Non-Topochemical reduction of iron oxides
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h y d r o g e n r e d u c t i o n of n a t u r a l and s y n t h e t i c h e m a t i t e , T u r k d o g a n and V i n t e r s 9 c o n c l u d e d t h a t the r a t e p r o c e s s e s involved a r e f a r m o r e c o m p l e x than t h o s e r e a l i z e d b y p r e v i o u s i n v e s t i g a t o r s . Depending on the t e m p e r a t u r e , p a r t i c l e s i z e and p o r o s i t y , and the l e v e l of r e d u c t i o n , t h r e e b a s i c r a t e p r o c e s s e s - u n i f o r m i n t e r n a l r e d u c t i o n , l i m i t i n g m i x e d c o n t r o l (diffusion in the p o r e s and r e a c t i o n on p o r e w a l l s ) , and g a s diffusion in r e d u c e d i r o n l a y e r , m a y c o n t r o l the r a t e of r e duction i n d i v i d u a l l y o r c o l l e c t i v e l y . Since a t , p , c h e m i c a l m o d e l d o e s not a c c u r a t e l y d e s c r i b e r e d u c t i o n in p o r o u s p a r t i c l e s o r at low t e m p e r a t u r e s , e f f o r t s have b e e n m a d e b y s e v e r a l w o r k e r s to develop more comprehensive models. B , w e n and Cheng 1~ p r o p o s e d a m o d e l which a l l o w s r e a c t i o n to t a k e p l a c e in a n a r r o w zone of a r b i t r a r y width o v e r which the c o n c e n t r a t i o n g r a d i e n t is a s s u m e d c o n s t a n t . No a n a l y s i s was m a d e of a n y e x p e r i m e n t a l d a t a . I s h i d a and Wen 1''t2 d e v e l o p e d a g e n e r a l i z e d m o d e l which r e d u c e s to a f o p , c h e m i c a l m o d e l when d i f f u s i o n is c o n t r o l l i n g and to h o m o g e n e o u s r e a c t i o n when c h e m i c a l k i n e t i c s is c o n t r o l l i n g . T h e i r m o d e l was r e s t r i c t e d to a s i n g l e , i s o t h e r m a l , f i r s t - o r d e r , i r r e v e r s i b l e r e a c tion with q u a s i - s t e a d y s t a t e f o r the g a s p h a s e and p a r t i c l e s of c o n s t a n t s i z e , p o r o s i t y , and e f f e c t i v e d i f f u s i v ity. S z e k e l y and E v a n s ~3'~4 f o r m u l a t e d a n o n - t , p , c h e m i c a l m o d e l b y a s s u m i n g that a p o r o u s p a r t i c l e c o n s i s t s of n u m e r o u s d e n s e s p h e r i c a l s u b p a r t i c l e s of i d e n t i c a l s i z e which r e a c t f o p , c h e m i c a l l y on a m i c r o s c o p i c s c a l e . T h i s m o d e l , l i m i t e d to a s i n g l e r e a c t i o n o c c u r r i n g in a p a r t i c l e of c o n s t a n t s i z e with d e n s e s p h e r i c a l s u b p a r t i c l e s of unchanging s i z e , was s u c c e s s f u l l y a p p l i e d to the r e d u c t i o n of n i c k e l oxide with h y d r o g e n b e l o w 620~ Above 620~ t h i s m o d e l p r e d i c t e d r e d u c t i o n r a t e s much g r e a t e r than o b s e r v e d . F r o m p r e d i c t i o n s of m o d e l s such a s t h o s e j u s t o u t l i n e d it is o b s e r v e d that f o p , c h e m i c a l r e a c t i o n o c c u r s in a p o r o u s p a r t i c l e only if d i f f u s i o n c o n t r
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