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Experimental studies using a single pellet high temperature diffusion cell reactor
Thermochimica Acta, 45 ( 1 9 8 1 ) 2 3 3 - - 2 4 3 Elsevier S c i e n t i f i c P u b l i s h i n g C o m p a n y , A m s t e r d a m - - P r i n t e d in B e l g i u m
233
EXPERIMENTAL STUDIES USING A SINGLE PELLET HIGH TEMPERATURE DIFFUSION CELL REACTOR
T E V F I K B A R D A K C I * a n d L A R R Y L. G A S N E R
Department o f Chemical Engineering, University o f Maryland, College Park, MD 20742
(U.S.A.) (Received 2 October 1980)
ABSTRACT I t is v e r y i m p o r t a n t t o k n o w t h e e f f e c t i v e diffusivities o f r e a c t a n t gases t h r o u g h t h e p o r o u s solid m a t r i c e s f o r a d i f f u s i o n l i m i t e d r e a c t i o n . T h e single pellet high t e m p e r a t u r e d i f f u s i o n cell r e a c t o r is used t o m e a s u r e t h e e f f e c t i v e diffusivities o f a r g o n a n d n i t r o g e n d u r i n g t h e s e q u e n c e o f c a l c i n a t i o n , sintering, salt a d d i t i o n a n d s u l f a t i o n o f G r e e r limes t o n e . This s y s t e m c a n be used t o s t u d y t h e gas--solid r e a c t i o n s y s t e m s w h e r e t h e solid
INTRODUCTION
T h e m o s t c o m m o n m e t h o d o f m e a s u r i n g c o u n t e r - d i f f u s i o n o f gases in p o r o u s solids has b e e n b y a s t e a d y - s t a t e t e c h n i q u e first u s e d b y Wick e a n d K a l l e n b a c h [1] a n d m o d i f i e d b y Weisz a n d S c h w a r t z [2] a n d W a k a o a n d S m i t h [ S ] . T w o p u r e gases f l o w past t w o sides o f a t h i n p e l l e t o f experim e n t a l m a t e r i a l . T h e c o u n t e r - d i f f u s i o n fluxes o f t h e t w o gases t h r o u g h t h e pellet are m e a s u r e d f r o m t h e c o m p o s i t i o n o f t h e gas exit s t r e a m s o n e a c h side o f t h e d i f f u s i o n cell. T h e p r e s s u r e g r a d i e n t across t h e p e l l e t m u s t b e m a i n t a i n e d at zero. F o r m e r l y , e x p e r i m e n t s w e r e c a r r i e d o u t at t e m p e r a t u r e s as h i g h as 3 0 0 ° C [ 4 ] . A n e w c o m p u t e r i z e d a d v a n c e d design a p p a r a t u s has b e e n d e v e l o p e d t o o b t a i n d i f f u s i o n d a t a o f gases w h i l e i n t e r n a l s t r u c t u r a l c h a n g e s are t a k i n g p l a c e w i t h i n t h e p o r o u s m a t r i x . Changes in gas effectiv e d i f f u s i v i t y d u e t o sintering o f t h e solid m a t r i x i n c l u d i n g t h e relative effects o f m a c r o p o r o s i t y a n d m i c r o p o r o s i t y c a n be d e t e r m i n e d . T h e t e m p e r a t u r e range o v e r w h i c h m e a s u r e m e n t s c a n b e e f f e c t i v e l y m a d e has b e e n e x t e n d e d t o b e t w e e n 1 0 0 0 a n d 1 2 0 0 ° C . S t r u c t u r a l c h a n g e s o c c u r r i n g d u r i n g c h e m i c a l r e a c t i o n c a n be f o l l o w e d s i m u l t a n e o u s l y w i t h t h e e x t e n t o f r e a c t i o n . This i n f o r m a t i o n is part i c u l a r l y v a l u a b l e w h e r e gaseous r e a c t a n t s are d e p o s i t e d in t h e p o r o u s m a t r i x as a f u n c t i o n o f r e a c t i o n e x t e n t a n d r e s u l t in a c h a n g e in s t r u c t u r e . Macrop o r e vs. m i c r o p o r e e f f e c t s c a n b e d e t e r m i n e d b y s e p a r a t e l y m e a s u r i n g t h e K n u d s e n a n d t h e b u l k e f f e c t i ve diffusivities, o b t a i n e d b y m e a s u r i n g s y s t e m p a r a m e t e r s at t w o d i f f e r e n t pressures. * Present address: Catholic University of America, Washington, DC, U.S.A. 0040-6031/81/0000--0000/$02.50 © 1 9 8 1 Elsevier ScientificPublishing C o m p a n y
234 EXPERIMENTAL
APPARATUS
A d i a m o n d coring drill bit is used to m a k e a Greer l i m e s t o n e c y l i n d e r w h i c h has a d i a m e t e r o f 0.75 in. This c y l i n d e r is c u t w i t h a c a r b o r u n d u m saw t o give 0.125 in. t h i c k pellets. T h e pellet is m o u n t e d in t h e single pellet high t e m p e r a t u r e diffusion cell (see Fig. 1) w i t h Sauereisen h i g h t e m p e r a t u r e cement. T h e flow c h a r t o f t h e a u t o m a t e d e x p e r i m e n t is s h o w n in Fig. 2 a n d t h e flow sheet o f t h e logical c o n t r o l l e d o p e r a t i o n in Fig. 3. D i f f e r e n t parts o f t h e e x p e r i m e n t are s h o w n in Figs. 4--6. T h e N2 a n d Ar are supplied in h i g h pressure cylinders. T h e pressure regulator, P R 1, reduces t h e stremrn pressure to a b o u t 45 psig. T h e o t h e r pressure regulator, P R 2, f u r t h e r reduces the N2 pressure to a b o u t 5 psig. Dtu-ing l o w pressure o p e r a t i o n s , t h e pressure in t h e d i f f u s i o n cell is d e t e r m i n e d b y P R 2. W h e n h i g h pressure o p e r a t i o n is perf o r m e d , t h e p n e u m a t i c c o n t r o l valve, V1, is o p e n e d , t h e r e b y b y p a s s i n g P R 2 a n d subjecting t h e d i f f u s i o n cell t o t h e pressure d e t e r m i n e d b y P R 1. T h e c h e c k valve, S1, p e r m i t s f l o w in t h e f o r w a r d d i r e c t i o n d u r i n g t h e l o w pressure m o d e b u t stops N~ flowing b a c k to P R 2 d u r i n g t h e h i g h pressure m o d e . T h e o p e n i n g o f t h e c o n t r o l valve, V 1 , is v e r y delicate. A n y rapid c h a n g e in pressure m a y result in d a m a g e to t h e pellet. T h e rate o f valve o p e n i n g is a n e x p o n e n t i a l f u n c t i o n o f time. T h e r e f o r e , t h e valve will o p e n s l o w l y at first a n d t h e n m o r e rapidly. T h e reverse is t r u e for closure o f t h e valve, i.e. at first r a p i d l y a n d t h e n m o r e slowly. T h e d i f f e r e n t i a l pressure b e t w e e n b o t h sides o f t h e pellet is c o n t r o l l e d d u r i n g t h i s cycling. If this d i f f e r e n t i a l pressure ever exceeds 4 in. o f water, t h e a c t i o n o f t h e c o n t r o l valve is immediate~.y reduced. This gives t i m e to equilibrate o n e i t h e r side o f t h e pellet. One o f t h e m a j o r r e q u i r e m e n t s f o r e x p e r i m e n t a l a c c u r a c y is having a zero pres~xre differential b e t w e e n b o t h sides o f t h e pellet. This d i f f e r e n t i a l pressure is m e a s u r e d b y t h e d / p cell, PI 5. PI 5 sends a signal to t h e p n e u m a t i c controller, C I , w h i c h adjusts t h e c o n t r o l valve, V 2 ; a c c o r d i n g l y , t h e upstrem~ pressure is regulated b y P R 3. T h i s pressure is h i g h e r t h a n t h e o p e r a t i n g pressure a n d so a d e q u a t e f l o w t h r o u g h t h e c o n t r o l valve c a n be obtained. The flow rate is determined by using a d/p cell to measure the pressure drop resulting from the flow of the process gas through an orifice. In Fig. 2, PI 1 measures the flow rate of N2, and PI 4 measures that of At. These flow rates are controlled by C2 and C3 pneumatic controllers by making adjustments to control valves V 3 and V4. B y controlling the pressure before NN 2
+° - - a
f / I / t/,/IN
.
NAt Fig. 1. Single pellet high temperature diffusion cell reactor.
(YN2)2 (YAr)2
235 F
V1
,~ N=
PRI
i r
[ {~P12 |, "r I
PR2 $I
'l II
o,,+ ; ,
]---7
r_~_~
.
~--
"
1'1~131
Ii
[
J
IV2 Ar + 02 + S02 or 0 2
I I
r-i--r~,,-,~:~°L, t" "///////
,
,
I
' I
I ,I
II;f
>~=
-
--
bl
,r~ I~4.~ !1I v.... -~---~1
i1~
I
Gas chromatoqraph
I
I-
~°2 "°a'~=er
='xhaust
Fig. 2. F l o w chart of the automated apparatus.
N2 inlet
Ar
Inlet
T I Measure
pressure
t
I
Measure temperature
+ I
t
Computer feedback to control pressure cycling
+ Diffusion cell
Measure differential
I
I
Measure differential pressure
pressure
I Pneumatic • controller
J~ iI
Regulate flow rate
Regulate flow rat~
I
+ Pneumatic controller
H
Measure flow rate +
I
+
Alternate gas flow
i chromatograph ,o+°o,-o,. i ,o+ o F-xhaust
Measure flOW rate
l
H " controller .....
I Measure S02 concentrations
Exhaust
Fig. 3. F l o w sheet o f the logical controlled operations.
236
:¢
Fig. 4. Overall view o f t h e a p p a r a t u s .
,2
F ',
@
".-;:.,
Q
Fig. 5. High t e m p e r a t u r e d i f f u s i o n cell r e a c t o r .
Q
237
\
. - ...f.-
..*
y~
Fig. 6. Open view of the diffusion cell reactor during the experiment. the diffusion cell and the flow rate after the cell, flow rates and the pressure can be changed independently. CI, C 2 and C 3 have proportional and integral action. C l and C 2 should be tuned according to their manual. T h e Am control, C3, should be handled in a different w a y since the An- pressure is also under pneumatic control. T h e flow rate and pressure are interacting. If V 2 is opened to increase the pressure in the diffusion cell the flow rate h~creases. This causes the controller, C8, to close V4, thus pressure increases more. T h e result is that the system tends to oscillate.This can be handled by turning controller C 8 loosely. T h e accurate measurement of pressure is one of the important factors in obtaining accurate results in this experiment. T w o indicators are used to m e a s u r e t h e p r e s s u r e . PI 2 is a d / p cell a n d m e a s u r e s l o w p r e s s u r e s u p t o 2 0 0 in. o f w a t e r . PI 3 is a p n e u m a t i c t r a n s m i t t e r w h i c h m e a s u r e s t h e p r e s s u r e u p t o 7 5 psig. B o t h PI 2 a n d PI 8 m e a s u r e t h e p r e s s u r e in t h e N~_ s t r e a m . T h e A r p r e s s u r e is c a l c u l a t e d f r o m t h e d i f f e r e n t i a l p r e s s u r e m e a s u r e d b y PI 5. T h e t e m p e r a t u r e in t h e cell is m e a s u r e d w i t h c h r o m e l - - a l u m e l t h e r m o couples on either side of the pellet. These thermocouples were placed 2 mm f r o m t h e G r e e t l i m e s t o n e p e l l e t in a n o l d s t y l e d i f f u s i o n cell. T h e y w e r e p l a c e d 5 m m f r o m t h e p e l l e t , in t h e e x i t gas s t r e a m p i p e s , in t h e m o d i f i e d d i f f u s i o n cell. T h e s a l t is l o a d e d in a h a n d m a d e s t a i n l e s s s t e e l sieve b o a t w h i c h is a t t a c h e d t o t h e e n d o f a n a l u m i n u m w i r e . T h e salt b o a t is p l a c e d in a d e a d - e n d o f a T c o n n e c t i o n l o c a t e d o n t h e A r i n l e t s t r e a m a n d o u t s i d e t h e o v e n . W h e n salt a d d i t i o n is d e s i r e d , t h e b o a t is p u s h e d w i t h t h e w i r e u n t i l t h e e n d o f t h e o u t s i d e p i p e is r e a c h e d , t h u s h a v i n g t h e b o a t c l o s e t o t h e p e l l e t .
238 T h e d i f f u s i v i t y calculations require t h e analysis o f t h e N2 a n d a~gon (or O2) s t r e - m s after leaving t h e d i f f u s i o n cell. These are o b t a i n e d b y gas chrom a t o g r a p h y . A t t h e p r o p e r t i m e , t h e c o m p u t e r sends a signal to a fou~-way switch, S10, t o load u p t h e i n j e c t i o n coil w i t h t h e N2 stream. The.N~ stream is passed t h r o u g h t h e i n j e c t i o n coil, sweeping o u t a n y gas r e m a i n i n g f r o m t h e previous sample. W h e n this is c o m p l e t e d , t h e h e l i u m carrier gas is passed t h r o u g h t h e i n j e c t i o n coil, t h u s injecting t h e a m o u n t o f gas c o n t a i n e d in t h e i n j e c t i o n coil. A similar p r o c e d u r e is f o l l o w e d f o r t h e A r stream. F r o m t h e i n j e c t i o n system, t h e "helium carrier gas t a k e s t h e sample d i r e c t l y i n t o t h e c o l u m n . T h e separation of Ar a n d N2 (or O2 a n d N~) is achieved b y using a 5 / ~ m o l e c u l a r sieve c o l u m n . T h e oven is o p e r a t e d a t r o o m t e m p e r a t u r e t o o b t a i n t h e m a x i m u m separation. T h e c o l u m n l e n g t h was 30 ft. I t takes approxim a t e l y , 20 rain to process. T h e areas u n d e r t h e p e a k s are d e t e r m i n e d b y t h e P D P 8 e c o m p u t e r using a variable gain. E f f e c t i v e d i f f u s i v i t y calculations
Nitrogen and argon enter the cell from opposite ends. Let the flow rates be QN2 (cm3 sec-1), and QAr (cm3 sec-1) for nitrogen and argon, respectively. F r o m gas chromatographic results, the volume ratios (or mole ratios) of gases can be calculated at each side of the cell (see Fig. l). If the argon side is analyzed by injecting a sample from this side to the gas chromatograph, first the argon peak will be obtained, followed by the nitrogen peak. If the corrected areas are (AA~)I and (A~2)I, the mole ratio of argon is (Y.~)~ = ( A A ~ ) I / [ ( A A r ) I + (AN2)1]
(1)
a n d t h e m o l e ratio o f n i t r o g e n is (Y~2)1 = ( A ~ 2 ) I / [ ( A A r ) I + (AN2)1]
(2)
When a sample f r o m t h e n i t r o g e n side is injected i n t o t h e gas c h r o m a t o g r a p h , (YA~)2 mud (Y~2)2 Can be calculated as o n t h e a r g o n side. The a m o u n t o f d i f f u s e d argon is (ON2)ou~ X (YA~)2 (cm 3 s e c - ' ) . F r o m a k n o w l e d g e o f t h e r o o m t e m p e r a t u r e a n d pressure, t h e n u m b e r o f moles o f diffused argon c a n be calculated. Since t h e d i f f u s i o n area o f t h e G r e e t limestone pellet is a l r e a d y k n o w n , t h e n u m b e r o f moles o f argon diffused per cm 2 per sec c a n be calculated. NAt
= -- P-~--" O,~+- ( Y A D ~ -- (YA~)~
RT
Ar
(3)
w h e r e Ar is t h e t h i c k n e s s o f t h e pellet in c m a n d NAt is t h e argon m o l a r flux in g moles cm -2 sec -1. T h e m o l a r f l u x ratio, NN2/NA~, is t h e same regardless o f t h e e x t e n t o f t h e K n u d s e n a n d b u l k diffusion. Evans et al. [6] have s h o w n this c o n s t a n t to be -
V
1.19
A correction is m a d e to obtain the right experimental results, i.e.
(4)
239 (NN2)exp + ZkN
(N~)exp -- AN
- 1.194
(5)
A N = [ 1 . 1 9 4 • (NAr)exp - - ( N N 2 ) e x p ] / 2 . 1 9 4
(6)
(NN2)cor" = (NN2)exp + ~
(7)
(NAt)cot"
(8)
(NAr)exp
=
--
~
I n t h e m o d i f i e d d i f f u s i o n cell f o r ( y ~ ) i a n d ( Y ~ ) 2 t h e a r i t h m e t i c m e a n o f t h e i n l e t a n d o u t l e t c o n c e n t r a t i o n s is u s e d , i.e. (y~), _ 0 + (Y~)I 2 '
(YA,)2 - 1 + (YAr)2 2
(9)
This r e p r e s e n t s t h e d r i v i n g f o r c e w e l l . (De)N2 a n d (De)A~ w i l l b e c a l c u l a t e d f o r 1 a n d 4 a t m . T h e b u l k d i f f u s i v i t y is d e p e n d e n t o n p r e s s u r e , w h e r e a s t h e K n u d s e n d f f f u s i v i t y is n o t w h e n t h e m e a n f r e e p a t h d o e s n o t c h a n g e . T h e C h a p m a n e q u a t i o n is
T312(I/MA~ (DAr_N2)Bul k = 0 . 0 0 1 8 5 8 8
(DAr)Knud.~en The
re
mean
pore
~
radius
can
I/MN:) I12
r
-
Sg
(10) (II)
be defined
as
20
2Vg =
• re - T~A
9700
=
+
Pc " o2;~-N2 " &"~Ar--N2
(12)
Sgpp
w h e r e 8 is t h e p o r o s i t y , Sg is t o t a l s u r f a c e a r e a in c m 2 g-*, a n d pp is t h e average p e l l e t d e n s i t y in g c m -3. S u b s t i t u t i n g e q n . ( 1 2 ) in e q n . ( 1 1 ) , t h e K n u d s e n diffusion coefficient for a porous pellet becomes
(DAr)K,e _ D E " 0
r
_
62
19 4 0 0
rSgpp
T~Ar
(13)
or 9 7 0 0 ~:• re • e V-M-? - -.-,, ~
(D~)K,e
=
(De)~ =
1 (1 - - YAr)/(D~--N2)e + [ ( I / D A r ) K , e ]
where a = 1 +
(14)
(15)
NN~/NAz.
B o s a n q u e t [ 7 ] s h o w e d t h e r e is n o s i g n i f i c a n t d i f f e r e n c e b e t w e e n t h e (De) ~ w h i c h w e r e o b t a i n e d f r o m e q n . ( 1 5 ) a n d t h e e q u a t i o n g i v e n b e l o w . 1
_
(D,)~
l--aylr
[D(~-N2~],
~
1
(16)
(D.~)K,,
L e t us w r i t e e q n . ( 1 6 ) f o r P2 a r m a n d P l a t m o s p h e r e a b s o l u t e p r e s s u r e s i
(De,At)p2
_
1 -- ~YA~
[D(~,N~),e] p2
+
1
[(DAr)K,e]p2
(17)
240 1
(De,t-~)pl
-
1 -- ~ y ~ 1 + [D(~,Nz)~]p i [(D~)z,e]p,
1 [(DAr)K.e]p~.
=
[D(A~,N2),e]p2 =
(18)
1 [(DAr)K.e]p 1
(19)
(Pl/P2) [D(A~--N2),e]pI
(20)
S u b t r a c t i n g eqn. (18) f r o m eqn. (17) a n d s u b s t i t u t i n g eqns. (19) a n d (20) gives
yh~)(p2--p~/~
I
\
i
]
(Do. ) IJ
(21)
( D e . ~ ) , 2 , a n d (De.A~)p, are k n o w n . [(DAr.N2)e]p~, t h e effective b u l k diffusivity of -At at 1 arm can be calculated from eqn. (21). B y substituting this value in eqn. (18), [(DA~)K,e]p~ can be found. The temperature and molecular weight of argon are known• If the porosity and tortuosity are known, the average pore radius can be calculated from eqn. (14)• (DA~--N~) Can be calculated from eqn (I0), and [(DA~--N )e]Pl is obtained from the experimental results. F r o m the following equatmn the tortuosit~, T, will be found [(D(Ar--N2)e]Pl = (DAr--N2)Pl •-r
(22)
r = (DAr--~-2)pl " e/[(DAr.~2)e]pl
(Ts)
a n d t h e p o r o s i t y will be f o u n d f r o m t h e a m o u n t o f e v o l v e d C02• W h e n t h e p o r o s i t y a n d t o r t u o s i t y are k n o w n , t h e m e a n p o r e size can b e calctflated f r o m eqn. (24) (DA~)K.e " r l M/-M-~ re=
9-- 6 :
V
(24)
F r o m eqn. (3), t h e e x p e r i m e n t a l effective diffusivity o f argon is (De~)A~ = "--(NA~)eor. " RT" A / [ p " ((Y~)2 - - (YA~)I)]
(25)
(De~)N2 will be c a l c u l a t e d in t h e same way.
SAMPLE R U N t i n e x p e r i m e n t at 8 4 3 ° C is carried o u t for 110 h (see Fig. 7). T h e diffusivity of argon and nitrogen is increased as a function of calcination time. After 45 h of calcination~ a salt boat is pushed close to the pellet. The salt vapor is allowed to open up the pores. The diffusivity of gases is increased. After 74.9 h of calcination, the sulfation is s t Y . Instead of argon, 540 p p m SO2 and 1.02% 02 in argon is used. The diffusivity of argon and nitrogen is
241 I
l
I
I
1
I
I
O DN2
0.16
OAr • DN= (High pressure) • DAr (High ]oressure)
m
~
O
0
0-12
•uE
nO
o
O
O& Z~
i~ o.o8 ~3
ooo A,l.lt.
A ~
0.04
o
I
I
I
4
8
12
l
I
t
I
16 Time, h r
I
I
I
20
24
28
I
I
I
32
DN2
,~- DAr
0.1E
e DN2 (H~gh pressure) • DAr (High pressure) O0
O0 I e3
E012 u
I tA t i
&
4=_
> 0.08 °e e
e oi !
• AA
••&
.%
,I
..°
•AA
I
Satt addition !i
0.04
1 I I
I 36
3:2
I 40
i I 44
I
T=me,
| -
I
t
I
48
I
52
56
i
I
I
60
64
hr
I
I
DN2 A DAr o DN2 (High pressure) & DAr (High pressure)
o
oo
0 . 1 6 -,..o,o--
O.12u
2
008-
Qe
oe &A
~3 o
0.04 Su I f a t i o n is s~ar{ed !
64
68
I
72
t
I
I
i
76
80
84
88
Time, h r
pIi 92
96
242 I
I
I
l
I
I
t
o DN2 DAr o DN2 ( H i g l l pressure) A DAr (High pressure)
016 u
u
0C4
96
a~d,t,=n,i 100
1 104
I 108
I 112 Time,
I~- I I ~ 118
I--120
Q
!--124
128
hr
Fig. 7. D i f f u s i v i t y o f a r g o n a n d n i t r o g e n t h r o u g h c a l c i n e d G r e e r l i m e s t o n e d u r i n g calcin a t i o n , salt a d d i t i o n a n d s u l f a t i o n . T e m p e r a t u r e 8 4 3 . 1 ° C ; r u n n o . C6.
d e c r e a s e d as t h e sulfation r e a c t i o n t a k e s place. T h e r e was n o sulfur d i o x i d e o n t h e N2 steam exit. A t 99.8 h salt is a d d e d t o t h e system; t h e diffusivities are increased again d u r i n g t h e sulfation.
CONCLUSIONS
T h e single p e l l e t h i g h t e m p e r a t u r e d i f f u s i o n cell r e a c t o r can b e u s e d t o m e a s u r e t h e effective diffusivity o f gases t h r o u g h t h e p o r o u s pellets at l o w a n d h i g h t e m p e r a t u r e s ( 2 0 - - 1 2 0 0 ° C ) . T h e c h a n g e in t h e diffusivity o f gases d u e t o t h e c h e m i c a l r e a c t i o n t h a t t a k e s place in t h e p e l l e t can be d e t e r m i n e d durLug t h e r e a c t i o n . T h e effective diffusivity o f gases can also b e d e t e r m i n e d at d i f f e r e n t pressures u p t o 45 psig. F o r a d i f f u s i o n l i m i t e d r e a c t i o n , t h e k n o w l e d g e o f effective diffusivity is o n e o f m a j o r c o n c e r n . T h e single pellet h i g h t e m p e r a t u r e d i f f u s i o n cell can b e u s e d as a v e r y i m p o r t a n t t o o l in measuring t h e diffusivities so t h e r e a c t i o n can b e u n d e r s t o o d a n d m o d e l e d in a better way.
NOMENCLATURE A Def~ M N p Q Ar y
u n i t area u n d e r t h e peaks effective diffusivity o f a gas (cm 2 sec - z ) m o l e c u l a r weight (g) rate o f d i f f u s i o n (g m o l e c m -2 sec - I ) t h e pressure o f t h e gas ( a t m ) t h e f l o w rates ( c m 3 / s e c ) t h e t h i c k n e s s o f t h e pellet ( c m ) t h e m o l e ratio o£ gas
243
REFERENCES 1 2 3 4 5 6 7
E. Wicke and R. Kallenbach, Kolloid-Z., 97 (1941) 135. P.B. WeLsz and A.B. Schwartz~ J. C a t a l , 1 (1962) 399. N. Wakao and J.M. Smith, Chem. Eng. Sci., 17 (1962) 825. D.S. Scott and K.E. Cox, Can. J. Chem. Eng., 3 (1960) 201. T. Bardakci, Ph.D. Thesis, University of Maryland, 1980. R.B. Evans III, G.M. Watson and E.A. Mason, J. Chem. Phys., 35 (1961) 2076. C.H. Bosanquet, Phys. Rev., 73 (1948) 762.
233
EXPERIMENTAL STUDIES USING A SINGLE PELLET HIGH TEMPERATURE DIFFUSION CELL REACTOR
T E V F I K B A R D A K C I * a n d L A R R Y L. G A S N E R
Department o f Chemical Engineering, University o f Maryland, College Park, MD 20742
(U.S.A.) (Received 2 October 1980)
ABSTRACT I t is v e r y i m p o r t a n t t o k n o w t h e e f f e c t i v e diffusivities o f r e a c t a n t gases t h r o u g h t h e p o r o u s solid m a t r i c e s f o r a d i f f u s i o n l i m i t e d r e a c t i o n . T h e single pellet high t e m p e r a t u r e d i f f u s i o n cell r e a c t o r is used t o m e a s u r e t h e e f f e c t i v e diffusivities o f a r g o n a n d n i t r o g e n d u r i n g t h e s e q u e n c e o f c a l c i n a t i o n , sintering, salt a d d i t i o n a n d s u l f a t i o n o f G r e e r limes t o n e . This s y s t e m c a n be used t o s t u d y t h e gas--solid r e a c t i o n s y s t e m s w h e r e t h e solid
INTRODUCTION
T h e m o s t c o m m o n m e t h o d o f m e a s u r i n g c o u n t e r - d i f f u s i o n o f gases in p o r o u s solids has b e e n b y a s t e a d y - s t a t e t e c h n i q u e first u s e d b y Wick e a n d K a l l e n b a c h [1] a n d m o d i f i e d b y Weisz a n d S c h w a r t z [2] a n d W a k a o a n d S m i t h [ S ] . T w o p u r e gases f l o w past t w o sides o f a t h i n p e l l e t o f experim e n t a l m a t e r i a l . T h e c o u n t e r - d i f f u s i o n fluxes o f t h e t w o gases t h r o u g h t h e pellet are m e a s u r e d f r o m t h e c o m p o s i t i o n o f t h e gas exit s t r e a m s o n e a c h side o f t h e d i f f u s i o n cell. T h e p r e s s u r e g r a d i e n t across t h e p e l l e t m u s t b e m a i n t a i n e d at zero. F o r m e r l y , e x p e r i m e n t s w e r e c a r r i e d o u t at t e m p e r a t u r e s as h i g h as 3 0 0 ° C [ 4 ] . A n e w c o m p u t e r i z e d a d v a n c e d design a p p a r a t u s has b e e n d e v e l o p e d t o o b t a i n d i f f u s i o n d a t a o f gases w h i l e i n t e r n a l s t r u c t u r a l c h a n g e s are t a k i n g p l a c e w i t h i n t h e p o r o u s m a t r i x . Changes in gas effectiv e d i f f u s i v i t y d u e t o sintering o f t h e solid m a t r i x i n c l u d i n g t h e relative effects o f m a c r o p o r o s i t y a n d m i c r o p o r o s i t y c a n be d e t e r m i n e d . T h e t e m p e r a t u r e range o v e r w h i c h m e a s u r e m e n t s c a n b e e f f e c t i v e l y m a d e has b e e n e x t e n d e d t o b e t w e e n 1 0 0 0 a n d 1 2 0 0 ° C . S t r u c t u r a l c h a n g e s o c c u r r i n g d u r i n g c h e m i c a l r e a c t i o n c a n be f o l l o w e d s i m u l t a n e o u s l y w i t h t h e e x t e n t o f r e a c t i o n . This i n f o r m a t i o n is part i c u l a r l y v a l u a b l e w h e r e gaseous r e a c t a n t s are d e p o s i t e d in t h e p o r o u s m a t r i x as a f u n c t i o n o f r e a c t i o n e x t e n t a n d r e s u l t in a c h a n g e in s t r u c t u r e . Macrop o r e vs. m i c r o p o r e e f f e c t s c a n b e d e t e r m i n e d b y s e p a r a t e l y m e a s u r i n g t h e K n u d s e n a n d t h e b u l k e f f e c t i ve diffusivities, o b t a i n e d b y m e a s u r i n g s y s t e m p a r a m e t e r s at t w o d i f f e r e n t pressures. * Present address: Catholic University of America, Washington, DC, U.S.A. 0040-6031/81/0000--0000/$02.50 © 1 9 8 1 Elsevier ScientificPublishing C o m p a n y
234 EXPERIMENTAL
APPARATUS
A d i a m o n d coring drill bit is used to m a k e a Greer l i m e s t o n e c y l i n d e r w h i c h has a d i a m e t e r o f 0.75 in. This c y l i n d e r is c u t w i t h a c a r b o r u n d u m saw t o give 0.125 in. t h i c k pellets. T h e pellet is m o u n t e d in t h e single pellet high t e m p e r a t u r e diffusion cell (see Fig. 1) w i t h Sauereisen h i g h t e m p e r a t u r e cement. T h e flow c h a r t o f t h e a u t o m a t e d e x p e r i m e n t is s h o w n in Fig. 2 a n d t h e flow sheet o f t h e logical c o n t r o l l e d o p e r a t i o n in Fig. 3. D i f f e r e n t parts o f t h e e x p e r i m e n t are s h o w n in Figs. 4--6. T h e N2 a n d Ar are supplied in h i g h pressure cylinders. T h e pressure regulator, P R 1, reduces t h e stremrn pressure to a b o u t 45 psig. T h e o t h e r pressure regulator, P R 2, f u r t h e r reduces the N2 pressure to a b o u t 5 psig. Dtu-ing l o w pressure o p e r a t i o n s , t h e pressure in t h e d i f f u s i o n cell is d e t e r m i n e d b y P R 2. W h e n h i g h pressure o p e r a t i o n is perf o r m e d , t h e p n e u m a t i c c o n t r o l valve, V1, is o p e n e d , t h e r e b y b y p a s s i n g P R 2 a n d subjecting t h e d i f f u s i o n cell t o t h e pressure d e t e r m i n e d b y P R 1. T h e c h e c k valve, S1, p e r m i t s f l o w in t h e f o r w a r d d i r e c t i o n d u r i n g t h e l o w pressure m o d e b u t stops N~ flowing b a c k to P R 2 d u r i n g t h e h i g h pressure m o d e . T h e o p e n i n g o f t h e c o n t r o l valve, V 1 , is v e r y delicate. A n y rapid c h a n g e in pressure m a y result in d a m a g e to t h e pellet. T h e rate o f valve o p e n i n g is a n e x p o n e n t i a l f u n c t i o n o f time. T h e r e f o r e , t h e valve will o p e n s l o w l y at first a n d t h e n m o r e rapidly. T h e reverse is t r u e for closure o f t h e valve, i.e. at first r a p i d l y a n d t h e n m o r e slowly. T h e d i f f e r e n t i a l pressure b e t w e e n b o t h sides o f t h e pellet is c o n t r o l l e d d u r i n g t h i s cycling. If this d i f f e r e n t i a l pressure ever exceeds 4 in. o f water, t h e a c t i o n o f t h e c o n t r o l valve is immediate~.y reduced. This gives t i m e to equilibrate o n e i t h e r side o f t h e pellet. One o f t h e m a j o r r e q u i r e m e n t s f o r e x p e r i m e n t a l a c c u r a c y is having a zero pres~xre differential b e t w e e n b o t h sides o f t h e pellet. This d i f f e r e n t i a l pressure is m e a s u r e d b y t h e d / p cell, PI 5. PI 5 sends a signal to t h e p n e u m a t i c controller, C I , w h i c h adjusts t h e c o n t r o l valve, V 2 ; a c c o r d i n g l y , t h e upstrem~ pressure is regulated b y P R 3. T h i s pressure is h i g h e r t h a n t h e o p e r a t i n g pressure a n d so a d e q u a t e f l o w t h r o u g h t h e c o n t r o l valve c a n be obtained. The flow rate is determined by using a d/p cell to measure the pressure drop resulting from the flow of the process gas through an orifice. In Fig. 2, PI 1 measures the flow rate of N2, and PI 4 measures that of At. These flow rates are controlled by C2 and C3 pneumatic controllers by making adjustments to control valves V 3 and V4. B y controlling the pressure before NN 2
f / I / t/,/IN
.
NAt Fig. 1. Single pellet high temperature diffusion cell reactor.
(YN2)2 (YAr)2
235 F
V1
,~ N=
PRI
i r
[ {~P12 |, "r I
PR2 $I
'l II
o,,+ ; ,
]---7
r_~_~
.
~--
"
1'1~131
Ii
[
J
IV2 Ar + 02 + S02 or 0 2
I I
r-i--r~,,-,~:~°L, t" "///////
,
,
I
' I
I ,I
II;f
>~=
-
--
bl
,r~ I~4.~ !1I v.... -~---~1
i1~
I
Gas chromatoqraph
I
I-
~°2 "°a'~=er
='xhaust
Fig. 2. F l o w chart of the automated apparatus.
N2 inlet
Ar
Inlet
T I Measure
pressure
t
I
Measure temperature
+ I
t
Computer feedback to control pressure cycling
+ Diffusion cell
Measure differential
I
I
Measure differential pressure
pressure
I Pneumatic • controller
J~ iI
Regulate flow rate
Regulate flow rat~
I
+ Pneumatic controller
H
Measure flow rate +
I
+
Alternate gas flow
i chromatograph ,o+°o,-o,. i ,o+ o F-xhaust
Measure flOW rate
l
H " controller .....
I Measure S02 concentrations
Exhaust
Fig. 3. F l o w sheet o f the logical controlled operations.
236
:¢
Fig. 4. Overall view o f t h e a p p a r a t u s .
,2
F ',
@
".-;:.,
Q
Fig. 5. High t e m p e r a t u r e d i f f u s i o n cell r e a c t o r .
Q
237
\
. - ...f.-
..*
y~
Fig. 6. Open view of the diffusion cell reactor during the experiment. the diffusion cell and the flow rate after the cell, flow rates and the pressure can be changed independently. CI, C 2 and C 3 have proportional and integral action. C l and C 2 should be tuned according to their manual. T h e Am control, C3, should be handled in a different w a y since the An- pressure is also under pneumatic control. T h e flow rate and pressure are interacting. If V 2 is opened to increase the pressure in the diffusion cell the flow rate h~creases. This causes the controller, C8, to close V4, thus pressure increases more. T h e result is that the system tends to oscillate.This can be handled by turning controller C 8 loosely. T h e accurate measurement of pressure is one of the important factors in obtaining accurate results in this experiment. T w o indicators are used to m e a s u r e t h e p r e s s u r e . PI 2 is a d / p cell a n d m e a s u r e s l o w p r e s s u r e s u p t o 2 0 0 in. o f w a t e r . PI 3 is a p n e u m a t i c t r a n s m i t t e r w h i c h m e a s u r e s t h e p r e s s u r e u p t o 7 5 psig. B o t h PI 2 a n d PI 8 m e a s u r e t h e p r e s s u r e in t h e N~_ s t r e a m . T h e A r p r e s s u r e is c a l c u l a t e d f r o m t h e d i f f e r e n t i a l p r e s s u r e m e a s u r e d b y PI 5. T h e t e m p e r a t u r e in t h e cell is m e a s u r e d w i t h c h r o m e l - - a l u m e l t h e r m o couples on either side of the pellet. These thermocouples were placed 2 mm f r o m t h e G r e e t l i m e s t o n e p e l l e t in a n o l d s t y l e d i f f u s i o n cell. T h e y w e r e p l a c e d 5 m m f r o m t h e p e l l e t , in t h e e x i t gas s t r e a m p i p e s , in t h e m o d i f i e d d i f f u s i o n cell. T h e s a l t is l o a d e d in a h a n d m a d e s t a i n l e s s s t e e l sieve b o a t w h i c h is a t t a c h e d t o t h e e n d o f a n a l u m i n u m w i r e . T h e salt b o a t is p l a c e d in a d e a d - e n d o f a T c o n n e c t i o n l o c a t e d o n t h e A r i n l e t s t r e a m a n d o u t s i d e t h e o v e n . W h e n salt a d d i t i o n is d e s i r e d , t h e b o a t is p u s h e d w i t h t h e w i r e u n t i l t h e e n d o f t h e o u t s i d e p i p e is r e a c h e d , t h u s h a v i n g t h e b o a t c l o s e t o t h e p e l l e t .
238 T h e d i f f u s i v i t y calculations require t h e analysis o f t h e N2 a n d a~gon (or O2) s t r e - m s after leaving t h e d i f f u s i o n cell. These are o b t a i n e d b y gas chrom a t o g r a p h y . A t t h e p r o p e r t i m e , t h e c o m p u t e r sends a signal to a fou~-way switch, S10, t o load u p t h e i n j e c t i o n coil w i t h t h e N2 stream. The.N~ stream is passed t h r o u g h t h e i n j e c t i o n coil, sweeping o u t a n y gas r e m a i n i n g f r o m t h e previous sample. W h e n this is c o m p l e t e d , t h e h e l i u m carrier gas is passed t h r o u g h t h e i n j e c t i o n coil, t h u s injecting t h e a m o u n t o f gas c o n t a i n e d in t h e i n j e c t i o n coil. A similar p r o c e d u r e is f o l l o w e d f o r t h e A r stream. F r o m t h e i n j e c t i o n system, t h e "helium carrier gas t a k e s t h e sample d i r e c t l y i n t o t h e c o l u m n . T h e separation of Ar a n d N2 (or O2 a n d N~) is achieved b y using a 5 / ~ m o l e c u l a r sieve c o l u m n . T h e oven is o p e r a t e d a t r o o m t e m p e r a t u r e t o o b t a i n t h e m a x i m u m separation. T h e c o l u m n l e n g t h was 30 ft. I t takes approxim a t e l y , 20 rain to process. T h e areas u n d e r t h e p e a k s are d e t e r m i n e d b y t h e P D P 8 e c o m p u t e r using a variable gain. E f f e c t i v e d i f f u s i v i t y calculations
Nitrogen and argon enter the cell from opposite ends. Let the flow rates be QN2 (cm3 sec-1), and QAr (cm3 sec-1) for nitrogen and argon, respectively. F r o m gas chromatographic results, the volume ratios (or mole ratios) of gases can be calculated at each side of the cell (see Fig. l). If the argon side is analyzed by injecting a sample from this side to the gas chromatograph, first the argon peak will be obtained, followed by the nitrogen peak. If the corrected areas are (AA~)I and (A~2)I, the mole ratio of argon is (Y.~)~ = ( A A ~ ) I / [ ( A A r ) I + (AN2)1]
(1)
a n d t h e m o l e ratio o f n i t r o g e n is (Y~2)1 = ( A ~ 2 ) I / [ ( A A r ) I + (AN2)1]
(2)
When a sample f r o m t h e n i t r o g e n side is injected i n t o t h e gas c h r o m a t o g r a p h , (YA~)2 mud (Y~2)2 Can be calculated as o n t h e a r g o n side. The a m o u n t o f d i f f u s e d argon is (ON2)ou~ X (YA~)2 (cm 3 s e c - ' ) . F r o m a k n o w l e d g e o f t h e r o o m t e m p e r a t u r e a n d pressure, t h e n u m b e r o f moles o f diffused argon c a n be calculated. Since t h e d i f f u s i o n area o f t h e G r e e t limestone pellet is a l r e a d y k n o w n , t h e n u m b e r o f moles o f argon diffused per cm 2 per sec c a n be calculated. NAt
= -- P-~--" O,~+- ( Y A D ~ -- (YA~)~
RT
Ar
(3)
w h e r e Ar is t h e t h i c k n e s s o f t h e pellet in c m a n d NAt is t h e argon m o l a r flux in g moles cm -2 sec -1. T h e m o l a r f l u x ratio, NN2/NA~, is t h e same regardless o f t h e e x t e n t o f t h e K n u d s e n a n d b u l k diffusion. Evans et al. [6] have s h o w n this c o n s t a n t to be -
V
1.19
A correction is m a d e to obtain the right experimental results, i.e.
(4)
239 (NN2)exp + ZkN
(N~)exp -- AN
- 1.194
(5)
A N = [ 1 . 1 9 4 • (NAr)exp - - ( N N 2 ) e x p ] / 2 . 1 9 4
(6)
(NN2)cor" = (NN2)exp + ~
(7)
(NAt)cot"
(8)
(NAr)exp
=
--
~
I n t h e m o d i f i e d d i f f u s i o n cell f o r ( y ~ ) i a n d ( Y ~ ) 2 t h e a r i t h m e t i c m e a n o f t h e i n l e t a n d o u t l e t c o n c e n t r a t i o n s is u s e d , i.e. (y~), _ 0 + (Y~)I 2 '
(YA,)2 - 1 + (YAr)2 2
(9)
This r e p r e s e n t s t h e d r i v i n g f o r c e w e l l . (De)N2 a n d (De)A~ w i l l b e c a l c u l a t e d f o r 1 a n d 4 a t m . T h e b u l k d i f f u s i v i t y is d e p e n d e n t o n p r e s s u r e , w h e r e a s t h e K n u d s e n d f f f u s i v i t y is n o t w h e n t h e m e a n f r e e p a t h d o e s n o t c h a n g e . T h e C h a p m a n e q u a t i o n is
T312(I/MA~ (DAr_N2)Bul k = 0 . 0 0 1 8 5 8 8
(DAr)Knud.~en The
re
mean
pore
~
radius
can
I/MN:) I12
r
-
Sg
(10) (II)
be defined
as
20
2Vg =
• re - T~A
9700
=
+
Pc " o2;~-N2 " &"~Ar--N2
(12)
Sgpp
w h e r e 8 is t h e p o r o s i t y , Sg is t o t a l s u r f a c e a r e a in c m 2 g-*, a n d pp is t h e average p e l l e t d e n s i t y in g c m -3. S u b s t i t u t i n g e q n . ( 1 2 ) in e q n . ( 1 1 ) , t h e K n u d s e n diffusion coefficient for a porous pellet becomes
(DAr)K,e _ D E " 0
r
_
62
19 4 0 0
rSgpp
T~Ar
(13)
or 9 7 0 0 ~:• re • e V-M-? - -.-,, ~
(D~)K,e
=
(De)~ =
1 (1 - - YAr)/(D~--N2)e + [ ( I / D A r ) K , e ]
where a = 1 +
(14)
(15)
NN~/NAz.
B o s a n q u e t [ 7 ] s h o w e d t h e r e is n o s i g n i f i c a n t d i f f e r e n c e b e t w e e n t h e (De) ~ w h i c h w e r e o b t a i n e d f r o m e q n . ( 1 5 ) a n d t h e e q u a t i o n g i v e n b e l o w . 1
_
(D,)~
l--aylr
[D(~-N2~],
~
1
(16)
(D.~)K,,
L e t us w r i t e e q n . ( 1 6 ) f o r P2 a r m a n d P l a t m o s p h e r e a b s o l u t e p r e s s u r e s i
(De,At)p2
_
1 -- ~YA~
[D(~,N~),e] p2
+
1
[(DAr)K,e]p2
(17)
240 1
(De,t-~)pl
-
1 -- ~ y ~ 1 + [D(~,Nz)~]p i [(D~)z,e]p,
1 [(DAr)K.e]p~.
=
[D(A~,N2),e]p2 =
(18)
1 [(DAr)K.e]p 1
(19)
(Pl/P2) [D(A~--N2),e]pI
(20)
S u b t r a c t i n g eqn. (18) f r o m eqn. (17) a n d s u b s t i t u t i n g eqns. (19) a n d (20) gives
yh~)(p2--p~/~
I
\
i
]
(Do. ) IJ
(21)
( D e . ~ ) , 2 , a n d (De.A~)p, are k n o w n . [(DAr.N2)e]p~, t h e effective b u l k diffusivity of -At at 1 arm can be calculated from eqn. (21). B y substituting this value in eqn. (18), [(DA~)K,e]p~ can be found. The temperature and molecular weight of argon are known• If the porosity and tortuosity are known, the average pore radius can be calculated from eqn. (14)• (DA~--N~) Can be calculated from eqn (I0), and [(DA~--N )e]Pl is obtained from the experimental results. F r o m the following equatmn the tortuosit~, T, will be found [(D(Ar--N2)e]Pl = (DAr--N2)Pl •-r
(22)
r = (DAr--~-2)pl " e/[(DAr.~2)e]pl
(Ts)
a n d t h e p o r o s i t y will be f o u n d f r o m t h e a m o u n t o f e v o l v e d C02• W h e n t h e p o r o s i t y a n d t o r t u o s i t y are k n o w n , t h e m e a n p o r e size can b e calctflated f r o m eqn. (24) (DA~)K.e " r l M/-M-~ re=
9-- 6 :
V
(24)
F r o m eqn. (3), t h e e x p e r i m e n t a l effective diffusivity o f argon is (De~)A~ = "--(NA~)eor. " RT" A / [ p " ((Y~)2 - - (YA~)I)]
(25)
(De~)N2 will be c a l c u l a t e d in t h e same way.
SAMPLE R U N t i n e x p e r i m e n t at 8 4 3 ° C is carried o u t for 110 h (see Fig. 7). T h e diffusivity of argon and nitrogen is increased as a function of calcination time. After 45 h of calcination~ a salt boat is pushed close to the pellet. The salt vapor is allowed to open up the pores. The diffusivity of gases is increased. After 74.9 h of calcination, the sulfation is s t Y . Instead of argon, 540 p p m SO2 and 1.02% 02 in argon is used. The diffusivity of argon and nitrogen is
241 I
l
I
I
1
I
I
O DN2
0.16
OAr • DN= (High pressure) • DAr (High ]oressure)
m
~
O
0
0-12
•uE
nO
o
O
O& Z~
i~ o.o8 ~3
ooo A,l.lt.
A ~
0.04
o
I
I
I
4
8
12
l
I
t
I
16 Time, h r
I
I
I
20
24
28
I
I
I
32
DN2
,~- DAr
0.1E
e DN2 (H~gh pressure) • DAr (High pressure) O0
O0 I e3
E012 u
I tA t i
&
4=_
> 0.08 °e e
e oi !
• AA
••&
.%
,I
..°
•AA
I
Satt addition !i
0.04
1 I I
I 36
3:2
I 40
i I 44
I
T=me,
| -
I
t
I
48
I
52
56
i
I
I
60
64
hr
I
I
DN2 A DAr o DN2 (High pressure) & DAr (High pressure)
o
oo
0 . 1 6 -,..o,o--
O.12u
2
008-
Qe
oe &A
~3 o
0.04 Su I f a t i o n is s~ar{ed !
64
68
I
72
t
I
I
i
76
80
84
88
Time, h r
pIi 92
96
242 I
I
I
l
I
I
t
o DN2 DAr o DN2 ( H i g l l pressure) A DAr (High pressure)
016 u
u
0C4
96
a~d,t,=n,i 100
1 104
I 108
I 112 Time,
I~- I I ~ 118
I--120
Q
!--124
128
hr
Fig. 7. D i f f u s i v i t y o f a r g o n a n d n i t r o g e n t h r o u g h c a l c i n e d G r e e r l i m e s t o n e d u r i n g calcin a t i o n , salt a d d i t i o n a n d s u l f a t i o n . T e m p e r a t u r e 8 4 3 . 1 ° C ; r u n n o . C6.
d e c r e a s e d as t h e sulfation r e a c t i o n t a k e s place. T h e r e was n o sulfur d i o x i d e o n t h e N2 steam exit. A t 99.8 h salt is a d d e d t o t h e system; t h e diffusivities are increased again d u r i n g t h e sulfation.
CONCLUSIONS
T h e single p e l l e t h i g h t e m p e r a t u r e d i f f u s i o n cell r e a c t o r can b e u s e d t o m e a s u r e t h e effective diffusivity o f gases t h r o u g h t h e p o r o u s pellets at l o w a n d h i g h t e m p e r a t u r e s ( 2 0 - - 1 2 0 0 ° C ) . T h e c h a n g e in t h e diffusivity o f gases d u e t o t h e c h e m i c a l r e a c t i o n t h a t t a k e s place in t h e p e l l e t can be d e t e r m i n e d durLug t h e r e a c t i o n . T h e effective diffusivity o f gases can also b e d e t e r m i n e d at d i f f e r e n t pressures u p t o 45 psig. F o r a d i f f u s i o n l i m i t e d r e a c t i o n , t h e k n o w l e d g e o f effective diffusivity is o n e o f m a j o r c o n c e r n . T h e single pellet h i g h t e m p e r a t u r e d i f f u s i o n cell can b e u s e d as a v e r y i m p o r t a n t t o o l in measuring t h e diffusivities so t h e r e a c t i o n can b e u n d e r s t o o d a n d m o d e l e d in a better way.
NOMENCLATURE A Def~ M N p Q Ar y
u n i t area u n d e r t h e peaks effective diffusivity o f a gas (cm 2 sec - z ) m o l e c u l a r weight (g) rate o f d i f f u s i o n (g m o l e c m -2 sec - I ) t h e pressure o f t h e gas ( a t m ) t h e f l o w rates ( c m 3 / s e c ) t h e t h i c k n e s s o f t h e pellet ( c m ) t h e m o l e ratio o£ gas
243
REFERENCES 1 2 3 4 5 6 7
E. Wicke and R. Kallenbach, Kolloid-Z., 97 (1941) 135. P.B. WeLsz and A.B. Schwartz~ J. C a t a l , 1 (1962) 399. N. Wakao and J.M. Smith, Chem. Eng. Sci., 17 (1962) 825. D.S. Scott and K.E. Cox, Can. J. Chem. Eng., 3 (1960) 201. T. Bardakci, Ph.D. Thesis, University of Maryland, 1980. R.B. Evans III, G.M. Watson and E.A. Mason, J. Chem. Phys., 35 (1961) 2076. C.H. Bosanquet, Phys. Rev., 73 (1948) 762.