Pore diffusion-limited metallurgical extraction from ground ore particles
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h y d r o m e t a l l u r g i c a l and v a p o m e t a l l u r g i c a l p r o c e s s e s often involve o r e s that have been p r e v i o u s l y ground, with the p r o c e s s feed l i m i t e d to a c l a s s i f i e r u n d e r s i z e . When the v a l u a b l e m i n e r a l is s u b s t a n t i a l l y l i b e r a t e d , the c h e m i c a l r e a c t i o n is likely to o c c u r on the p a r t i c l e s u r f a c e and the p a r t i c l e core will s h r i n k as the r e a c t i o n p r o c e e d s . If the c h e m i c a l r e a c t i o n p r o d u c t s a r e solid m a t e r i a l s then a solid shell, u s u ally p o r o u s , will f o r m a r o u n d the s h r i n k i n g c o r e . This is known as the c o r e - s h e l l or t o p o c h e m i c a l r e a c t i o n model. Using a s p h e r i c a l a p p r o x i m a t i o n for the p a r t i c l e s , equations have b e e n developed to e x p r e s s the 9 extent of c h e m i c a l c o n v e r s i o n of the p a r t i c l e , d e p e n d ing on which one of the following p r o c e s s or m a s s t r a n s p o r t steps is r a t e c o n t r o l l i n g : 1 1) c h e m i c a l r e a c tion at the p a r t i c l e s u r f a c e , 2) diffusion t h r o u g h the t h i c k e n i n g r e a c t i o n p r o d u c t shell, or 3) m a s s t r a n s port through a fluid b o u n d a r y l a y e r s u r r o u n d i n g the p a r t i c l e . P e t e r s and S k r i v a n e k 2 have t r e a t e d b o u n d a r y l a y e r t r a n s p o r t c o n t r o l l e d p r o c e s s e s with a p a r t i c l e size d i s t r i b u t i o n in c o n j u n c t i o n with batch leaching. In a p r e v i o u s p a p e r 3 t h e s e equations were coupled with the G a t e s - G a u d i n - S c h u h m a n n equation 4,s d e s c r i b i n g the d i s t r i b u t i o n of p a r t i c l e s i z e s r e s u l t i n g f r o m c o m m i n u t i o n of r o c k s and other b r i t t l e solids to develop r e a c t i o n y i e l d c u r v e s e x p r e s s i n g the weight f r a c t i o n of m e t a l or other v a l u a b l e component of the feed that was c h e m i c a l l y c o n v e r t e d as a function of r e s i d e n c e t i m e . T h i s was done for a) batch, b) c o n t i n u o u s plug flow, and c) continuous b a c k - m i x flow (continuous s t i r r e d tank) r e a c t o r s or p r o c e s s v e s s e l s . To make the c u r v e s of g e n e r a l r a t h e r than s p e c i a l u t i l i t y , the r e s i d e n c e t i m e ( a v e r a g e r e s i d e n c e t i m e for b a c k - m i x r e a c t o r s ) was n o r m a l i z e d to a d i m e n s i o n l e s s t i m e by dividing by the t i m e r e q u i r e d to c o m p l e t e l y c h e m i c a l l y c o n v e r t the l a r g e s t p a r t i c l e in the feed to r e a c t i o n p r o d u c t s . This l a t t e r t i m e , T., depends on the k i n e t i c or t r a n s p o r t c o e f f i c i e n t s of the r a t e - d e t e r m i n i n g step, which m u s t be d e t e r m i n e d in the l a b o r a t o r y for each case, an~i the r a d i
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