51 Diffusion of Carbon Dioxide in Type 5A Molecular Sieve Downloaded by NANYANG TECHNOLOGICAL UNIV on June 4, 2016 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch051
R. W. H. S A R G E N T and C. J. WHITFORD Imperial College, London, England
The self-diffusion of carbon dioxide in single pellets of commercial type 5A molecular sieve has been studied using C O 14
2
as a tracer. Experiments were carried out at atmos-
pheric pressure between
+25°
and
-25°C.
Using a simple
model of the pellet structure, it was possible to deduce effective diffusivities for both pore and crystal diffusion. Ordinary gas diffusion occurs in the pores; crystal diffusivities have values of the order of 10
-11
cm /sec. 2
Diffusion in porous pellets is often the rate-limiting process in industrial adsorption or catalytic processes. Much useful work in thisfieldhas been done by Smith and coworkers (3, 5), but for molecular sieve pellets the situation is complicated by diffusion in the zeolite crystal itself, as well as through the pores formed between the crystals. Few studies have been made of zeolite crystal diffusion, but Barrer and Brook (1) reported some results on diffusion of simple gases in various cation-substituted mordenites, and Wilson (7) gives some indirect results from the study of separation of C O from air using afixedbed of type 4A zeolite pellets. In the present work, results have been obtained by studying self-diffusion of CO2 in a single pellet of type 5A zeolite under controlled conditions. The experimental results were fitted satisfactorily by a very simplified model of the pellet structure, which made it possible to deduce approximate values of the self-diffusion coefficients for both pore and crystal diffusion. 2
Experimental Apparatus and Procedure Full details of the experimental work are given by Whitford (6), and a diagram of the diffusion cell arrangement is shown in Figure 1. Commercial 1/8-inch diameter pellets were selected from a batch to fit 155
Flanigen and Sand; Molecular Sieve Zeolites-II Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
156
MOLECULAR
SIEVE
ZEOLITES
II
C02/C 02 ,4
M A
/ / / / ^CRYOSTAT LID / / /
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ACETONE LEVEL
THERMOCOUPLE
SIEVE PELLET
GLASS SPACING ROD
HEATER ACETONE LEVEL DURING REGENERATION Figure 1.
Schematic arrangement of the diffusion cell
t i g h t l y i n t o a V i r i d i a tube, c l o s e d at o n e e n d w i t h t h e squared-off e n d of t h e p e l l e t flush w i t h t h e other o p e n e n d . T h i s t u b e w a s i n t u r n a close fit i n t h e c l o s e d s i d e - a r m o f a c a p i l l a r y t u b e T - p i e c e , w i t h t h e e n d of t h e p e l l e t a g a i n flush w i t h t h e m o u t h o f t h e s i d e - a r m . T h e s i d e - a r m w a s w o u n d w i t h a n electric heater f o r degassing t h e pellet. T h e t h r o u g h section o f t h e T - p i e c e w a s c o n n e c t e d at its i n l e t t o t h e gas p r e p a r a t i o n a n d flow-control system a n d at its outlet t o a s m a l l - v o l u m e s c i n t i l l a t i o n counter. T h i s c o u n t e r u s e d anthracene crystals m o u n t e d o n glass discs a n d v i e w e d b y a p h o t o m u l t i p l i e r ; t h e response t i m e o f t h e c o u n t e r w a s 1.3 nanoseconds. A thermostat b a t h c o u l d b e r a i s e d t o i m m e r s e t h e c o m p l e t e test section d u r i n g a t r i a l , o r l o w e r e d to a l l o w r e g e n e r a t i o n , w i t h out d i s t u r b i n g t h e apparatus o r t h e thermostat t e m p e r a t u r e . A h i g h v a c u u m system m a d e i t p o s s i b l e t o evacuate t h e test section t o 10" m m m e r c u r y absolute, b u t w h e n degassing t h e p e l l e t at temperatures a b o v e 5
Flanigen and Sand; Molecular Sieve Zeolites-II Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
51.
CO in Type 5A Molecular Sieve
SARGENT AND WHITFORD
2
157
3 0 0 ° C , t h e pressure d i d n o t f a l l b e l o w 10" m m ; degassing w a s a s s u m e d to b e c o m p l e t e w h e n these c o n d i t i o n s h a d b e e n m a i n t a i n e d f o r 3 h o u r s . A f t e r degassing, the p e l l e t w a s saturated w i t h C 0 u n d e r t h e d e s i r e d c o n d i t i o n s , the v o l u m e of gas a d m i t t e d b e i n g m e a s u r e d a c c u r a t e l y w i t h a gas burette. A stream of u n l a b e l l e d C 0 w a s passed t h r o u g h t h e test section, a n d b o t h c o u n t rate a n d c u m u l a t i v e c o u n t w e r e r e c o r d e d . A f t e r a b o u t 3 hours i n most cases, the c o u n t rate h a d d r o p p e d to t h e b a c k g r o u n d v a l u e ; t h e thermostat w a s l o w e r e d a n d t h e p e l l e t h e a t e d t o 3 0 0 ° C to e x p e l the r e m a i n i n g gas, w h i c h also w a s c o u n t e d to g i v e a n accurate e n d - p o i n t v a l u e f o r t h e t o t a l a m o u n t s o r b e d a n d to cross-check the i n i t i a l v a l u e . B a c k g r o u n d c o u n t rates w e r e d e t e r m i n e d separately, a n d blank runs were made under identical conditions, b u t w i t h the pellet t u b e r e p l a c e d b y a s o l i d glass b l a n k . T h i s m a d e possible measurements of d e a d space a n d amounts s o r b e d o n glass surfaces, as w e l l as correc t i o n of the start-time to the t i m e at w h i c h u n l a b e l l e d gas a c t u a l l y arrives at the p e l l e t surface. 3
1 4
2
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2
The Pellet Model T h e p e l l e t is saturated w i t h C 0 is r e p l a c e d g r a d u a l l y b y C
1 2
0
2
2
t h r o u g h o u t a test r u n , b u t C
1 4
0
2
b y d i f f u s i o n , first t h r o u g h the " p o r e s , "
or interstices b e t w e e n the crystals a n d b i n d e r , a n d t h e n t h r o u g h the crystals themselves.
T h i s is analogous to t h e s i t u a t i o n i n a fixed-bed a d
s o r p t i o n process, w h e r e t h e crystals are analogous to t h e p o r o u s pellets, except that the transfer process i n the interstices is a d i f f u s i v e flow r a t h e r t h a n a b u l k gas
flow.
Smith (5) considered complex detailed models
for t h e various flow paths i n a fixed-bed process, b u t as there is i n e v i t a b l y some a p p r o x i m a t i o n i n v o l v e d i n d e s c r i b i n g t h e structure of t h e i n t e r stices, a m u c h s i m p l e r a p p r o a c h has b e e n u s e d here. It is a s s u m e d that e a c h c r y s t a l is s u r r o u n d e d c o m p l e t e l y b y gas at a u n i f o r m c o n c e n t r a t i o n , w h i c h means that d i r e c t transfer b e t w e e n crystals is n e g l e c t e d a n d that a l l t h e c r y s t a l surface is accessible to t h e gas. T h e 2 assumptions are s e l f - c o m p e n s a t i n g , b u t o n e c o u l d expect serious errors if there is significant c r y s t a l - b i n d e r a g g l o m e r a t i o n . I t is a s s u m e d f u r t h e r that a l l t h e crystals are u n i f o r m l y - s i z e d spheres, m a i n l y f o r m a t h e m a t i c a l s i m p l i c i t y . O f course, 5 A crystals are i n fact c u b i c , b u t w i t h the corners cut off, so that the s p h e r i c a l a p p r o x i m a t i o n is n o t unreasonable.
The
u n i f o r m size is a m o r e drastic a s s u m p t i o n , w h i c h is d i s c u s s e d b e l o w . T h e d i f f u s i o n processes i n b o t h crystals a n d pores are a s s u m e d to b e g o v e r n e d b y F i c k ' s l a w . F o r t h e pores, a n effective diffu s i v i t y ( D ) is u s e d , w h i c h p
c a n b e r e l a t e d to t h e b u l k gas diffu s i v i t y ( D ) b y t h e r e l a t i o n : G
D, =
( 1 )
w h e r e c is the p e l l e t p o r o s i t y a n d τ is t h e tortuosity. B e c a u s e of t h e s i m -
Flanigen and Sand; Molecular Sieve Zeolites-II Advances in Chemistry; American Chemical Society: Washington, DC, 1971.
158
MOLECULAR
SIEVE
ZEOLITES
p i e g e o m e t r y of the e x p e r i m e n t a l system, p o r e c o n c e n t r a t i o n o n l y w i t h distance (x)
II
( ν ) varies
f r o m the o p e n e n d , a n d f o r self-exchange of C 0
2
there are n o t h e r m a l effects a n d the w h o l e system is i s o t h e r m a l . W i t h these assumptions, the f o l l o w i n g equations describe the system
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P o r e DiflFusion:
Crystal D
i f t l s i
o„,
*
=
„ . (β
+
? £)
(3,
w h e r e : v, w are the concentrations ( m o l e / l i t e r ) of C c r y s t a l phases, r e s p e c t i v e l y ; D ,
D
v
1 2
0
i n the pore and
2
are the c o r r e s p o n d i n g effective d i f -
c
fusivities; t is t i m e ; a n d r is the r a d i a l c o o r d i n a t e i n s i d e a c r y s t a l . It is a s s u m e d that instantaneous t h e r m o d y n a m i c e q u i l i b r i u m exists at the c r y s t a l surface, a n d that b o t h C
1 2
0
and C
2
1 4
0
h a v e the same
2
equilibrium isotherm P o r e - c r y s t a l surface:
(w)
r=
= Kv
R
(4)
w h e r e Κ is a constant o b t a i n e d f r o m the e q u i l i b r i u m i s o t h e r m . T h e r e is, of course, s y m m e t r y at the center of the c r y s t a l t >
0
(dw/dr)
r
=
=
0
0
(5)
= 0
(6)
v
(7)
T h e 2 b o u n d a r y c o n d i t i o n s for the pores are Closed end:
t >
Open end:
0
(dv/dx) = x
t >
0
(v) = x
L
0
=
0
w h e r e v is the m o l a r d e n s i t y ( m o l e / l i t e r ) of C 0
I n i t i a l l y the p e l l e t contains n o C At t =
0: ν =
1 2
0
u n d e r test c o n d i t i o n s .
2
0 , so w e h a v e
1 2
2
0, 0 < χ < L, w =
0, 0 < r
