~ j . (B3)

Here Nor is the number of orifices in the grid, with No~ = 116in the pilot-scale reactor used in the present study. The aboverelations for estimating the bubble size were developed forfreely bubbling beds, i.e. without internals. The presence ofvertical internals in the bed may significantly affect thebubble size. The sensitivity of the model pred ictions tobubble size estimations is explored in this paper.

Because of the net increase in the to tal number of molesdue to reaction, the superficial gas velocity, Uo, changes withheight. Equations (B1) and (B2) are therefore re-used at eachstep in height to recalculate db. The model uses experi-mentally measured values for the expanded bed height, H, asdiscussed in an earlier paper (Adris et a l . , 1993). Because thebubble diameter increases with height, the ratio, ab, ofbubble surface area per volume, given by the relation,ab = 6/db, decreases with height.

A mean value is used for the volume fraction of bedoccupied by solids dispersed in the bubble phase, ~b. Kuniiand Levenspiel (1969) found that 0.001eb < ~b

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1622 A. M. Adris e t a l .H e re th e bubb le r i s in g v e lo c i ty i s c a lc u la t e d by th e c o m -m o n ly us e d r e l a t io n (D av id s o n an d H ar r i s o n , 1 9 63):

U b = U o - - U m f + 0 . 7 1 1 ( g . d b ) 1 /2 . (B5)The v o lum e frac t ion occupied by the dense phase so l ids , Od ,is appro xim ated by inc lud ing a l l o f the so l ids in the c louds ,w ake s an d e m uls io n in th e d e n s e p h as e an d a s s um in g th ed e n s e -p has e v o id ag e to be c o n s tan t an d e qua l t o e m I T h us ,O~ can be es t imated (Grace , 1986) as

Od = (1 - eb)(1 -- t~I ) ' (B6)

The in te rphase mass exchange coef f ic ien t fo r component i ,k i~ , i s ca lcula ted us ing the semi-emp ir ica l equa t ion of S i t andGrace (1981):U m y [ ' 4 D i e e ,m I V b ~ 1 /2k,q = ~ + ~ - - ) (B7)

where D~e, the e f fec tive mole cular d iffusiv ity o f com pone nti in the gas mixture , i s e s t imated based on the averagecom pos i t io n of the bubble p hase and dense phase [ i. e .(C i b + C i d ) / 2 ] us ing a re la t io n g iven by W ilke and Lee (1995) .