Mathematical Modeling of Sulfide Flash Smelting Proces

7/29/2019 Mathematical Modeling of Sulfide Flash Smelting Proces

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M a t h e m a t i c a l M o d e l i n g o f S u l f i d e F l a s h S m e l t i n gP r o c e s s : P a r t I . M o d e l D e v e l o p m e n t a n dV er i fi ca tion w i th Lab or a tor y an d P i lo t P lan tM e a s u r e m e n t s f o r C h a l c o p y r i t e C o n c e n t r a t e S m e l t i n gY . B . H A H N a nd H . Y . S O H NA m a t h e m a t i c a l m o d e l h a s b e e n d e v e l o p e d t o d e s c r ib e t h e v a r i o u s p r o c e s s e s o c c u r r i n g i n a fl a s hf u r n a c e s h a ft . T h e m o d e l i n c o r p o r a t e s t u r b u l en t f l u i d d y n a m i c s , c h e m i c a l r e a c ti o n k i n e ti c s , a n dh e a t a n d m a s s t r a n sf e r . T h e k e y f e a t u r e s i n c l u d e t h e u s e o f t h e k - e t u r b u l e n c e m o d e l , i n c o r -p o r a t i n g t h e e f f e c t o f p a r t i c l e s o n th e t u r b u l e n c e , a n d t h e f o u r - f l u x m o d e l f o r r a d i a t i v e h e a tt r a n sf e r . T h e m o d e l p r e d i c t io n s w e r e c o m p a r e d w i t h m e a s u r e m e n t s o b t a i n e d i n a l a b o r a t o r y fl a s hf u r n a c e a n d a p i l o t p l a n t f l a s h f u r n a c e . G o o d a g r e e m e n t w a s o b t a i n e d b e t w e e n t h e p r e d i c t e da n d m e a s u r e d d a t a i n t e r m s o f t h e S O 2 a n d O 2 c o n c e n t r a ti o n s , t h e a m o u n t o f s u l f u r r e m a i n i n gi n t h e p a r t i c l e s , a n d t h e g a s t e m p e r a t u r e . M o d e l p r e d i c t i o n s s h o w t h a t t h e r e a c t i o n s o f s u l f i d ep a r ti c le s a r e m o s t l y c o m p l e t e d w i t h i n a b o u t 1 m o f th e b u r n e r , a n d t h e d o u b l e - e n t r y b u r n e rs y s t e m w i t h r a d i a l f e e d i n g o f t h e c o n c e n t r a t e p a r t ic l e s g i v e s b e t t e r p e r f o r m a n c e t h a n t h e s i n g l e -e n t r y b u r n e r s y s t e m . T h e m o d e l t h u s v e r i f i e d w a s u s e d t o f u r th e r p r e d i c t v a r io u s a s p e c t s o fi n d u s t r ia l f l a s h f u r n a c e o p e r a t i o n . T h e r e s u l t s i n d i c a te t h a t f r o m t h e v i e w p o i n t o f s u l f i d e o x i -d a t i o n , s m e l t i n g r a t e c a n b e s u b s t a n t i a l l y i n c r e a s e d i n m o s t e x i s t i n g i n d u s t r i a l f l a s h f u r n a c e s .

I . I N T R O D U C T I O NI N t h e f l a s h s m e l t i n g p r o c e s s , f i n e p a r t ic l e s o f d r y s u l-f i d e c o n c e n t r a t e a n d f l u x a r e i n j e c t e d i n t o t h e f u r n a c ew i t h o x y g e n - e n r i c h e d a i r , f o r m i n g a p a r t i c l e - l a d e n t u r -b u l e n t j e t . T h e c o n c e n t r a t e p a r t i c l e s a r e q u i c l ~ l y h e a t e dt o t h e t e m p e r a t u r e a t w h i c h s u l f i d e p a r t i c l e s u n d e r g o i g -n i t i o n . A s t h e p a r t i c l e s t r a v e l d o w n t h e r e a c t i o n s h a f tw i t h i n t h e t u r b u l e n t f l o w , t h e y e x c h a n g e m o m e n t u m ,m a s s , a n d e n e r g y w i t h th e s u r r o u n d i n g g a s . E v e n t u a l l y ,t h e m o l t e n p a r t i c l e s s e t t l e t o t h e f u r n a c e b o t t o m a n d a r ed i v i d e d i n t o m o l t e n s l a g a n d m a t t e l a y e r s .

I n s p i t e o f t h e i n c r e a s i n g i n d u s t r i a l s t a t u r e o f t h e p r o -ce s s , t he de s i gn o f a f l a s h s m e l t i ng f u r nace r em a i ns l a r ge l ya n a r t . T h i s i s m a i n l y d u e t o t h e d i f f i c u l t y o f u n d e r -s t a n d i n g t h e c o m p l e x i n t e r a c ti o n s o f th e i n d i v i d u a l s u b -p r o c e s s e s t a k i n g p l a c e i n a f l a s h f u m a c e . I n o r d e r t oe n h a n c e t h e s y s t e m a t i c u n d e r st a n d i n g o f t h e o v e r a ll p r o -c e s s , a r e li a b le m a t h e m a t i c a l m o d e l w o u l d b e v e r y h e l p -f u l. S u c h a m o d e l c a n a l s o b e u s e d t o p r e d i c t th e b e h a v i o ro f t h e c o m p l e x r e a c t i n g p a r t i c l e- l a d e n t u r b u l e n t g a s j e t sw i t h a m i n i m u m a m o u n t o f e x p e r i m e n t a l w o r k . I t i s o n l yv e r y r e c e n t l y t h a t a t t e n t i o n h a s b e e n d i r e c t e d t o t h em a t h e m a t i c a l m o d e l i n g o f th e f l a s h s m e l t in g p r o c e s s .T h e p r e v i o u s s t u d i e s o n m a t h e m a t i c a l m o d e l i n g o f t h ef l a s h s m e l t i n g p r o c e s s h a v e a s s u m e d t h e f l a m e t o b e a

one - d i m ens i ona l ( l - D ) s t r eam , tl,2~ a t w o - d i m e ns i on a l ( 2 - D )f ree j e t , t31 or a 2-D co nf i ne d je t . t4]T h e m e l i s a n d c o - w o r k e r s ]1,2J d e v e l o p e d a 1 - D m a t h -e m a t i c a l m o d e l t o d e s c r i b e t h e t r a n s p o r t p h e n o m e n a o c -c u r r in g i n th e f l a sh s m e l t in g p r o c e s s . T h e y a s s u m e d t h a tY . B . H A H N , f o r m e r l y G r a d u a t e S tu d e n t , D e p a r t m e n t o fM e t a l l u r g i c a l E n g i n e e r i n g , U n i v e r s i t y o f U t a h , i s R e s e a r c h E n g i n e e rw i th Lucky M eta l s Corpo ra t ion , S eou l , K orea . H .Y . S O H N , P ro fes s o r ,i s w i t h t h e D e p a r t m e n t o f M e t a l l u r g i c a l E n g i n e e r i n g , U n i v e r s i t y o fU t a h , S a l t L a k e C i t y , U T 8 4 1 1 2 - 1 1 8 3 .M a n u s c r i p t s u b m i t t e d D e c e m b e r 1 3 , 1 9 8 8.

t h e r e a c t i o n o f s u l f i d e d r o p l e t s w a s c o n t r o l l e d b y t h ec o m b i n a t i o n o f m a s s t r a n s f e r o f o x y g e n t o t h e s u r f a c e ,d i f f u s io n t h r o u g h t h e r e a c t e d l a y e r , a n d i n t e r f a c i a l c h e m -i c a l r e a c t io n . T h e e f f e c t s o f p h a s e t r a n s f o r m a t i o n a n dp a r t ic l e f r a g m e n t a t i o n o n t h e r a te o f f l a s h o x i d a t i o n o fs u l fi d e s w e r e i n c o r p o r a te d . T h e y c o n s i d e r e d o n l y 1 - Da x i a l f l o w o f th e g a s a n d p a r t i c l e s , n e g l e c t i n g t h e r a d i a le x p a n s i o n o f th e j e t a s w e l l a s t h e ra d i a l d i s p e r s i o n o fp a r t i c l e s , t2j D u e t o t h e 1 - D n a t u r e o f t h e m o d e l , t h e r a -d i a l d i s p e r s i o n o f f l u i d p r o p e r t i e s , t h e c o n t r i b u t i o n o ft u r b u l e n t d i f f u s i o n t o t h e g a s - p h a s e m o m e n t u m , t h e t u r -b u l e n c e e f f e c t o n t h e f l o w f i e l d , t h e e f f e c t o f p a r t i c l e so n t u r b u l e n c e , a n d t h e d i s p e r s i o n o f p a r t i c l e s d u e t o t u r -b u l e n t f l u c t u a t i o n s c o u l d n o t b e d e s c r i b e d .F u k u n a k a et a l . [3] c a r r i e d o u t a m o d e l i n g s t u d y o n t h ef l a sh s m e l t in g o f p y r i t e p a r t ic l e s b a s e d o n t h e p r e v i o u s l ys t u d ie d b e h a v i o r o f a f r e e g a s j e t w i t h t h e a i d o f c o r r e -l a t i o n e q u a t i o n s . T h e i r m o d e l w a s l i m i t e d o n l y t o t h ef u ll y d e v e l o p e d d o w n s t r e a m z o n e . T h e u p s t r e a m r e g i o n ,i n w h i c h p a r t i c l e s a r e i g n i t e d a n d u n d e r g o t h e r m a l d e -c o m p o s i t i o n , w a s n o t c o n s i d e r e d . T h e y f u r t h e r d i d n o tc o n s i d e r t h e o x i d a t i o n r e a c t i o n o f p y r i t e p a r t i c l e s , t h ee f f e c t o f t h e p r e s e n c e o f p a r t ic l e s o n t u r b u l e n c e , t h e d i s -p e r s i o n o f p a r t ic l e s d u e t o t u r b u l e n t f l u c t u a t i o n s , a n d t h eg r a v i t a t i o n a l f o r c e a c t i n g o n t h e p a r t i c l e .A s f o r a 2 - D m o d e l o f th e f l a s h s m e l t i n g p r o c e s s i n ac o n f i n e d f u r n a c e s h a f t , t h e o n l y e f f o r t r e p o r t e d i n t h el i t e r a t u r e i s t h a t b y R u o t t u . [ 4 ] H e c o n s i d e r e d t h a t c h a l c o -p y r i t e a n d p y r i te w e r e f i r s t t h e r m a l l y d e c o m p o s e d t o p r o -d u c e C u 2 S , F e S , a n d g a s e o u s $ 2 , a n d t h e n c o m b u s t i o nt o o k p l a c e . T o d e s c r i b e t h e tu r b u l e n c e , h e u s e d t h e o n e -e q u a t i o n m o d e l u n d e r t h e a s s u m p t i o n o f c o n s ta n t m i x i n gl e n g t h , c o n t r a r y t o t h e f a c t t h a t i t d e p e n d s s t r o n g l y o nl o c a l c o n d i ti o n s . H e d i d n o t a c c o u n t f o r t h e e f f e c t o f t h ep r e s e n c e o f p a r ti c le s o n t u r b u l e n c e . H e a l s o a s s u m e d t h a tt h e g a s p h a s e h a d t h e s a m e t e m p e r a t u r e a s t h e p a r t i c l ep h a s e . T h e s e a s s u m p t i o n s a r e n o t r e a s o n a b l e f o r a f l a s h

M ETA LLU RG ICA L TRA N S A CTIO N S B V O LU M E 21B, D ECEM BER 1990- -945


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s m e l t i n g s y s t e m i n w h i c h , i n t h e u p s t r e a m z o n e , c o l ds u l f i d e p a r t i c l e s a r e f i r s t h e a t e d t o t h e i g n i t i o n t e m p e r -a t u re b y c o n v e c t i o n f r o m t h e s u r r o u n d in g h o t g a s a n dr a d i a t i o n f r o m t h e f u r n a c e w a l l a n d t h e n p a r t i c l e s u n d e r -g o i g n i t i o n , d e c o m p o s i t i o n , a n d r e a c t i o n w i t h o x y g e n ,a d d i n g a l a r g e a m o u n t o f h e a t t o t h e g a s p h a s e a s t h e yt r a v e l a l o n g t h e f u r n a c e s h a f t . H i s a s s u m p t i o n m a y b eva l id i n t he dow ns t re a m re g ion fa r f rom the bu rne r , w he ret h e h e a t e x c h a n g e b e t w e e n t h e t w o p h a s e s i s n o t s i g n i f -i c a n t . F u r t h e r m o r e , h e n e g l e c t e d t h e s c a t t e r i n g c o n t r i -b u t i o n t o t h e c a l c u l a t i o n o f t h e r a d i a t i o n f i e ld , o n l yc o n s i d e r i n g t h e a b s o r b i n g a n d e m i t t i n g p h e n o m e n a , i ns p i t e o f t h e f a c t th a t r a d i a t i o n b y s c a t t e r in g i s a v e r yi m p o r t a n t s u b p r o c e s s i n a p a r t i c l e - l a d e n f l o w s y s t e m .H a h n a n d S o h n , I5,6] i n t h e i r p r e v i o u s w o r k a s p a r t o fa n o v e r a l l i n v e s t ig a t i o n o f f l a s h s m e l t i n g p r o c e s s e s , h a v ee x t e n s i v e l y s tu d i e d t h e f l o w p h e n o m e n a i n c o n f i n e d t u r -b u l e n t f l o w s y s t e m s w i t h o r w i t h o u t p a r t i c l e s . T h e y e x -a mine d the e f fe c t s o f boun da ry c ond i t i ons , e spe c i a l ly t hosea t t h e i n l e t , o n n u m e r i c a l r e s u l t s TM a n d i n v e s t i g a t e d t h et r a j e c to r i e s a n d d i s t r i b u t io n o f p a r t i c le s i n a f l a s h f u r n a c es h a f t . [ 6 ] I n t h e l a t t e r , t h e y t e s t e d t w o p o s s i b l e m o d e s o ffe e d ing the d i s t r i bu t ion (o r p r ima ry ) s t r ea m: the a x i a l f l owo f th i s s t r e a m w i t h t h e z e r o r a d i a l - v e l o c i t y c o m p o n e n ta n d t h e r a d i al f l o w w i t h t h e z e r o a x i a l - v e l o c i t y c o m p o -n e n t a t t h e i n l e t . ( T h e f l o w c o n f i g u r a t i o n s f o r t h e i n l e ts t r e a m s w i l l b e i l l u s tr a t e d l a t e r i n S e c t i o n V . ) T h e y c o n -c l u d e d t h a t t h e r a d i al f e e d i n g m o d e o f th e d i s t r i b u t io ns t r e a m p roduc e d more un i fo rm d i spe r s ion o f pa r t i c l e s t ha nt h e a x i a l f e e d i n g m o d e .T h e o v e r a l l g o a l o f th i s r e s e a r c h w a s t o d e v e l o p ac 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 f o r th e p r o c e s s e st a k ing p l a c e in t he f l a sh fu rna c e sha f t , i nc o rpo ra t ing mos to f t h e i m p o r t a n t s u b p r o c e s s e s b a s e d o n f i r s t p r i n c i p l e s .T h e f l as h s m e l t in g o f c h a l c o p y r i t e c o n c e n t r a te w a s u s e da s a n e x a m p l e . I n o r d e r t o p r e d i c t t h e o v e r a l l p h e n o m e n ao c c u r r i n g i n t h e f l a s h s m e l t i n g f u r n a c e , t h e c o m p r e h e n -s i v e m o d e l m u s t c o m b i n e t h e t u r b u l e n t f l u i d d y n a m i c so f a p a r t i c l e - la d e n g a s j e t , c h e m i c a l k i n e t i c s , a n d t h et r a n s f e r o f h e a t a n d m a s s .I n t h i s s t u d y , t h e f o l l o w i n g a s p e c t s w e r e i n c l u d e d :( 1 ) t h e t w o - e q u a t i o n (k-e) t u r b u l e n c e m o d e l t h a t a c -c o u n t s f o r t h e d e p e n d e n c y o f t h e m i x i n g l e n g t h o n t h el o c a l c o n d i t i o n s i n a f l o w s y s t e m ;( 2 ) t h e e f f e c t o f p a r t i c l e s o n t u r b u l e n c e ;( 3 ) t h e d i s p e r s i o n o f p a r t i c l e s d u e t o t h e t u r b u l e n tf luc tua t ions ; a nd( 4 ) t h e f o u r - f l u x m o d e l f o r r a d i a ti v e h e a t t r a n s f e r c o m -b i n i n g t h e a b s o r b i n g , e m i t t i n g , a n d a n i s o t r o p i c s c a t t e r -i n g p h e n o m e n a .

I I. M O D E L E Q U A T I O N ST h e f l a s h f u r n a c e s h a f t c a n b e s c h e m a t i c a l l y r e p r e -s e n t e d , a s s h o w n i n F i g u r e 1 . T h e p r i m a r y p a r t i c l e - la d e ng a s s t r e am w i t h o r w i t h o u t a n o x y g e n - e n r i c h e d s e c o n d -a r y ( o r p r o c e s s ) a i r s t r e a m e n t e r s t h e s y s t e m t h r o u g h t h eb u r n e r n o z z l e a n d e x p a n d s r a d i a ll y . T h e m o d e l i n g e q u a -t i o n s t o d e s c r i b e t h e o v e r a l l p h e n o m e n a o f a r e a c t i n gp a r t i c l e - l a d e n t u r b u l e n t g a s j e t i n s u c h a c o n f i n e d s y s t e mo f t h e f l as h s m e l t i n g f u r n a c e c a n b e e x p r e s s e d b y t h ee q u a t i o ns o f c o n t i n u i ty , m o m e n t u m , a n d e n e r g y f o r e a c hp h a s e .

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A. Gas-Phase EquationsT h e g a s p h a s e i s v i e w e d f r o m t h e E u l e r i a n f r a m e w o r k .T h e c o n t i n u i t y a n d m o m e n t u m e q u a t i o n s , c o m b i n e d w i t ht h e e f f e c t o f t h e p r e s e n c e o f t h e r e a c t in g p a r t i c l e s , c a n ,r e sp e c t iv e ly , be e xp re ss e d a s 17-~~

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vO t ( p V ) + V . ( p V V ) = - V p - V . ~ + p g + S p + V S ~"[2 ]

w h e r e t h e b o l d c h a r a c t e r s a r e v e c t o r s a n d t h e d o u b l eo v e r b a r r e p r e s en t s a s e c o n d - o r d e r t e n s o r .I n E q . [ 1 ] , t h e f ir s t t w o t e r m s r e p r e s e n t t h e ra t e o fm a s s c h a n g e a n d t h e n e t r a te o f m a s s e f f l u x p e r u n i tv o l u m e . T h e t e r m S~" s h o w s t h e n e t r a t e o f m a s s a d d i t i o n9 4 6 - - V O L U M E 2 1 B , D E C E M B E R 1 9 90 M E T A L L U R G I C A L T R A N S A C T IO N S B


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t o t h e g a s p h a s e p e r u n i t v o l u m e d u e t o t h e r e a c t i o n o fs o l i d p a r t i c l e s . I n E q . [ 2 ], t h e t w o t e r m s o n t h e l e f t - h a n ds i d e a re t h e ra t e o f m o m e n t u m i n c r e a s e a n d t h e ra t e o fm o m e n t u m g a in b y c o n v e c t i o n p e r u n it v o l u m e , r e s p e c -t i v e l y ; o n t h e r ig h t - h a n d s i d e , t h e f i r s t t h r e e t e r m s r e p -r e s e n t t h e p r e s s u r e f o r c e o n f l u i d e l e m e n t s , t h e r a t e o fm o m e n t u m g a i n b y v i s c o u s t r a n s f e r , a n d t h e g r a v i t a -t i o n a l f o rc e a c t i n g o n t h e f l u i d p e r u n i t v o l u m e , r e s p e c -t i v e l y . T h e f o u r t h a n d l a s t t e r m s r e p r e s e n t m o m e n t u ms o u r c e s t o t h e g a s p h a s e d u e t o t h e p r e s e n c e o f p a r ti c l esa n d t h e a d d i t i o n o f m a s s t o t h e g a s p h a s e p e r u n i t v o l -u m e , r e s p e c t iv e l y . T h e l a s t t e r m b e c o m e s z e r o f o r a n o n -r e a c ti n g p a r ti c l e- l a d en g a s j e t. T h e m e t h o d f o r c o m p u t i n gt h e s e s o u r c e t e r m s i s d e s c r i b e d i n S e c t i o n I V .I n o r d e r t o r e d u c e t h e a b o v e e q u a t io n s t o s i m p l e r f o r m s ,t h e f o l l o w i n g a s s u m p t i o n s w e r e m a d e :( 1 ) t h e s y s t e m i s a t s te a d y s t a t e a n d a x i s y m m e t r i c in c y -l i n d r i c a l c o o r d i n a t e s ;( 2 ) b o d y f o r c e s s u c h a s t h e g r a v i t y f o r c e c a n b e n e g l e c t e d ;( 3 ) c o n t r i b u t io n o f t h e g a s - p h a s e m o m e n t u m d u e t o t h ed i l a ti o n o f g a s , w h i c h d e s c r i b e s th e v o l u m e c h a n g e o f af l u id e l e m e n t d u e t o e x p a n s i o n , c a n b e n e g l e c t e d ; a n d( 4 ) g a s e o u s p r o p e r t i e s a r e a t i n s t a n t a n e o u s l o c a le q u i l i b r i u m .

B a s e d o n t h e a b o v e a s s u m p t i o n s f o r t h e g as p h a s e , t h et i m e - a v e r a g e d e q u a t io n s f o r th e c o n s e r v a t i o n o f f l o wp r o p e r t i e s a r e e x p r e s s e d i n t h e f o l l o w i n g g e n e r a l f o r m :

O x ( ~ a 4 0 + r - O r -- (r ~ g 4 ~) - - - O x r e

1 0 r F e = S ~ [3 ]r 0 rw h e r e 4 ~ r e p r e s e n t s a d e p e n d e n t v a r i a b l e a n d S , i s t h e" s o u r c e t e r m " w h i c h i n c l u d e s a l l o t h e r t e r m s i n th e g o v -e m i n g e q u a t i o n s n o t e m b o d i e d i n t h e f i r s t f o u r t e r m s .T h e t e r m F e d e n o te s a n e f f e c t i v e t ra n s p o r t e x c h a n g ec o e f f i c i e n t f o r i n d i v i d u a l v a r i a b l e s i n a tu r b u l e n t f l o w .T h e c o r r e s p o n d i n g f o r m s o f 4 ~ , F e , a n d S ~ a r e l i s t e d i nT a b l e I .To q u a n t i t a t i v e l y d e s c r i b e t u r b u l e n c e , t h e t wo - e q u a t i o n

( k - e ) m o d e l [l~ w a s u s e d . T h e m o d e l i n v o l v e s t h es o l u t i o n s o f th e e q u a t i o n s f o r t u r b u l e n t k i n e t i c e n e r g y ( k )a n d i t s d i s s i p a t i o n r a t e ( e ) ( T a b l e I ) a n d r e l a t e s t h e t u r -b u l e n t k i n e m a t i c v i s c o s i t y t o k a n d e a s f o l l o w s :

' = C ~ k 2 / e [4 ]~ gT h e v a l u e s o f t u r b u l en c e c o n s t a n ts u s e d i n th i s w o r k a r eg i v e n i n T a b l e I I .T h e p r e s e n c e o f s o l i d o r m o l t e n p a r t i c l e s a f f e c t s t h et u r b u l e n t f l o w f i e l d . T o a c c o u n t f o r t h i s e f f e c t , th e f o l -l o w i n g s e m i e m p i r i c a l c o r r e l a t i o n p r o p o s e d b y M e l v i l l ea n d B r a y ~31 w a s u s e d t h r o u g h o u t :

t t( V g ) p a r t ic l e s = ( / " g ) n o p a r ti c le s [ + (Pbp]lpg )] -0"5 [ 5 ]w h e r e Pbp r e p r e s e n t s t h e m e a n p a r t i c l e b u l k d e n s i t y ( i . e . ,m a s s o f p a r ti c le s p e r u n i t v o l u m e o f t h e j e t) . T h e e q u a -t io n s u g g e s t s t h a t t h e a m o u n t o f g a s - p h a s e t u r b u l e n c ed e c r e a s e s a s t h e p a r t i c l e n u m b e r d e n s i t y i n c r e a s e s .

O t h e r d e t a i ls o f t h e g a s - p h a s e e q u a t i o n s c a n b e f o u n di n R e f e r e n c e s 5 a n d 6 .B . P a r t i c l e - P h a s e E q u a t i o n s

T h e p a r t i c l e p h a s e i s d e s c r i b e d u s i n g t h e L a g r a n g i a nf r a m e w o r k u n d e r t h e f o l lo w i n g a s s u m p t i o n s :( 1 ) t h e in t e r a c t i o n s b e t w e e n p a r t i c l e s a r e n e g l i g i b l e , b e -c a u s e t h e p a r t i c l e c o n c e n t r a t i o n i n t h e f l a s h s m e l t i n g f u r -n a c e i s v e r y l o w ;( 2 ) t h e p r e s s u r e g r a d i e n t , v i r t u a l m a s s e f f e c t , a n d B a s s e tf o r c e a re n e g l ig i b l e c o m p a r e d w i t h t h e a e r o d y n a m i c d r a gfo rc e; ~8,14] an d( 3 ) t h e r e a c t i o n r a t e o f p a r t i c l e s w i t h g a s e o u s r e a c t a n t i ss l o w c o m p a r e d t o t h e t u r b u le n c e s c a le b u t f a st c o m p a r e dw i t h t h e m e a n g a s v e l o c i t y . T h i s a s s u m p t i o n a l l o w s t h ep a r t i c l e p r o p e r t i e s t o b e c a l c u l a t e d f r o m t h e m e a n g a sp r o p e r t i e s i n s t e a d o f f l u c t u a t i n g g a s p r o p e r t i e s , t8,9~

T a b l e I I . T u r b u l e n c e M o d e l C o n s t a n t sCk~ C1 C 2 o" or

0 .09 1 .44 1 .92 0 .9 1 .22

T a b l e I . C o n s e r v a t i o n E q u a t i o n s C o r r e s p o n d i n g t o E q u a t i o n [1 ]Equat ion of ~b re S 4,Cont inui ty 1 0 SpAx ial mo me ntu m a ~[~eRa d i a l m o m e n t u m ~ /x eKine t i c energy k ]sDiss ipa t ion ra te e ] s e / / O ' eMass f rac t ion of gas spec ies j r~ j [sEn t h a l p y h g [s

2 ( O V I 2 ( ~ ) 2 ] ( 0 1 2 O ~ t 2 ~ a n d l . t e = t Z t ~ tW oroO + _ _ _ - , - + + +~ L L k O x / \ O r ~ ~ r O x / J

O pOX OX r Oro ( o ) ( O jrP + - - I~ e + - - - - r lX e - - 2 1 ~ e g / r 2 + S ; + g S'~Or Ox r OrG - [Je

C l G e / k - C 3 p e i / k+ m_ ( s p ) ja r g + a ~ J c f f ~ - a hOx Or

METALLURGICALTRANSACTIONSB VOLUME 21B, DECEMBER 1990 -- 947


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T h e c o n s e r v a t i o n e q u a t i o n s f o r t h e p a r t i c l e p h a s e a r eg ive n in Ta b le H I . The de t a i l e d de sc r ip t ions c a n be foundi n R e f e r e n c e 6 . I t is n o t e d t h a t s i n c e t h e E u l e r i a n p a r t i c l ev e l o c i t y fi e l d c a n n o t b e o b t a i n e d f r o m t h e L a g r a n g i a np a r t i c l e - p h a s e i n f o r m a t i o n , t h e p a r t i c l e n u m b e r d e n s i t yi s o n l y a p p r o x i m a t e d u s i n g t h e g a s - p h a s e E u l e r i a n v e -l o c i t y f i e l d .I n o r d e r t o a c c o u n t f o r t h e d i s p e r s i o n o f p a r t i c l e s d u et o t h e t u r b u l e n t f l u c t u a t i o n s , t h e p a r t i c l e v e l o c i t y i s b r o -k e n d o w n i n t o a c o n v e c t i v e a n d a t u r b u l e n t d i f f u s i v eco m po ne nt , [9,15-17] as fo l lo ws :

V p : V p c "~- V p d [6 ]w h e r e s u b s c r i p t s p c a n d p d d e n o t e t h e c o n v e c t i v e a n dd i f f u s i v e v e l o ci t ie s , r e s p e c t i v e l y . T h e c o n v e c t i v e v e l o c -i t y o f t he pa r t i c le c a n be de f ine d a s t he ve loc i ty t ha t w ou ldr e s u l t i n t h e a b s e n c e o f t u r b u l e n c e o r t h a t b a s e d o n t h em e a n g a s v e l o c it y . T h i s v e l o c i t y c an b e o b t a i n e d f r o mE q . [ I II - 1 ] in T a b l e I I I a l o n g a t r a j e c t o r y b y n u m e r i c a li n t e g r a t i o n . T h e t u r b u l e n t d i f f u s i v e v e l o c i t y a c c o u n t i n gf o r t h e t u r b u le n t f l u ct u a t io n s c a n b e m o d e l e d b y a s s u m -i n g t h e t u r b u l e n t d i f f u s i o n o f p a r ti c l e s t o b e p r o p o r t i o n a lto t he g ra d ie n t o f me a n pa r t i c l e nu m be r de n s i ty , E9,15-17]as sh ow n in Eq . (111-5). In Eq . ( I I I - 6) , Up and o-~ a re thet u r b u l e n t p a rt i c le e d d y v i s c o s i ty a n d t h e S c h m i d t n u m b e rfo r pa r ti c l e s , r e spe c t ive ly . Fo r t he p re se n t w ork , t he va lueo f 0 . 3 5 w a s u s e d f o r t r y , a s r e c o m m e n d e d i n R e f e r e n c e 9 .E q u a t i o n ( 11 1- 7) f o r t h e t u r b u l e n t k i n e m a t i c v i s c o s i t y o ft h e p a r t i c l e i s a c o r r e l a t i o n b y M e l v i l l e a n d B r a y . u31O n t h e r i g h t - h a n d s i d e o f t h e p a r t i c l e - p h a s e e n e r g ye q u a t i o n ( E q . ( I I I - 8 ) ) , t h e f i r s t t e r m r e p r e s e n t s t h e h e a to f r e a c t i o n o f s u l f i d e p a r ti c l e s , a n d t h e s e c o n d t e r m i st h e r a d i a t i o n h e a t t r a n s f e r b e t w e e n t h e p a r t i c l e s a n d t h e

s u r r o u n d i n g s . T h e r a d i a t i o n c o n t r i b u t i o n , q w , w h i c h i sa v e r y i m p o r t a n t m o d e o f h e a t t r a n s f e r , i s d i s c u s s e d i nd e t a i l s e p a r a t e l y i n t h e a c c o m p a n y i n g P a r t I I u81 b e c a u s eo f t h e c o n s i d e r a b l e c o m p l e x i t y i n v o l v e d i n q u a n t i ta t i v e l yd e s c r i b i n g i t . T h e t h i r d t e r m s h o w s t h e h e a t l o s s t o t h eg a s p h a s e b y c o n v e c t i o n , t h e f o u r t h t e r m i s t h e h e a t l o s sd u e t o t h e v o l a t i l iz a t i o n o f m e t a l s p e c i e s , a n d t h e l a s tt e r m r e p r e s e n t s t h e h e a t l o s s d u e t o t h e t h e r m a l d e c o m -p o s i t i o n o r m e l t i n g o f t h e p a r t i c l e.Fo r e a c h pa r t i c l e s i z e , t he he a t l o ss due to t he ga s -pha sec o n v e c t i o n i s o b t a i n e d b y t h e f o l l o w i n g e q u a t i o n :

Q p = 7 r d j k g ( 2 + 0 . 6 5 R e ) / 2 P r l / 3 ) (Tpj - Tg) [7 ]T h e h e a t l o s s d u e t o v o l a t i l i z a t io n o f c o p p e r s p e c i e si s c a l c u l a t e d b y

H v = E rv ihv i [8 ]iw h e r e s u b s c r i p t i d e n o t e s t h e v o l a t i l e c o p p e r s p e c i e s , r v ii s t h e v o l a t i l iz a t i o n r a te o f s p e c i e s i , a n d h v / r e p r e s e n t st h e e n t h a l p y r e q u i r e d f o r v o l a t i l i z a t i o n . T o a c c o u n t f o rthe he a t c onsumpt ion by me l t i ng o f t he pa r t i c l e , R ic ha rds 'l a w w a s u s e d t o o b t a i n t h e e n t h a l p y o f f u s i o n :

/~/f = 9 . 2 4 ( n u m b e r o f a to m s ) ( T m p / M p ) [ J / k g ] [ 9 ]w h e r e T , ,p a n d M p a r e t h e m e l t i n g p o i n t a n d t h e m o l e c -u l a r w e i g h t o f t h e p a r t i c l e , r e s p e c t i v e l y . O n c e t h e m e l t -i n g t e m p e r a t u r e i s r e a c h e d , t h e h e a t a v a i l a b l e to m e l t t h ep a r t i c l e i s o b t a i n e d b y t h e f o l l o w i n g r e l a t i o n s h i p :l~ Im = I~ Ir "Jr" qrp - - Q p - l~ Iv [ 1 0 ]

B e f o r e a n d a f t e r th e m e l t i n g i s r e a c h e d , / 5 /m i s s e t t o b ee q u a l t o z e r o .Ta bl e I I L Pa r t i c l e - Pha s e Equ a t i o ns

Mome n tum:

wherem p - - - -d V p 1d t 2 C o P s A n I V 8 - V p l ( V , - V . ) + m p g

24CD ~ee(1 + 0 . 1 5 R e 0 "6 87 )R e = pg IVg - Vpl dp/p .g

Particle number density (j-th size particle):3 ( f f r i j ) + ( r Y f f ,) - - D p ~ r D e - ~ r ) 0Ox r Or 3x \ Ox / r Or

Dispersion of particles:w he re

Energy:

V p a ~ j = D ~ V ~ j

o t p = t t12p O'pU p = l / J [ 1 + ( % l t t ) ]

df i t ( m p h p ) = I S l r + q r p - - Q p - - I S lv - - 15 1m

[III-11

[III-2][111-3]

[111-4]

[III-51

[1II-6][III-7]

[III-8]

9 4 8 - - V O L U M E 2 1 B , D E C E M B E R 1 9 90 M E T A L L U R G I C A L T R A NS A CT IO N S B


5/14

C . R e a c t i o n K i n e t i c s o f C h a l c o p y r i t e P a r t i c l e sI n o r d e r t o d e v e l o p a c o m p r e h e n s i v e m a t h e m a t i c a lm o d e l o f th e f l a s h s m e l t in g p r o c e s s , c h e m i c a l k i n e t ic s

m u s t b e i n c o r p o r a t e d w i t h th e f l u i d d y n a m i c s o f t h et w o - p h a s e t u r b u l e n t f l o w a n d t h e t r a n s f e r o f h e a t a n dm a s s . T h e r e a c t i o n o f c h a l c o p y r i t e p a rt i cl e s u n d e r f l a s hs m e l t i n g c o n d i t i o n s w a s s t u d i e d b y C h a u b a l a n dS o h n . [ 19 "2 0'2 1] T h i s s e c t i o n s u m m a r i z e s t h e i r r e s u l t s o n t h ek i n e t i c s o f o x i d a t i o n o f c h a l c o p y r i t e p a r t i c l e s .

1 . C h e m i c a l r e a c t io n sC o p p e r c o n c e n t r a t e c h a r g e d t o t h e f l a s h f u r n a c e g e n -e r a l ly c o n t a in s t h r e e m a j o r p h a s e s o f c h a l c o p y r i te , p y -r i te , a n d s i l i c a . I n th e f u r n a c e s h a f t , c h a l c o p y r i t e a n dp y r i t e w i l l u n d e r g o o x i d a t i o n .W h e n t h e c o n c e n t r a t e p a r t i c l e i s i n s o l i d s t a t e a n d b e l o w8 7 3 K , t h e f o l l o w i n g r e a c t i o n s a r e a s s u m e d t o o c c u r :

15Cu Fe S2 ( s ) + 3 - O2 ( g ) - -> Cu SO 4 ( s )1+ ~ F e 2 0 3 ( s ) + S O 2 ( g ) [ 1 1 ]

3 1FeSx ( s ) + (x + ~)O2 (g) - -* 5Fe203 ( s ) + xS O 2 (g)[12]

A t t e m p e r a t u re s b e t w e e n 8 7 3 a n d 1 1 53 K , w h i c h i st h e r e p o r t e d m e l t i n g p o i n t o f c h a l c o p y r i t e , t22~ t h e o x i -d a t i o n o f s o l i d p a r t i c l e s p r o c e e d s p r i m a r i l y t h r o u g h t h ed e c o m p o s i t i o n o f s u l f id e s . T h e o v e r a l l r e a c t i o n s o f s o l i dp a r t i c l e s i n t h i s t e m p e r a t u r e r a n g e a r e t h e n e x p r e s s e d a s

1 1Cu FeS 2 (s ) + ~O2 (g) ~ ~Cu2S ( s ) + FeS ( s ) + 1 5 0 2 (g )[131

FeSx ( s ) + (x - 1)O2 (g) - --> Fe S ( s ) + (x - 1)SO2 (g)[141

O n c e t h e p a r t ic l e s b e c o m e m o l t e n , t h e y a r e c o n s i d e r e dt o b e m a d e u p o f C u2 S a n d F e S . T h e o v e r a l l r e a c t i o n o ft h e m o l t e n p a r t i c l e c a n b e e x p r e s s e d a s3Fe S (1) + 50 2 (g ) - --> Fe 30 4 ( s , 1) + 3S O 2 (g) [151

Cu2 S (1) + 02 (g) -' -'>2 C u (1 ) + SO2 ( g ) [ 1 6 ]A l t h o u g h s o m e F e S m a y r e a c t w i t h s il ic a in t h e p a r t ic l et o p r o d u c e f a y a l i t e , th e m a j o r o x i d a t i o n p r o d u c t i s m a g -n e t i t e . T h e p r o d u c e d m a g n e t i t e a n d t h e i n i t i a l s i l i c a i nt h e p a r t i c l e a r e a s s u m e d t o m e l t a t 1 8 7 3 K, wh i c h i s c l o s et o t h e m e l t i n g p o i n t o f m a g n e t i t e a n d s i l i c a , t19,z21 Re -

a c t i o n [ 1 6 ] is a s s u m e d t o o c c u r o n l y a f t e r a ll F e S i sc o n s u m e d f r o m a g i v e n p a r t i c l e .2 . R e a c t i o n k i n e t i c sT h e s u l f u r r e m o v a l r a t e i s r e l a t e d t o t h e o x y g e n c o n -s u m p t i o n b y s t o i c h i o m e t r i c c o e f f i c i e n t s i n o x i d a t i o n r e -

a c t io n s . B e l o w t h e m e l t i n g p o i n t o f c o n c e n t r a t e p a r t i c le s ,t h e f o l l o w i n g e q u a t i o n w a s s u g g e s t e d f o r th e r a t e o f o x -y g e n c o n s u m p t i o n : t19,2~/dX , \

N o 2 . , ~ T t ) = No2. ,ko ex p ( - E / R T p ) f , ( p o 2 ) f 2 ( X ) f 3 ( d p )[17]

w h e r e i i s e i t h e r c h a l c o p y r i t e o r p y r i t e a n d N o 2 . i i s t h em o l e s o f o x y g e n r e q u i r e d t o r e a c t c o m p l e t e l y w i t h e i t h e rs u l f i d e i n t h e p a r t i c l e . T h e t e r m X r e f e r s t o th e o v e r a l lf r a c ti o n a l d e g r e e o f s u f f u r r e m o v e d a t a c e r ta i n t i m e . T h ev a l u e s o f p a r a m e t e r s i n E q . [1 7 ] w e r e d e t e r m i n e d b yC h a u b a l a n d S o h n [19,2~ a n d a r e g i v e n i n T a b l e I V . I n -f o r m a t i o n o n t h e o x i d a t i o n o f p y r i t e i s n o t a v a i l a b le , b u ti t h a s b e e n s u g g e s t e d t h a t t h e p y r i t e o x i d a t i o n b e a s -s u m e d t o o c c u r a t t h e s a m e r a t e a s th a t o f c h a l c o p y r i t eox ida t ion , t20j

O n c e t h e p a rt i c le s b e c o m e m o l t e n , t h e r a te o f o x i d a -t i o n o f s u l f u r i s c o n s i d e r e d t o b e e q u a l t o t h e r a t e o fe x t e r n a l m a s s t r a n s f e r o f o x y g e n f r o m t h e b u l k . A s s u m -i n g m a s s t r a n s f e r c o n tr o l , t h e r e a c t i o n r a t e o f t h e m o l t e np a r t i c l e c a n b e o b t a i n e d b y

d XN ~ -~ t = km C o~ A pf s [181w h e r e k m a n d f i a r e , r e s p e c t i v e l y , t h e m a s s t r a n s f e r c o e f -f i c ie n t o f o x y g e n a n d t h e f r a c t i o n o f th e e x t e r n a l s u r f a c ea r e a o c c u p i e d b y t h e s u l f i d e s, w h i c h a c c o u n t s f o r th ef a c t t h a t t h e p r o d u c e d o x i d e p h a s e s r e d u c e t h e a v a i l a b l es u r f a c e a r e a f o r o x y g e n t r a n s f e r f r o m t h e b u l k . T h e v a l u eo f f i i s a s s u m e d t o b e t h e s a m e a s t h e v o l u m e f r a c t i o no c c u p i e d b y t h e s u l f i d e s . T h e a b o v e e q u a t i o n i m p l i e s t h a tt h e r e a c t i o n b e t w e e n t h e o x i d e a n d t h e m o l t e n , s u l f i d e si n t h e p a r t i c l e i s n e g l i g i b l e c o m p a r e d t o t h e r e a c t i o n o fs u l f i d e s w i t h o x y g e n g a s .

3 . V o l a t i l iz a t i o n o f c o p p e rT h e c o p p e r l o s s b y v o l a t i l i z a t i o n m a y b e s u b s t a n t i a la t t h e c o n d i ti o n s o f h i g h o x y g e n c o n t e n t a n d h i g h t e m -p e r a t u r e . J o r g e n s e n ~23~ s u g g e s t e d t h a t c o p p e r v o l a t i l i z a -t i o n c o u l d p l a y a n i m p o r t a n t r o l e i n c o n t r o l l i n g t h e p a r t i c l e

T a b l e I V . R e a c t i o n R a t e P a r a m e t e r s t19~

ko E f i (Po2 ) fz(X ) f3 (dp)1 . Chalcopyr i t e

Tp < 754 K 2 .4 l08 215 Po2 0 .0 7/ [e xp (X/0 .0 7) ] 1/d2p7 5 4 < Tp < 8 7 3 K 0 . 0 2 6 7 1 . 4 Po2 0 . 0 7 / [ e x p ( X/ 0 . 0 7 ) ] l i d 2Sul fur vapor iza t ion: 2 .72 109 2 0 8 - - (1 - - X ) 2 1 / d ~

2. Pyri teSul fur vapor iza t ion: 4 .5 10 l~ 279 - - (1 - X ) 2 /3 i / d 2

Note: ko in cm2/(s-kPa), Po2 in kPa, E in kJ/mol, and dp in cm.M E T A L L U R G IC A L T R A N S A C T IO N S B V O L U M E 2 1 B , D E C E M B E R 1 9 9 0 - -9 4 9


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t e m p e r a t u r e . C h a u b a l a n d S o h n [19,2~ a l s o i n c o r p o r a t e dt h e c o p p e r l o s s b y v o l a t i l i z a t i o n u s i n g t h e f o l l o w i n ge q u a t i o n :

d m ( Pc , , e -- km,cu Pcu,b) A p f s [19]d t R TI n th e a b o v e e q u a t i o n , t h e p a r t ia l p r e s s u r e a t t h e p a r t ic l es u r f a c e i s a s s u m e d t o b e e q u a l t o t h e e q u i l i b r i u m p a r t i a lp r e s s u r e , w h i c h i s o b t a i n e d b y m u l t i p l y i n g t h e v a p o rp r e s s u r e v a l u e s g i v e n i n T a b l e V b y t h e a t o m i c f r a c t i o no f c o p p e r i n t h e m o l t e n s u l f i d e d r o p l e t s .D . P h y s i c a l P r o p e r t ie s

T h i s s e c t i o n s u m m a r i z e s t h e p h y s i c a l p ro p e r t i e s n e c -e s s a r y f o r s o l v in g t h e g a s - p h a s e a n d p a r t i c l e -p h a s e m o d -e l i n g e q u a t i o n s . Th e p r o p o s e d e q u a t i o n s I8,9,241 f o r t h e s ep r o p e r t i e s a r e s u m m a r i z e d i n T a b l e V I . T h e m a s s t r a n s -f e r c o e f f i c i e n t ( k i n ) i s c a l c u l a t e d f r o m t h e f o l l o w i n g e m -p i r i c a l c o r r e l a t i o n f o r t h e S h e r w o o d n u m b e r : t9,24~

S h = 2 + 0 . 6 R e : / 2 S c 1/3 [20]w h e r e " S c " r e p r e se n t s th e S c h m i d t n u m b e r f o r g a s sp e c i e s.

S i n c e c h a n g e s i n p a r t i c l e s i z e a r e e x p e r i m e n t a l l y o b -se rve d, ~2'23,25,261 the pa r t i c l e s i ze i s a l lo w ed to ch an ge l in-e a r l y w i t h t h e e x t e n t o f o v e r a l l c o n v e r s i o n o f s u l f id e , a sf o l l o w s :

dj = (1 - X ) d ;o + d f X [ 2 1 ]

Tab le V. Va por Pressur e o f Copp er Spec ies E19'~1Va p o r P r e s su r e ( N / m 2)

Reac t ion Spec ies 1500 K 1800 K 2000 KCu (1) --~ Cu (g) Cu (g) 0.973 56.7 435 .7

w h e r e d jo a n d d : a r e t h e i n i t i a l a n d t h e f i n a l p a r t i c l e s i z e s ,r e s p e c t i v e l y . T h e r e i s , a t p r e s e n t , c o n s i d e r a b l e u n c e r -t a i n t y a b o u t h o w t h e p a r t i c l e s i z e v a r i e s d u r i n g t h e r e -a c t i o n . I n t h i s wo r k , t h e e x p e r i m e n t a l l y d e t e r m i n e d v a l u eo f 2 5 / x m t231 w a s u s e d f o r d : . T h e e f f e c t o f c h a n g e s i nt h e p a r t i c le s i z e o n v a r i o u s a s p e c t s o f f l a s h s m e l t i n g i sc u r r e n t l y b e i n g i n v e s t i g a t e d i n t h i s l a b o r a t o r y .

I I I . B O U N D A R Y C O N D I T I O N SA c o m p l e t e s p e c i fi c a ti o n o f b o u n d a r y c o n d i ti o n s i sn e c e s s a r y f o r s o l v i n g t h e g o v e r n i n g e q u a t i o n s . T h e d e -

t a i le d d e s c r i p t i o n s o f b o u n d a r y c o n d i t i o n s f o r f l u i d p r o p -e r ti e s , e x c e p t t h o s e f o r g a s - p h a s e e n t h a l p y , c a n b e f o u n di n R e f e r e n c e s 5 a n d 6 .I n t h e i n l e t , t h e g a s - p h a s e e n t h a l p y i s s p e c i f i e d b y i n l e tt e m p e r a t u r e . A t t h e c en t e r li n e , t h e s y m m e t r y c o n d i ti o nw a s u s e d ; i . e . , O h ~ O r = O .F o r a n o n a d i a b a t i c r e a c t o r , t h e h e a t l o s s e s b y c o n v e c -t i o n a n d c o n d u c t i o n t h r o u g h t h e w a l l m u s t b e c o n s i d -e r e d . T h e f o l l o w i n g l o g a r i t h m i c w a l l f u n c t i o n s , d e r i v e di n th e s e m i l a m i n a r r e g io n n e a r t h e w a l l b y L a u n d e r a n dS p a l d i n g t m a n d K h a l i l et a l . , I271 w e r e u s e d f o r th e w a l lb o u n d a r y c o n d i t i o n o f t he g a s - p h a s e e n e r g y:S i d e w a l l s :

q w , , = - ( T w - T ) C p , m i x f i C ~ / 4 k 1 /2

"-- { ~ - ~ l n [ E C ~ / 4 k ~ / 2 y , f ~ / t x ][ ] [ . ] ,: 4 }+ 9. 24 o'h h,,tr h - - - 1 [ 2 2 ]O'h,t ~ h

T a b le V I . E q u a t io n s fo r P h y s i c a l P r o p e r t i e sGas spec ies conduct iv i ty

Gas mixture conduct iv i tyGas species viscosityGas mixture v iscos i ty

In te rac t ion parameter in the equa t ions for kg and /XgGas spec ies d i f fus iv i ty

Gas mixture d i f fus iv i ty

Par t i c l e hea t capac i tyWal l and par t i c l e emiss iv i t i es

. 1 ,

/x = 2 .67 10 -6 (MiTg)l/2/o'2~'~ [VI-3], 7 , 4 ,

. , ( M , I ' " ] 2, v , _ , ,

= ) - s . , , r ,, i- 6

O ,m = ( 1 - x , ) / Z ( x j / D u ) [VI-71/ i~-jCp ; = Z (wkCp k l j [VI-81k

e = 0 .8 [VI -9]

950--VOL UM E 21B, DECEMBER 1990 METALLURGICALTRANSACTIONSB


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T o p w a l l :T ~r ~.~ 1/4~ /2q w,x = - ( T - ~wz~p,mixP~.~/x /~

O u t l e t :

"- ( - ~ l n [ E C ~ / 4 k ~ / 2 x , p / tz ]

I 1 I O " I 1 /49 . 2 4 O'h h,tO 'h - - - -1O'h, t Z [23]

O T- - = 0 [ 2 4 1OX

T h e v a l u e s o f o- a n d o'h,t i n Eqs . [22 ] a nd [23 ] a re g ive na s 0 . 8 a n d 0 . 9 , r e s p e c t i v e l y . [1~ T h e s e c o n d t e r m i nt h e d e n o m i n a t o r i n E q s . [ 2 2 ] a n d [ 2 3 ] i s a n e m p i r i c a lc o r r e l a t i o n te r m t o c o r r e c t t h e P r a n d t l n u m b e r i n t h es e m i l a m i n a r r e g i o n n e a r t h e f u r n a c e w a l l s . [29] T h e w a l lt e m p e r a t u r e a l s o n e e d s t o b e s p e c i f i e d a s a f u n c t i o n o fp o s i t i o n .F o r o t h e r v a r i a b l e s a t t h e w a l l , t h e c o n d i t i o n s o f z e r on o r m a l d e r i v a t i v e a r e u s e d ; t h a t i s( a - ~ l = 0 f o r t h e s i d e w a l l [ 2 5 ]\ o r / w( O~ - x ~ ) = 0 f o r t h e t o p w a l lw [26 ]

I V . N U M E R I C A L M E T H O D SM o d e l i n g e q u a ti o n s , e x c e p t f o r t h e m o m e n t u m e q u a -t i o n s f o r p a r t i c l e p h a s e , c a n b e e x p r e s s e d i n t h e f o r m o fE q . [ 3 ] . E q u a t i o n [ 3 ] c a n b e c a s t i n t o f i n i t e - d i f f e r e n c e

e q u a t i o n s t o b e s o l v e d b y l i n e - b y - l i n e o r t r i d i a g o n a l m a -t ri x a lg o r it h m . T h e T E A C H c o d e d e v e l o p ed b y G o s m a na n d P u n t3 ~ w a s u s e d t o s o l v e t h e g a s - p h a s e e q u a t i o n s .The S IM PL ER a lgo r i t hm de v i se d by Pa t a nka r [31] w a s u se dt o c a l c u l a t e t h e p r e s s u r e f i e l d .The La g ra ng ia n e qua t ions fo r t he pa r t i c l e pha se , w h ic ha r e e a s i e r t o s o l v e th a n t h e E u l e r i a n g a s - p h a s e e q u a t i o n s ,w e r e s o l v e d b y t h e p a r t i c l e - s o u r c e - i n - c e l l ( P S I - C E L L )t e c h n i q u e d e v e l o p e d b y C r o w e et a l . [14]T h e P S I - C E L Lt e c h n i q u e h a s b e e n f o l l o w e d d i r e c t l y to t a k e a c c o u n t o ft h e p a r t i c le f i e l d i n th e g a s f i e l d . T h e o v e r a l l s c h e m e f o rnum e r i c a l so lu t ions u se d in t h i s s tudy i s show n in F igu re 2 .I n o r d e r t o i n c l u d e t h e e f f e c t o f t h e p r e s e n c e o f r e -a c t i n g p a r t i c l e s , t h e p a r t i c l e - p h a s e e q u a t i o n s m u s t b ec oup le d to t he Eu le r i a n ga s f i e ld t h rough the sou rc e t e rmsi n t h e e q u a t i o n s o f c o n s e r v a t i o n f o r t h e g a s p h a s e .T h e s o u r c e t e r m , S p , i n a c e l l ( o r a c o n t r o l v o l u m e )c a n b e o b t a i n e d b y

(S2)cel l = ~ T l i ' j [ ( m p i j ) ~ - - ( m p i j ) i n ] cel l[27]

w he re Vcel t, hO, an d m p o r e p r e s e n t t he v o l u m e o f t h e c e l l,t h e p a r t i cl e n u m b e r f l o w r a t e , a n d t h e m a s s o f p a r t ic l e s

] In i t ia l i z a t i o n o f f l o w f ie l d [, _ ~ _ . _ ~ S o l v e th e g a s - p h a s e L~ " 1 b y T E A C H c o d e ]

1L ~ ( C o n v e r g e d ? )~[Yes

[ U p d a t e g a s p r o p e r t ie s J[ S o l v e p a r ti c le n u m b e r d e n s i ty .J

I ' S o l v e r a d i a t io n f ie l d II n i t i a l iz a t io n o f p a r t ic l e tr a j e c t o r y I

I S o l v e L a g r a n g i a n p a r t ic l e p h a s ee q u a t io n s b y P S I -C E L L a l g o r it h m

N o~ : ( A l l t r a j e c t o r i e s s o l v e d ? . )

Y e s

( O v e r a l l c o n v e r g e n c e ? )@ te ,F i g . 2 - - C o m p u t a t io n a l s c h e m e J 9~

r N o

o f i - t h s i z e f r a c t i o n i n j e c t e d t h r o u g h t h e j - t h s t a r ti n g l o -c a t i o n a t t h e i n l e t , r e s p e c t i v e l y .T h e m o m e n t u m s o u r c e te r m s f o r u a n d v c o m p o n e n t so f t h e g a s -p h a s e m o m e n t u m a r e s im i l a r ly d e s c r i b e d ,r e s p e c t i v e ly , b y

( S ~ ) c e l l = g c e l l ~ i j [ ( U p i j m p i j ) ~ ( u p i j m p i j ) i n cel l[28[

(S;)cell = ~ h O [ ( V p o m p o ) ~ ( v p i s m " o ) " d cell[291

T h e s o u r c e o r s i n k t e r m o f g a s e o u s s p e c i e s k d u e t ot h e r e a c t i o n s o f p a r t i c l e s c a n b e o b t a i n e d b y(S' f l )k = ~ hi j[(Wk)o.t - - (wDi~] [301cel l

w h e r e W k i S t h e a m o u n t o f t h e c o n s u m e d o r p r o d u c e dga se ous spe c i e s k re su l t i ng f rom the r e a c t ions o f pa r t i c le s .M E T A L L U R G IC A L R A N S A C T IO N S V O L U M E 2 1 B , D E C E M B E R 1 9 9 0 - - 9 5 1


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The energy source term for the gas phase is given byh l { ~ j h i j [ ( h p i j m p i j ) o u t _ ( h p # m p i j ) { n ]( S p ) c e l l - V c e l l c e ll

[31]It is noted that the enthalpy of the particle is calculatedby incorporating the radiative heat transfer between par-ticles and their surroundings, as shown in Eq. [III-8] inTable III.

V . R E S U L T S A N D D I S C U S S I O NIn order to verify the mathematical model developedin this work, the model predictions were compared withexperimental data obtained from a laboratory flash fur-nace tlgJ and an Out oku mpu pilo t flash furnace , t321 The

boundary conditions determined in the referenced ex-periments were used for calculations whenever appli-cable. After the model was verified by these comparisons,predictions for various aspects of the industrial flash fur-nace operation were made.A . C o m p a r i s o n s b e t w e e n P r e d i c t io n s a n dM e a s u r e m e n t s i n a L a b o r a t o r y F l a s h F u r n a c e

Experiment al work was carried out by Chaubal t~9] tomeasure the centerline profiles of the SO2 concentration,the amount of sulfur remaining in the particles, and thegas temperature in a laboratory flash furnace describedin Table VII. In this system, the gas and solid particleswere uniformly mixed in a mixing chamber prior to being

injected as a single stream. The burner was a straightcylinder of 2-cm diameter. Chaubal investigated the ef-fects of oxygen content in the inlet stream and solidsloading on the reaction of chalcopyrite concentrate.Figure 3 shows the comparison between model pre-dictions and measurements obtained for target matte grades

A 30

2O0O 1 0t~t0O 0

A

0 1om

i0 0 . 2 5 0 . 5 0 . 7 5

S O 2

It

i

1 . 0 1 . 2 5

En-

:3u)

1 0 0

50 50 % Cu70 % Cu

t~ 9

0 ~ 0 ' 5 0 ' 7 5 , : 0 , 2 5A x i a l D i s t a n c e f r o m T o p ( m )

Fig. 3--Effect of matte grade on the reaction of chalcopyrite con-centrate: measure d data (0 70 pct Cu, 50 pet Cu, and 21 pet O2)v spredictions ( ). (Conditions for the laboratory runs are givenin Table VII.)

T a b l e V I I . E x p e r i me n t a l C o n d i t i o n s f o r t h e L a b o r a t o r y F l a s h F u r n a c e t191Inlet Geometry:

d I (m)d (m)Ly (m)

Inlet Stream:Gas flow (m3/h)O~ content (pct)Temperature (K)Concentrate feed rate (kg/h)Target matte grade (pct Cu):

single-entry0.020.231.2

Te s t Nu m b e r1 2 3 4

4.57 4.57 4.57 4.5721 21 21 30303 303 303 3034.8 3.8 3.3 4.750 60 70 70

Concentrate: Cu (pct) 26Fe (pct) 27S (pct) 30SiO2 (pct) 15Particle size: 47.3 /.~m (mass mean diameter)Particle density: 4300 kg/ m 3

Wall temperature (K):Top wall Tw = 1100Side walls Tw = 1120 at0_-- 0.4 mBottom surface Tbo = 800 K (for radiation calculation only)Turbulence intensity at the inlet: 0.02**

*x denotes the axial distance from the top ceiling.**Estimated value.

95 2- - VOLUME 21B, DECEMBER 1990 METALLURGICAL TRANSACTIONS B


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o f 5 0 a n d 7 0 p c t w i t h 2 1 p c t O2 a n d t h e i n j e c t i o n v e -l o c i ty o f 4 m / s ( te s ts 1 t h ro u g h 3 i n T a b l e V I I ) . R e a -s o n a b l e a g r e e m e n t b e t w e e n t h e p r e d i c t e d r e s u l t s a n d t h em e a s u r e d d a t a w a s o b t a i n e d , e x c e p t n e a r th e f u r n a c eb o t t o m . I t i s n o t e w o r t h y t h a t th e m o d e l a d e q u a t e l y p r e -d i c t s th e i g n i t i o n p o i n t o f p a r t i c l e s , w h i c h i s i m p o r t a n tt o p r o p e r l y p r e d i c t t h e s m e l t i n g p r o c e s s o c c u r r i n g i n t h ef l a sh f u r n a c e s h a f t. T h e d e v i a t io n n e a r t h e b o t t o m o f t h ef u r n a c e i s d u e t o t h e a i r l e a k i n g i n t o t h e f u r n a c e f r o ma n o p e n i n g a t t h e b o t t o m f o r t h e s a m p l e p r o b e . [19] A l -t h o u g h n o t i l lu s t r a t e d , t h e c o m p a r i s o n r e s u l t s f o r t h e t a r -g e t m a t t e g r a d e o f 6 0 p c t l i e b e t w e e n t h o s e f o r 5 0 a n d7 0 p c t .T h e e f f e c t o f o x y g e n c o n c e n t r a t io n i n t h e i n le t is s h o w ni n F i g u r e 4 ( t e s ts 3 a n d 4 i n T a b l e V I I ) . T h e o x y g e nc o n t e n t i n th e i n l et s t r e a m w a s v a r i e d f r o m 2 1 t o 3 0 p c tw i t h t h e i n j e ct io n v e l o c i t y o f 4 m / s a n d 7 0 p c t m a t t eg r a d e . T h e p r e d i c te d a n d t h e m e a s u r e d r e s u l ts s h o w t h a tt h e r e a c t i o n r a t e i n c r e a s e s s o m e w h a t a s t h e 0 2 c o n c e n -t r a t i o n i n c r e a s e s . A l t h o u g h t h e d e v i a t i o n n e a r t h e f u r -n a c e b o t t o m d u e t o a i r i n f i l t r a t i o n i s o b s e r v e d a g a i n , t h eo v e r a l l a g r e e m e n t i s s a t i s f a c t o r y .B . C o m p a r i s o n b e t w e e n P r e d i c t io n s a n dM e a s u r e m e n t s i n a P i l o t - S c a le F l a s h F u r n a c e

I n f l a s h s m e l t i n g p r o c e s s e s , t h e r e a r e t w o t y p e s o fb u r n e r c o n f i g u r a t i o n s : [6] a s i n g l e - e n t r y b u r n e r s y s t e m t h a ta l l o w s t h e o x y g e n - e n r i c h e d p r o c e s s a i r a n d c o n c e n t r a t ep a r t i c l e s t o e n t e r t h e f u r n a c e t h r o u g h a s i n g l e - e n t r y n o z -z l e w i t h o u t a d i s t r i b u t i o n a i r s t r e a m a n d a d o u b l e - e n t r yb u r n e r s y s t e m i n w h i c h t h e d i s t r ib u t i o n a i r , t o g e t h e r w i t hc o n c e n t r a t e p a r t ic l e s , e n t e r s th e f u r n a c e s e p a r a t e l y f r o mt h e o x y g e n - e n r i c h e d p r o c e s s a i r . A s c h e m a t i c d i a g r a mo f t h e l a t te r t y p e o f b u r n e r i s s h o w n i n F i g u r e 5 .

A

r

3O

2O

1 0 -

0

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30 % O ~ ~ e 9

i i i

0.25 0.5 0.75 1.0 1.25

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._ =

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r

1 0 0

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0 0.25 0.5 0.75 1,0 1.25Ax ia l D is t a nc e f rom Top ( m)

F i g . 4 - - E f f e c t o f o x y g e n c o n t e n t o n t he r e a c t i o n o f c h a l c o p y r i te c o n -c e n t r a t e : m e a s u r e d d a t a ( 0 2 1 p c t 0 2 , [ ] 3 0 p c t 0 2 , a n d 7 0 p c t C u )vs pred ic t ions ( ) . (Cond i t ions fo r the l abo ra to ry runs a r e g ive ni n T a b l e V I I . )

T h e m a t h e m a t i c a l m o d e l d e v e l o p e d i n t h i s w o r k w a su s e d t o p r e d i c t t h e p e r f o r m a n c e o f th e O u t o k u m p u p i l o tf l a s h f u r n a c e w h o s e d i m e n s i o n s a n d e x p e r i m e n t a l c o n -d i ti o n s a r e d e s c r i b e d i n T a b l e V I I I . T h e v a l u e s c o r r e -s p o n d i n g t o t e s ts 1 t h r o u g h 3 r e p r e s e n t th e e x p e r i m e n t a lc o n d i t io n s f o r t h e O u t o k u m p u d o u b l e - e n t r y b u r n e r s y s -t e m i n w h i c h t h e d i s t r i b u t i o n a i r i s f e d r a d i a l l y i n t o t h ef u r n a c e , w h i l e t e s t s 4 a n d 5 r e p r e s e n t t h o s e f o r a s i n g l e -e n t r y b u r n e r s y s t e m . T h e t e m p e r a t u r e a t t h e f u r n a c e w a l lw a s a s s u m e d t o b e 1 4 7 3 K . t33]

T o p r e d i c t th e p e r f o r m a n c e o f th e f l a s h s m e l t i n g f u r -n a c e w i t h t h e d o u b l e - e n t r y b u r n e r s y s t e m , t h e r a d i a lf e e d i n g m o d e o f t h e d i s tr i b u ti o n a i r w a s u s e d w i t h U = 0a n d v~ = 1 1 8 m / s ( e q u i v a l e n t s l it w i d t h = 0 . 2 5 r a m ) .F i g u r e 6 s h o w s t h e r e s u l ts o f t h e c o m p a r i s o n b e t w e e np r e d i c ti o n s a n d m e a s u r e m e n t s f o r t e st s 1 t h r o u g h 3 . I nt h e s e f i g u r e s , t h e p r o f i l e s a l o n g t h e c e n t e r l i n e o f t h e S O 2a n d 0 2 c o n c e n t r a t i o n s a n d t h e a m o u n t o f o x y g e n c o n -s u m e d t o p r o d u c e o x i d e p h a s e s a r e p l o t te d . B o t h t h e p r e -d i c te d a n d m e a s u r e d r e s u l ts f o r t h e t h r e e t e st s s h o w a l m o s tt h e s a m e p r o f i l e s , b e c a u s e t h e i n le t c o n d i ti o n s w e r e s i m -i l a r . A l t h o u g h t h e m e a s u r e d d a t a a r e s o m e w h a t s c a t -t e r e d , t h e o v e r a l l a g r e e m e n t i s s a t i s f a c t o r y . M o d e lp r e d i c t i o n s i n d i c a t e t h a t t h e r e a c t i o n o f c h a l c o p y r i t e p a r -t ic l es m o s t l y o c c u r s i n t h e u p p e r z o n e o f t h e f u r n a c es h a f t , i . e . , b e t w e e n th e b u r n e r e x i t a n d x = 1 m . H e n c e ,w e c a n c o n c l u d e t h a t th e u p p e r p a r t o f t h e f la s h f u r n a c ew i t h i n a b o u t 1 m o f t h e t o p i s a n i m p o r t a n t r e g i o n i nd e t e r m i n i n g t h e e x t e n t o f s u l f id e p a r t i c l e s r e a c t e d . I t isw o r t h w h i l e t o n o t e t h a t al l o f t h e m e a s u r e d d a t a w e r eo b t a i n e d b e y o n d t h i s u p p e r r e g i o n . H e n c e , a l t h o u g h t h em o d e l s a t i s f a c t o r i l y p r e d i c t s t h e a v a i l a b l e e x p e r i m e n t a ld a t a , c o m p a r i s o n c o u l d n o t b e m a d e i n th e u p p e r r e g i o n

U s u S

Vp

F i g . 5 - - S c h e m a t i c d i a g r a m o f a d o u b l e - e n t r y b u r n e r s y s t e m w i t h r a -d i a l f e e d i n g o f t h e d i s t r i b u t io n g a s a n d c o n c e n t r a t e p a r t i c le s .M ETA LLU RG ICA L TRA N S A CTIO N S B V O LU M E 21B, D ECEM BER 1990- -953


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T a b l e V I I I . B o u n d a r y C o n d i t i o n s fo r a n O u t o k u m p u P i lo t F l a s h F u r n a c e

Furnace geometry:

Particle size:Particle density:Turbulence intensities at the inlet:Wall temperature:

dl (m)d2 (m)ds (m)L (m)50 ~m (mass mean diameter)4300 kg/m 3Ii = 0.02* (0.15"*), 12 = 0.08*Top and side walls Tw = 1473 K tBottom surface

Test Number1 through 3 4 and 5

0.09 0.130.21 . 2 1 . 26 5

Tbo = 1523 K (for radiation calculation only)Primary (Distribution) Stream:Gas flow (Nm3/h)02 content (pct)Temperature (K)Concentrate feed rate (kg/h)Cu (pct)Fe (pct)S (pct)Si02 (pct)Secondary (Process) Stream:Gas flow (Nm3/h)(axial velocity m/s)02 content (pct)Temperature (K)Matte Grade:

Test Number1 2 3 4 5

30* 30* 30* 13268 882821 21 21 28 28298 298 298 298 463470 500 500 1390 96018.1 17.7 19.2 17.7 18.137.6 38.1 29.1 35.3 35.835.9 36.1 35.4 36.3 35.53.55 3.65 2.61 5.6 5.0555 570 560 - - - -(6.2) (6.2) (6.3) - - - -27 28 28 - - - -298 298 298 - - - -

76.4 71.4 75.2 56 59*Estimated values for tests 1 through 3.**Estimated values for tests 4 and 5.*Assumed wall temperature, t33~*Equivalent linear radial velocity = 118 m/ s.~Axial feeding.

of the furnace due to the lack of experimental data at thepresent time.For the single-entry burner system, the predicted andmeasured results of the SO2 and O2 concentrations, theamount of oxygen consumed to produce oxides, and thegas temperature along the centerline are plotted inFigure 7. Figures 7(a) and (b) show the results for theinlet gas temperature of 298 and 463 K, respectively.Predicted results show that reactions occur somewhat fasterwith a higher inlet temperature (Figure 7(b)) than witha lower temperature. Comparing these results with thosefor the double-entry burner system (Figure 6), it is seenthat the complete reaction of sulfide particles is attainedfarther from the burner in the single-entry system. Thisindicates that the wide dispersion of particles in the ra-dial direction by the radial feeding of the distribution airfacilitates the effective utilization of the furnace volumeand, consequently, enhances the smelting rate of the sul-fide mineral compared to the single-entry burner system.Again, the model predictions in the upper region of thefurnace could not be compared with measurements dueto the lack of data, but the overall agreement is quitesatisfactory. F igure 7(c) shows the comp arison of thepredicted and measured gas-phase temperatures obtainedby varying the preheating temperature of the inlet gas.Again, the agreement is reasonable.

Figure 8 shows the comparison between the gas tem-perature and the averaged particle temperature along thecenterline for the conditions of test 4 in Table VIII. Thesolid squares represent the gas-phase temperatures mea-sured by Outok umpu . [32] It is seen that the predict ed par-ticle temperature is considerably higher than the gastemperature, especially in the upper region of the furnace.C. Prediction of Industrial Flash Furnace Operations

In order to predict the performance of an industrialflash smelting furnace, the system described in Table IXwas used. The dimensions of the system were chosen tobe close to an industrial Outokumpu flash furnace. Theprimary air (or the distribution air), laden with concen-trate particles, and the secondary air (or the oxygen-enriched process air) enter the furnace radially and axially,respectively. The distribution air stream had velocitycomponent s of ul = 0 and Vl = 120 m/ s ( equivalent slitwidth = 0.62 mm). The oxyg en-enri ched process air(50 vol pct 02) preheated to 473 K enters the furnaceaxially.Figure 9 shows the contours of the 02 and SO2 con-centrations and the gas-phase temperature for the case ofa process gas velocity of 15 m/ s. These contours indi-cate that in an industrial flash smelting furnace, the

95 4- - VOLUME 2I B, DECEMBER 1990 METALLURGICAL TRANSACTIONS B


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3O ( a ) S O 2 ( b ) 0 2 ( M e x OA

rOt -OOmm( 5

A

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(a)(b )

I I

3

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I . , L .

4

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(a)9 AF 9 9 v

(b )A ,.

(c ), . , I . n 9 " I I I

1 2 3 4

( I I I )

9 (a)(b )&

'~ + I a I i I 4,1 2 3 4

A x i a l D i s t a n c e f r o m T o p ( m )Fig. 6-- Co m pa riso n between the predicted and measured resul ts :(I) test 1, (II) test 2, ([I/) test 3; ( ) prediction of this wo rk, (41,A+)measurem ents by Ou tokumpu . (Con ditions for the pilot plant tests witha double-entry burner are given in Table V III .)

30~ " ~ T O = 2 9 8 K 9 9

O0 1 0

1 2

(a )S O 2

0 2 ( M e x O y )i

3

9, . 30 ~ T = 463 K9 S O 2

t -O( " ) 1 0 O 2 ( M e x O y )(5

0 ' :':0 1 2 3

( b )

' ~ ' 1750

' ~ 1 2 5 0OQ,,EO 7 5 0I- "

(5 2 5 0

~ . ~ 2 98 K

(c)

0 1 2 3 4A x i a l D i s t a n c e f r o m T o p ( m )

Fig . 7 - -Co mp ar i so n between the pr edic t ed and measured r esul ts f orvarious preheating temperatures: (a) test 4, (b) test 5, (c) gas tem -perature: To = 298 (A ) , 463 K ( l l ) . (OA [Tx ) measurements byOutokum pu, ( ) predictions. (Conditions for the pilo t plan t testswith a s ingle-entry burner are give n in Table VIII .)

r e a c t i o n s o f s u l fi d e p a r t ic l e s o c c u r m o s t l y w i t h i n a b o u t1 m o f th e t o p . R e l a t i v e l y u n i f o r m p r o f i l e s o f th e 0 2 a n dS O 2 c o n c e n t r a t i o n s a n d t h e g a s t e m p e r a t u r e a r e o b s e r v e db e y o n d 1 m f r o m t h e t o p .

A l t h o u g h n o t i l l u s t r a t e d , t h e c o m p u t e d r e s u l t s o b -t a i n e d b y v a r y i n g t h e m a t t e g r a d e f r o m 5 0 t o 7 0 p c t C us h o w e d t h a t i g n i t i o n ta k e s p l a c e s o m e w h a t n e a r e r to t h eb u r n e r w i t h h i g h e r m a t t e g r a d e , b e c a u s e p a r t i c l e s a reh e a t e d u p f a s t fo r t h e h i g h e r m a t t e g r a d e d u e t o t h e l o w e rs o l i d s l o a d i n g .

T h e e f f e c t o f i n l e t v e l o c i ty o f t h e p r o c e s s a i r w a s t e s t e dw i t h th e v a l u e s o f 1 5 a n d 6 0 m / s . M o d e l p r e d i c t i o n ss h o w e d t h at p a r t ic l e s w e r e s o m e w h a t m o r e u n i f o r m l yd i s p e r s e d w i t h h i g h e r i n j e c t i o n v e l o c i t y o f th e p r o c e s sa i r. T h e p r e d i c t e d r e s u l t s i n te r m s o f O 2 c o n c e n t r a t i o na r e s h o w n i n F i g u r e 1 0 . It i s i n d i c a t e d , a s e x p e c t e d , t h a tt h e r e a c t i o n o f s u lf i d e m i n e r a l s w i t h a n i n j e c t i o n v e l o c i t yo f 6 0 m / s o c c u r s f a r t h e r f r o m t h e b u r n e r ti p c o m p a r e dt o t h a t w i t h 1 5 m / s . H o w e v e r , i t i s n o t e w o r t h y t h a t t h e

-1

EOI, -

2 0 0 0

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0 I I i I I I i

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5 4 . 0

A x i a l D i s t a n c e f r o m T o p ( m )Fig . 8- - Ce nter l i n e prof i les of t he gas (Tg ) and par t icle (T p ) temper-atures fo r test 4 w ith a single-entry burner in Tab le VIII. (11) Gastemp erature mea sured by Outoku mp u, t32~ ( ) prediction of this work .

M E T A L L U R G I C A L T R A N S A C T I O N S B V O L U M E 2 1 B , D E C E M B E R 1 9 9 0 - - 9 5 5


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T a b l e I X . B o u n d a r y C o n d i t i o n s f o r a n I n d u s t r i a l F l a s h F u r n a c eG e o m e t r y :

P r i m a r y s t r e a m ( d i s t r i b u t i o n a i r ) :

S e c o n d a r y s t r e a m ( p r o c e s s a i r ):

C o n c e n t r a t e i n t h e p r i m a r y s t r e a m :

M a t t e g r a d e :W a l l t e m p e r a t u r e : T o p a n d s i d e w a l l sB o t t o m s u r f a c eT u r b u l e n t i n t e n s i t i e s :

d l = 0 . 3 6 md2 = l md i = 4 mL i = 7 mR a d i a l f e e d in g m o d eG a s fl o w = 3 0 7 m 3 / h ( v l = 1 2 0 m / s )0 2 c o n t e n t = 2 1 p c tT e m p e r a t u r e = 3 0 0 KG a s fl o w = 3 3 , 4 2 0 ; 1 3 3 , 6 7 0 m 3 / h( L i n e a r v e l o c i t y = 1 5 ; 6 0 m / s )0 2 c o n t e n t = 5 0 p c tT e m p e r a t u r e = 4 7 3 KC o n c e n t r a t e fe e d r a t e = 4 6 , 0 8 0 ; 1 8 4 , 3 20 k g / hC u ( p c t ) 2 8 . 8 5F e ( p c t ) 2 8 . 9 1S ( p c t ) 3 3 . 4 8SiO2 (pct ) 5 .93P a r t i c l e d e n s i t y = 4 3 0 0 k g / m 3P a r t ic l e m e a n d i a m e t e r = 5 0 / x m7 0 p c t C uTw = 1473 KTbo = 1 5 2 3 K ( f o r r a d i a t i o n c a l c u l a t i o n o n l y )I ~ = 0 . 0 2 ; 1 2 = 0. 1 f o r u 2 = 1 5 m / s1 2 = 0 . 1 5 f o r u 2 = 6 0 m / s

Contours of 0 Concent rat ion (%)5 21 .~ /~ 0.5__~11(JO 'i - ~ -3 / / , / - 50.0 1.0 2,0 3.0

l r

25 Cont ours of SO 2 Concentrat ion (%)

0 ,5/ / ~ f ~ -3 3~ 3 4 " ~ 3 4 /0.0 1.0 2,0 3.0

1000 1700 Con to urs o f G a s Temperature (K)1.0 '~Yi ~ 1800~ 2 0 0 0473 1900-2000~) ~ 2100 ----.._._.__~2000"- - i I I i

0 1 2A x i a l D i s t a n c e f r o m T o p ( m )

Fig. 9 - - Predicted contours of the SO 2 and 02 concentrations and thegas temperature in an indus trial flash smelting furnace.

d i s t r ib u t i o n o f t h e 0 2 c o n c e n t r a t i o n f o r t h e h i g h e r i n l e tv e l o c i t y is m o r e u n i f o r m i n t h e ra d i a l d i re c t i o n t h a n f o rt h e l o w e r i n l e t v e l o c i t y . I n b o t h c a s e s , o x y g e n i s a l m o s ta l l c o n s u m e d a t a b o u t 2 m f r o m t h e b u r n e r . T h e s e r e s u lt si n d i c a t e t h a t fr o m t h e v i e w p o i n t o f s u l fi d e o x i d a t i o n , t h es m e l t i n g r a t e c a n b e s u b s t a n t i a l l y in c r e a s e d , o r t h e s h a f th e i g h t r e d u c e d , i n m o s t e x i s t i n g i n d u s tr i a l f l a s h f ur -n a c e s . T h i s , i n fa c t , w a s d e m o n s l ~ a t e d b y P h e l p s D o d g e ' sH i d a l g o s m e l t e r , w h e r e t h e o r i g i n a l f u r n a c e h e i g h t o f4 5 f e e t w a s r e d u c e d b y 1 0 f e e t w i t h o u t m u c h a d v e r s e

Contou rs of 0 2 Concentrat i on (%)Sl'0 1 ~ f-/ J5~110 ' i t ~ 1~ , ,~111~)~~ ~ l! 0 1 x ( a ).010 -51.6x1020-50.~0.0"0.0 1.0 20 3.0

I. -530-50. 0.0 1.0 2.0

(b ) -51x103.0

Axia l D is tance f rom Top (m)Fig . 1 0- -E f f ec t o f i n le t ve loci ty of the proces s a i r: ( a ) 15 m /s and(b) 60 m/s .

956- -VO LUM E 21B, DECEMBER 1990 METALLURGICAL TRANSACTIONS B


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e f fe c t . ~26} Th e re a re a n um be r o f p r a c t i c a l r e a so ns w h yt h e f u r n a c e h e i g h t c a n n o t b e a s s h o r t a s w h a t t h e c a l -c u l a t e d r e s u lt s w o u l d i n d i c a t e , s u c h a s l e s s r e a c t i v e r e -c yc l e ma te r i a ls a nd a g g lome ra t ion o f the c onc e n t ra t e fe e d .H o w e v e r , t h e h e i g h ts o f i n du s t ri a l f u r n a ce s m a y , i n g e n -e r a l , b e e x c e s s i v e .A f t e r t he i n i t i a l p re pa ra t ion o f t h i s ma nusc r ip t , K e mor iet a l . [341 p u b l i s h e d d a t a o n t h e c o m p o s i t i o n o f c o p p e rc o n c e n t r a t e p a r t i c l e s c o l l e c t e d f r o m a p i l o t f l a s h f u r n a c e .T o g e t h e r w i t h t h e i r e ar l ie r m e a s u r e m e n t s o n o x y g e n p a r -t i a l p r e s s u r e a n d p a r t i c l e s i z e , t h e s e d a t a r e p r e s e n t av a l u a b le s o u r c e f o r f u r t h e r c o m p a r i s o n . T i m e a n d r e -s o u r c e s p e r m i t t i n g , i t w o u l d b e o f i n t e r e s t t o s i m u l a t et h e ir e x p e r i m e n t s u s i n g t h e m a t h e m a t i c a l m o d e l d e v e l -o p e d i n t h i s w o r k .

V I. C O N C L U D I N G R E M A R K SThe nume r i c a l p re d ic t ions o f t he f l a sh sme l t i ng fu rna c es h o w s a t i s f a c t o r y o v e r a l l a g r e e m e n t w i t h e x p e r i m e n t a ld a t a i n s p i te o f th e c o m p l e x n a t u r e o f t h e s y s t e m a n d t h em a t h e m a t i c a l m o d e l . T h i s l e a d s t o t h e c o n c l u s i o n t h a tt h e t w o - e q u a t i o n ( k - e ) t u r b u l e n c e m o d e l i n c o r p o r a t -i n g t h e e f f e c t o f p a r t i c l e s o n t u r b u l e n c e c a n a d e q u a t e l y

b e u s e d f o r th e m o d e l i n g o f t h e f la s h s m e l t in g f u r n a c ew h e n c o m b i n e d w i t h t h e e x p r e s s i o n s f o r c h e m i c a l k i -n e t i c s a n d h e a t / m a s s t r a n s f e r .M o d e l p r e d i c t io n s f o r t h e p e r f o r m a n c e o f t h e f l a s hs m e l t i n g f u r n a c e p o i n t t o t h e f o l l o w i n g c o n c l u s i o n s :1 . R e a c t i o n s o f s u l f i d e p a r t i c l e s a r e m o s t l y c o m p l e t e di n t h e u p p e r z o n e o f t h e f l a s h f u r n a c e s h a f t , w i t h i na b o u t 1 m o f t h e b u r n e r t i p in m o s t c a s e s . T h u s , j u s tf r o m t h e v i e w p o i n t o f s u l f i d e o x i d a t i o n , t h e s m e l t i n gr a t e c a n b e s u b s t a n t i a l l y i n c r e a s e d , o r t h e s h a f t h e i g h tr e d u c e d , i n m o s t e x i s t i n g i n d u s t r i a l f l a s h f u r n a c e s .2 . T h e d o u b l e - e n t r y b u r n e r s y s t e m w i t h t h e r a d i a l fe e d -i n g o f t h e c o n c e n t r a t e - l a d e n d i s t r i b u t i o n a i r s h o w sbe t t e r pe r fo rma nc e tha n the s ing le -e n t ry bu rn e r sy s t e m.3 . T h e i n l e t c o n d i t i o n s , s u c h a s p r e h e a t i n g t e m p e r a t u r ea n d o x y g e n c o n t e n t , h a v e a c o n s i d e r a b l e i n f l u e n c e o nt h e o v e r a l l p e r f o r m a n c e o f t h e fl a s h s m e l t i n g f u r n a c e .

T h e m a t h e m a t i c al m o d e l f o r t h e f l as h s m e l t i n g p r o c e s sd e v e l o p e d i n th i s w o r k i s b a s e d o n f i r s t p r i n c i p l e s . T h em o d e l w a s v e r i f i e d to a d e q u a t e l y d e s c r i b e v a r i o u s i m -p o r t a n t a s p e c t s o f t h e p h e n o m e n a o c c u r r i n g i n t h e f l a s hf u r n a c e s h a ft . T h u s , i t c a n b e u s e d w i t h c o n f i d e n c e f o rp r e d i c t i n g t h e p e r f o r m a n c e o f f l a s h f u r n a c e s w i t h d i f -f e r e n t o p er a t in g c o n d i t io n s a n d / o r d i f f e r e n t d im e n s i o n s .O t h e r b e n e f i t s o f t h e m o d e l i n c l u d e :a . i t w i l l f a c i l it a t e t h e i n t e r p r e t a t i o n o f e x p e r i m e n t a lm e a s u r e m e n t s ;b . i t w i l l b e h e l p f u l i n i d e n t i f y i n g t h e i m p o r t a n t v a r i -a b l e s o f t h e s m e l t i n g p r o c e s s ;c . i t p r o v i d e s a f u n d a m e n t a l b a s i s f o r th e d e s i g n a n do p t i m i z a t i o n o f t h e p r o c e s s ; a n dd . p r e d i c t i o n s c a n b e m a d e f o r o t h e r s p e c i f ic a s p e c ts o ff l a s h s m e l t i n g w i t h o u t r e s o r t i n g t o e x p e n s i v e t e s t s i na n i n d u s t r i a l o r p i l o t p l a n t f a c i l i t y .

N O M E N C L A T U R EAp p r o j e c t e d a r e a o f a p a r t i c l eC1, C2, C 3 c o n s t a n t s i n t u r b u l e n c e m o d e l

CDc ,d ld 2,t :o ;EghH mHrf - i v1kkgkmkoL :mjmpnhPPrqrpQpQrg?.RR eR:SS cS htt tTuvVwkxX

d r a g c o e f f i c i e n t g i v e n b y E q . [ 11 I- 2]s p e c i f i c h e a t c a p a c i t yd i a m e t e r o f t h e p r i m a r y s t r e a md i a m e t e r o f t h e s e c o n d a r y s t r e a md i a m e t e r o f t h e f u r n a c ep a r t i c l e d i a m e t e rt u r b u l e n t p a r t i c l e d i f f u s i v i t y g i v e n b yEq. [111-6]a c t i v a t i o n e n e r g yg r a v i t a t i o n a l a c c e l e r a t i o ne n t h a l p yr a t e o f h e a t lo s s d u e t o m e l t i n gr a t e o f h e a t p r o d u c t i o n b y r e a c t i o nr a t e o f h e a t l o s s d u e t o v o l a t i l iz a t i o nt u r b u l e n t i n t e n s i t yturb ulen t__ _k inet ic energ____y[ = l / 2 ( u '2 + v ' z + w ' 2 ) ]g a s - p h a s e h e a t c o n d u c t i v i t ym a s s t r a n s f e r c o e f f i c i e n tp r e = e x p o n e n t i a l f a c t o rf u r n a c e l e n g t hm a s s f r a c t i o n o f g a s s p e c i e s jm a s s o f a p a r t ic l ep a r t ic l e n u m b e r d e n s i t yp a r t ic l e n u m b e r f l o w r a t ep r e s s u r eP r a n d t l n u m b e rr a d i a t i v e h e a t t r a n s f e r r a t e f o r t h e p a r t i c l ep h a s er a t e o f h e a t l o s s d u e t o g a s - p h a s ec o n v e c t i o nv o l u m e t r i c h e a t t r a n s f e r r a t e b y g a s - p h a s er a d i a t i o nr a d i a l d i s t a n c e f r o m t h e a x i s o f s y m m e t r yu n i v e r s a l g a s c o n s t a n tR e y n o l d s n u m b e r d e f i n e d b y E q . [ 11 1-3 ]f u r n a c e r a d i u ss o u r c e o r s i n k t e r m i n c o n s e r v a t i o ne q u a t i o n sS c h m i d t n u m b e rS h e r w o o d n u m b e rt i m et i m e s c a l e o f t u r b u l e n c e ( = 1 . 5 C , k / e )t e m p e r a t u r ea x i a l v e l o c i t yr a d i a l v e l o c i t yv e l o c i t y v e c t o rm a s s o f g as s p e c i e s ka x i al d i s t a n c e f r o m t h e b u r n e r e x i to v e r a l l fr a c t i o n o f s u l f u r r e m o v e d

G r e e k S y m b o l sF e e f f e c t i v e t ra n s p o r t e x c h a n g e c o e f f i c i e n te d i s s i p a t i o n r a t e o f t u r b u l e n t k i n e t i c e n e r g y o re m i s s i v i t y/x v i sc os i tyu k i n e m a t i c v i s c o s i t yp d e n s i t y o r r e f l e c t i v i t yPbp b u l k p a r t i c l e d e n s i t y ( m a s s o f p a r ti c l e s p e rv o l u m e )o-~ P r a n d t l - S c h m i d t n u m b e r f o r ~b~- sh ear s t ress

M E T AL L UR GIC AL T R AN S AC T IO NS B VOL UM E 2 1 B , D E C E M B E R 1 9 9 0 - -9 5 7


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rp p a r ti c le r e la x a t io n t ime [ = m J ( 3 r~b genera l dependent va r iab leS u b s c r i p t se e f f e c t i v e v a l u e

f f u r n a c eg g a sl l a m i n a ro inle tp par t ic let tu rbulen tw w a l l1 p r i m a r y s t r e a m2 s e c o n d a r y s t r ea mS u p e r s c r i p t st t u r b u l e n t' f l u c t u a t in g c o m p o n e n tO v e r l i n e- t i m e - a v e r a g e d= s e c o n d - o r d e r t e n s o r

A C K N O W L E D G M E N T ST h e a u t h o r s w i s h t o e x p r e s s t h e i r a p p r e c i a t i o n t o D r .J . A s t e l j o k i , O u t o k u m p u M e t a l lu r g i c a l R e s e a r c h C e n t e r ,

P o r i , F i n l a n d , f o r p r o v i d i n g t h e p i l o t p l a n t d a t a u s e d i nt h i s w o r k , t o D r . K . J . R i c h a r d s , M r . D . B . G e o r g e , a n dD r . L . K . B a i l e y o f K e n n e c o t t , S a l t L a k e C i t y , U T , f o rh e l p f u l d i s c u s s i o n s , a n d to D r . P . J . S m i t h o f B r i g h a mY o u n g U n i v e r s i t y , P r o v o , U T , f o r p r o v i d i n g t h ei rc o m p u t e r p r o g r a m f o r a g a s - p a r t i c l e j e t . T h i s w o r k w a ss u p p o r t e d in p a rt b y t h e N a t i o n a l S c i e n c e F o u n d a t i o nu n d e r G r a n t N o . C P E - 8 2 0 4 2 8 0 a n d b y t h e D e p a rt m e n to f t h e I n t e r i o r ' s M i n e r a l I n s t i t u t e p r o g r a m a d m i n i s t e r e db y t h e B u r e a u o f M i n e s t h r o u g h t h e G e n e r i c M i n e r a lT e c h n o l o g y C e n t e r fo r P y r o m e t a ll u r g y u n d e r A l l o t m e n tG r a nt N o . G l 1 2 5 1 2 9 .

R E F E R E N C E S1. N.J. Themelis, J.K. Makinen, and N.D.H. Munroe: PhysicalChemistry of Extractive Metallurgy, V. Kudryk and Y.K. Rao,eds., TMS-AIME, Warrendale, PA, 1985, pp. 289-309.2. Y.H. Kim and N.J. Themelis: The Reinhardt Schuhmann Int.Syrup. on Innovative Technology and Reactor Design in ExtractionMetallurgy, D.R. Gaskell, J.P. Hager, J.E. Hoffmann, and P.J.Mackey, eds., TMS-AIME, Warrendale, PA, 1986, pp. 349-69.3. Y. Fukunaka, S. Nakashita, Z. Asaki, and Y. Kondo: in WorldMining and Metals Technology, A. Weiss, ed., AIME, New York,NY, 1976, vol. 1, pp. 481-504.4. S. Ruottu: Combust. Flame, 1979, vol. 34, pp. 1-11.5. Y.B. Hahn and H.Y. Sohn: Chem. Eng. Commun., 1987, vol. 61,pp. 39-57.6. Y.B. Hahn and H.Y. Sohn: Metall. Trans. B, 1988, vol. 19B,pp. 871-84.7. D.B. Spalding: Numerical Computation of Multiphase Flows,

Lecture Notes, Thermal Science and Propulsion, Purdue University,West Lafayet te, IN, 1979, pp. 161-90.8. L.D. Smoot and D.T. Pratt: Pulver ized Coal Combustion andGasification, Plenum Press, New York, NY, 1979, pp. 57-64,83-104, and 217-31.9. L.D. Smoot and P.J. Smith: User's Manual for a ComputerProgram fo r 2-Dimensional Coal Gasification or Combustion(PCGC-2), Combustion Laboratory, Brigham Young University,Provo, UT, 1983.10. L .D. Sm oot and P.J. Smith: Coal Combustion and Gasification,Plenum Press, New York, NY, 1985, pp. 245-64 and 349-71.11. B.E. Launder and D.B. Spalding: Mathematical Models ofTurbulence, Academic Press, London, 1972.12. B.E. Launder and D.B. Spalding: Comput. MethodsAppL Mech.Eng., 1974, vol. 3, pp. 269-89.13. E.K. Melvi lle and N.C. Bray: Int. J. HeatMass Transfer, 1979,vol. 22, pp. 647-56.14. C.T. Crowe, M.P. Sharma, and D.E. Stock: J. Fluids Eng., Trans.ASME, 1977, pp. 325-32.15. P.J. Smi th, T.H. Fletche r, and L.D. Smooth: 18th Symp. (Int.)on Combustion, The Combustion Institute, Pittsburgh, PA, 1981,pp. 1285-93.16. A.S. Abbas, S.S. Koussa , and F.C. Lockwood: 18th Symp. (Int.)on Combustion, The Combusti on Institute, Pittsburgh, PA, 1981,pp. 1427-37.17. T.H. Fletcher: Ph.D. Dissertation, Brigham Young University,Provo, UT, 1983.18. Y.B. Hahn and H.Y. Sohn: Metall. Trans. B, 1990, vol. 00B,pp. 959-66.

19. P.C. Chaubal: Ph.D. Dissertation, University of Utah, Salt LakeCity, UT, 1986.20. P.C. Chaubal and H_Y. Sohn: University of Utah, Salt Lake City,UT, unpublished research, 1987.21. P.C. Chaubal and H.Y. Sohn: Metall. Trans. B, 1986, vol. 17B,pp. 51-60.22. J.E. Dutrizac: Can. Mineral., 1976, vol. 14, pp. 172-81.23. F.R.A. Jorgensen: Proc. Australas. Inst. Min. Metall., 1983,vol. 288, pp. 37-46.24. R.B. Bird, W.E. Stewart, and E.N. Lightfoot: TransportPhenomena, John Wiley & Sons, Inc., New York, NY, 1960,p. 647.25. T. Kumura, Y. Ojima, Y. Moil, and Y. Ishii: The ReinhardtSchumann Int . Syrup. on Innovative Technology and Reac torDesign in Extraction Metallurgy, D.R. Gaskell, J.P. Hager, J.E.Hoffmann, and P.J. Mackey, eds., TMS-AIME, Warrendale, PA,1986, pp. 403-18.26. E. Partelpoeg: Flash Reaction Processes, Proc. of a Center forPyrometallurgy Conf., University of Utah, Salt Lake City, UT,June 15-17, 1988, D.G .C. Robertson, H.Y. Sohn, and N.J.Themeli s, eds., Center for Pyrometallurgy, University of Missour i-Rolla, Rolla, MO, 1988, pp. 35-45.27. E.E. Khalil, D.B. Spalding, and J.H. Whitelaw: Int. J. Heat MassTransfer, 1975, vol. 18, pp. 775-90.28. P.J. Smith: Ph.D. Dissertation, Brigham Young University, Provo,UT, 1979.29. P.J. Smith: Brigham Young University, Provo, UT, personalcommunication, Nov. 1987.30. A.D. Gosman and W.M. Pun: Lecture Notes for Course Entitled"Calculation of Recirculating Flows," Imperial College, London,1973.31. S.V. Patankar: Numerical Heat Transfer and Fluid FIow, McGraw-Hill , New York, NY, 1980, pp. 79-135.32. J. Asteljoki: Outokumpu Oy, Pori, Finland, personalcommunication, Feb. 1987.33. J. Makinen: Outokumpu Oy, Harjavalta, Finland, personalcommunication, Feb. 1987.34. N. Kemori, Y. Ojima, and Y. Kondo: Flash Reaction Processes,Proc. of a Center for Pyrometallurgy Conf., University of Utah,Salt Lake City, UT, June 15-1 7, 1988, D.G.C. Robertson, H.Y.Sohn, and N.J. Themelis, eds., Center for Pyrometallurgy,University of Missou il- Roll a, Rolla, MO, 1988, pp. 47-68.

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