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of 16,000 c c / m i n as is i l l u s t r a t e d i n F i g . 1. The effect of p o r e diffusion was difficult to e l i m i n a t e in spite of v e r y thin p e l l e t u s e d . F o r this r e a s o n , the c h e m i cal r a t e c o n s t a n t was deduced f r o m the m e a s u r e m e n t s of the i n i t i a l r a t e , when the c o n t r i b u t i o n of p o r e diff u s i o n was at its m i n i m u m . The i n t e r p r e t a t i o n of the r a t e data was c a r r i e d out u s i n g the g r a i n model. 9':~ If we a s s u m e f i r s t o r d e r r e a c t i o n , s l a b l i k e g e o m e t r y for the d i s k (which is r e a s o n a b l e , b e c a u s e of the s m a l l v a l u e of the r a t i o : t h i c k n e s s / d i a m e t e r ) and p o s t u l a t e , f u r t h e r m o r e , that the g r a i n s a r e s p h e r i c a l in shape, the c o n s e r v a t i o n e q u a t i o n s d e s c r i b i n g the s y s t e m m a y be w r i t t e n as: d2Cco De CO = dR 2

3 ( 1 - E)k (___~iO)2 Cco rNiO

= 0.

[1]*

*For the definitionof the symbolssee the nomenclature. Since i n i t i a l l y r = ~'NiO, at the i n i t i a l stage we m a y r e w r i t e Eq. [1 ] in the following f o r m :

d2Cco I' 3 ( 1 - e ) k ~ , ~ dR2 = \DeCOrNio]~CO.

[2]

The c o n s e r v a t i o n of the s o l i d r e a c t a n t is w r i t t e n a s :

dr

--PNiO ~t- = k CCO.

[3]

T h e i n i t i a l and b o u n d a r y c o n d i t i o n s a r e given a s : At t = 0, r = rNi O.

[4]

At R = Rp, CCO = CCOs.

[5a]

dC CO AtR : 0,~=0.

[5b]

In the i n t e r p r e t a t i o n of the m e a s u r e m e n t s it i s conv e n i e n t to use ~, the e f f e c t i v e n e s s f a c t o r , which is f r e q u e n t l y e m p l o y e d i n h e t e r o g e n e o u s c a t a l y s i s .:2 In e s s e n c e the e f f e c t i v e n e s s f a c t o r d e s i g n a t e s the f r a c t i o n of the t o t a l s u r f a c e a r e a within the p o r o u s solid which p a r t i c i p a t e s in the r e a c t i o n . When the o v e r a l l r a t e i s c h e m i c a l l y c o n t r o l l e d , ~ = 1; when diffusion c o n t r i b u t e s to the o v e r a l l r e s i s t a n c e , ~ < 1. It was found that the v a l u e of b, g a s - s o l i d r e a c t i o n modulus,

~r -~ Rp

[6]

2 Deco rNi O

p l a y s an i m p o r t a n t r o l e in d e t e r m i n i n g the c o n t r o l l i n g r a t e m e c h a n i s m . 11 When ~ < 0.3 the r e a c t i o n i s l a r g e l y c h e m i c a l l y controlled; when ~ > 3, the o v e r a l l r a t e is l a r g e l y diffusion c o n t r o l l e d . It is s e e n i n F i g . 6.7 of Ref. 12 that when ~ < 1/2, i t s v a l u e m a y be a p p r o x i m a t e d by the following r e l a tionship: 1

J. SZEKELY,formerlyProfessorof ChemicalEngineering,State Universityof NewYorkat Buffalo,Buffalo,NewYorkis presentlyProfessorof MaterialsEngineering,Departmentof MaterialsScienceand Engineering,MassachusettsInstitute of Technology,Cambridge,MA. 02139. C.I. LtN, formerlyGraduate Student,Departmentof ChemicalEngineering,State Universityof New York