Oxidation kinetic studies of zinc sulfide in a fluidized bed reactor
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DEVEIX)PMENT OF A MATHEMATICAL MODEL In a fluidized bed, gas is p a s s e d upward through a bed of solids at a rate high enough so that all the p a r t i c l e s a r e suspended. By e x a m i n a t i o n it has b e e n s e e n that the bed i s not homogeneous. Gas p e r c o l a t e s through K. NATESAN, formerly St. Joseph Lead Fellow, Department of Metallurgy and Materials Science, Carnegie-MellonUniversity, Pittsburgh, Pa., is at Argonne National Laboratory, Argonne, I11. W.O. PHILBROOK is Professor of Metallurgy and Materials Science, Carnegie-MellonUniversity. This paper is based on a thesis submitted by K. NATESANin partial fulfuUment of the requirements for the degree of Doctor of Philosophy in Metallurgy and Materials Science at CarnegieMellon University. Manuscript submitted May 12, 1969. METALLURGICALTRANSACTIONS
the solid and a l s o b u b b l e s up through the bed with little contacting of s o l i d s , while the s o l i d s move about in j e r k y t u r b u l e n t motion. In n o n c a t a l y t i c g a s - s o l i d r e a c t i o n s in which the c o n v e r s i o n of solid is of p r i m a r y i n t e r e s t , lack of i n f o r m a t i o n on the path of the c o n t a c t i n g gas through the bed is not c r i t i c a l . T h u s , the model to be p r o p o s e d will c o n c e n t r a t e p r i m a r i l y on the m e c h a n i s m s of solids c o n v e r s i o n . In a batch fluidized bed p r o c e s s , a l l the p a r t i c l e s m a y be a s s u m e d to undergo r e a c t i o n in the s a m e m a n n e r , but s t i l l the g e n e r a l equation for the d e g r e e of c o n v e r s i o n with time should i n c o r p o r a t e the change in the free oxygen c o n c e n t r a t i o n in the bulk gas phase with t i m e . As the r e a c t i o n p r o c e e d s , oxygen gas is c o n s u m e d and sulfur dioxide gas is g e n e r a t e d ; t h u s , the actual c o n c e n t r a t i o n of free oxygen is not only a function of axial position of the r e a c t o r but a l s o of t i m e of r e a c t i o n . In such a p r o c e s s it b e c o m e s n e c e s s a r y to write the m a t e r i a l b a l a n c e equations for v a r i o u s c o m ponents of the s y s t e m . A s c h e m a t i c d i a g r a m of the r e a c t o r is shown in Fig. l(a). C o n s i d e r a d i f f e r e n t i a l e l e m e n t of height 5z. The p r i m a r y t e r m s in the continuity e q u a t i o n for oxygen are* *Allnomenclatureis definedat the end of the paper.
O(uc) Oz
+
8c 8 (_ 8~) ~-[ + ~ Ez
+ y =0
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bulk a c c u m u l a t i o n eddy consumption convection diffusion by r e a c t i o n A s i m i l a r equation n e e d s to be w r i t t e n for the solid phase s i n c e it p a r t i c i p a t e s in oxygen exchange, and the r e s u l t i n g e q u a t i o n s m u s t be solved s i m u l t a n e o u s l y . In the c a s e of fluidized b e d s having s m a l l (L/D t) r a t i o s and o p e r a t i n g at a m a s s v e l o c i t y higher than that n e c e s s a r y for m i n i m u m f l u i d i z a t i o n , it i
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