Kinetics of Ethane Sorption on 4A Molecular Sieve Crystal Powder

53 Kinetics of Ethane Sorption on 4A Molecular Sieve Crystal Powder and Pellets EDWARD F. KONDIS and JOSHUA S. DRANOFF

Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch053

1

Department of Chemical Engineering, Northwestern University, Evanston, Ill. 60201

The sorption of ethane from dilute mixtures with helium by 4A sieve crystal powder and pellets made without binder has been studied with a microbalance in a flow system at temperatures between 25° and 117°C. Results show clearly that intracrystalline diffusion is the rate-controlling process and that it is represented well by a Fick's law diffusion model. Transient adsorption and desorption are characterized by the same effective diffusivity with an activation energy of 5660 cal/gram mole. 'T'he objective of the work reported here was to characterize clearly the kinetics of ethane sorption by 4A molecular sieves under isothermal conditions. Determination of the significant phenomena at work in adsorption and desorption is important for the basic understanding of the sorption process, as well as for the rational analysis and design of equipment for its application. The present study was undertaken to settle the question of the relative importance of micropore and macropore diffusion for one characteristic adsorbate and molecular sieve adsorbent. The experimental technique adopted for this work was the measurement of weight gain and loss as a function of time when small amounts of molecular sieve are exposed to gas streams of constant composition in a flow system. Comparison of experimental data with curves based on a suitable mathematical model permitted the determination of effective diffusivities for ethane. Equilibrium data also were obtained from these experiments. The present technique was chosen in preference to fixed-bed studies because of the increased sensitivity offered by the "single particle" approach. A

'Present address: Mobil Oil Corp., Paulsboro, N. J. 171 In Molecular Sieve Zeolites-II; Flanigen, E., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

172

MOLECULAR

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Π


Experimental Equipment. T h e b a s i c e q u i p m e n t u s e d i n this s t u d y w a s a m i c r o b a l a n c e ( T h e r m o - G r a v , A m e r i c a n I n s t r u m e n t C o . ). It consists essentially of a s m a l l s a m p l e h o l d e r c o n n e c t e d to a fine c a l i b r a t e d s p r i n g , the m o t i o n of w h i c h is f o l l o w e d b y a n e l e c t r i c a l t r a n s d u c e r a n d a u t o m a t i c a l l y re c o r d e d . T h e s a m p l e h o l d e r is c o n t a i n e d i n a s m a l l b o r o s i l i c a t e glass vessel ( s a m p l e t u b e ) t h r o u g h w h i c h gas m a y b e c i r c u l a t e d c o n t i n u o u s l y a n d w h i c h m a y be h e a t e d easily to h i g h temperatures b y a n e l e c t r i c a l f u r n a c e f o r r e g e n e r a t i o n purposes or s u b m e r g e d i n a c i r c u l a t i n g o i l b a t h f o r t e m p e r a t u r e c o n t r o l d u r i n g s o r p t i o n experiments. T h e apparatus w a s c o m p l e t e d b y the a d d i t i o n of suitable e q u i p m e n t for gas flow m e a s u r e m e n t a n d c o n t r o l a n d system c a l i b r a t i o n . Materials. T h e gases u s e d w e r e research g r a d e ethane a n d h e l i u m , b o t h 99.99 m o l e % p u r e . I m p u r i t i e s i n the h e l i u m w e r e not significant i n this w o r k . H o w e v e r , those present i n the ethane, p r i n c i p a l l y ethylene, w e r e of some c o n c e r n . T h e adsorbent w a s s t a n d a r d p u r e c r y s t a l l i n e L i n d e 4 A m o l e c u l a r sieve i n p o w d e r a n d p e l l e t i z e d f o r m ( L i n d e L o t N u m b e r 441079 ). T h e c y l i n d r i c a l pellets w e r e f o r m e d f r o m p u r e crystals i n a single p e l l e t press a n d w e r e 1/8 i n c h i n d i a m e t e r a n d 1/16 i n c h l o n g . T h e s e pellets h a d a d e n s i t y of 1.06 g r a m s / c c ( d r y a n d r e g e n e r a t e d ) . S i n c e t h e y c o n t a i n e d n o b i n d i n g clays, the pellets c o u l d w i t h s t a n d o n l y m i l d stress b u t this w a s not a p r o b l e m i n the present w o r k . Pellets w e r e m a d e f r o m the p u r e c r y s t a l p o w d e r as r e c e i v e d f r o m L i n d e a n d f r o m s u c h p o w d e r after e l l u t r i a t i o n to r e m o v e the finer particles. Samples u s e d i n s o r p t i o n runs r a n g e d f r o m 0.25 to a b o u t 6 grams. Procedure. T h e basic p a t t e r n f o r these experiments consisted of r e g e n e r a t i o n of the absorbent s a m p l e f o l l o w e d b y a d s o r p t i o n a n d d e s o r p t i o n runs. R e g e n e r a t i o n w a s a c c o m p l i s h e d b y h e a t i n g the s a m p l e to 5 5 0 ° C (at a rate of 2 0 ° C p e r m i n u t e ) a n d m a i n t a i n i n g it at that t e m p e r a ture u n d e r a h e l i u m p u r g e u n t i l a stable w e i g h t w a s r e a c h e d ( a b o u t 1 h o u r ) . T h e s a m p l e w a s a l l o w e d t h e n to c o o l to r o o m t e m p e r a t u r e after w h i c h the s a m p l e tube w a s s u b m e r g e d i n the constant-temperature b a t h a n d b r o u g h t to b a t h t e m p e r a t u r e w h i l e s t i l l u n d e r h e l i u m p u r g e . T h e w e i g h t of the s a m p l e w a s m o n i t o r e d c o n t i n u o u s l y d u r i n g this process to assure the absence of c o n t a m i n a t i o n . A n a d s o r p t i o n e x p e r i m e n t w a s i n i t i a t e d b y r e p l a c i n g the h e l i u m stream b y a pre-set m i x t u r e of ethane a n d h e l i u m . W h e n t h e s a m p l e w a s saturated w i t h ethane at the e x p e r i m e n t a l c o n d i t i o n s , a d e s o r p t i o n e x p e r i m e n t was c a r r i e d o u t b y r e p l a c i n g the f e e d gas b y p u r e h e l i u m . D e s o r p t i o n w a s c o n t i n u e d u n t i l the s a m p l e w e i g h t r e t u r n e d to its i n i t i a l v a l u e . E x p e r i m e n t s w e r e p e r f o r m e d at 2 5 . 2 ° , 7 3 . 8 ° , a n d 116.8 ° C , w i t h ethane c o n c e n t r a t i o n i n the f e e d gas of 2, 4, a n d 8 v o l u m e % , a n d at a t m o s p h e r i c pressure. T h e r e c o r d e d traces w e r e c o r r e c t e d to a c c o u n t f o r b u o y a n c y a n d d r a g a n d c o n v e r t e d to plots of w e i g h t g a i n a n d loss vs. t i m e . S p e c i a l care w a s r e q u i r e d to e l i m i n a t e a n u m b e r of u n d e s i r e d effects u n c o v e r e d i n p r e l i m i n a r y experiments. T h e s e i n c l u d e d s a m p l e c o n t a m i n a t i o n f r o m i m p u r i t i e s i n the ethane, w h i c h w a s e l i m i n a t e d b y p l a c i n g a s m a l l a m o u n t ( a b o u t 200 m g ) of 4 A sieve i n the base of t h e s a m p l e t u b e . T h i s m a t e r i a l , w h i c h w a s regenerated a u t o m a t i c a l l y e a c h t i m e a l o n g w i t h

In Molecular Sieve Zeolites-II; Flanigen, E., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

53.

KONDIS A N D D R A N O F F

Kinetics of Ethane Sorption

173


t h e s a m p l e , d i d n o t interfere w i t h the m a i n s o r p t i o n experiments b u t d i d p e r m i t r e p r o d u c i b l e o p e r a t i o n o f t h e system. I n a d d i t i o n , the p r o b l e m s of i n i t i a t i n g a s h a r p step c h a n g e i n gas c o m p o s i t i o n i n t h e s a m p l e t u b e a n d t h e e l i m i n a t i o n o f gas phase mass transfer effects w e r e s o l v e d b y c a r e f u l r e d e s i g n o f the s a m p l e t u b e a n d a n a n n u l a r s a m p l e h o l d e r , a n d v e r i f i e d b y a series o f experiments a t v a r i o u s gas flow rates a n d compositions.

0.2

0.6 Log

Figure 1.

e

1.0 of Crystal

1.4 Size

Log-normal size distributions for 4 A crystals

Crystal Size Measurement. T h e size d i s t r i b u t i o n o f the sieve crystals u s e d also w a s m e a s u r e d i n some a u x i l i a r y experiments. T h i s w a s d o n e b y first s u s p e n d i n g the sieve s a m p l e ( c r y s t a l p o w d e r o r c r u s h e d p e l l e t s ) i n a s o d i u m h y d r o x i d e s o l u t i o n ( t o h e l p disperse t h e e a s i l y - f o r m e d c r y s t a l agglomerates) a n d t h e n e x a m i n i n g t h e s o l u t i o n w i t h a c a l i b r a t e d o p t i c a l m i c r o s c o p e a t a m a g n i f i c a t i o n o f 5000. A b o u t 2 5 0 p a r t i c l e s p i c k e d at r a n d o m o n a s l i d e w e r e m e a s u r e d f o r e a c h s a m p l e . T h e particles, w h i c h h a v e a shape s o m e w h e r e b e t w e e n that o f a sphere a n d a c u b e , w e r e t r e a t e d as cubes w i t h the l e n g t h o f a side e q u a l t o 2a m i c r o n s . M o r e c o m p l e t e details o f e q u i p m e n t a n d e x p e r i m e n t a l t e c h n i q u e s are p r e s e n t e d b y K o n d i s ( 7 ) .


174

M O L E C U L A R

Results and

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II

Discussion

Crystal Size Distribution.

The measured

f o l l o w e d a l o g - n o r m a l f o r m , suggested particles b y H e r d a n (6).

c r y s t a l size d i s t r i b u t i o n

as characteristic

for most s m a l l

F i g u r e 1 shows results o b t a i n e d w i t h the 4 A

c r y s t a l p o w d e r a n d w i t h the 2 types of pellets f o r m e d f r o m it. H e r e a n d b e l o w , the L i n d e c r y s t a l p o w d e r as r e c e i v e d , the p e l l e t i z e d p o w d e r , a n d the pellets f o r m e d f r o m the e l u t r i a t e d p o w d e r w i l l be r e f e r r e d to C P R , C P S , a n d E C P S , respectively.

as

C l e a r l y , the p e l l e t i z i n g process d i d


n o t affect the size d i s t r i b u t i o n of the o r i g i n a l m a t e r i a l . F u r t h e r m o r e , the e l u t r i a t e d particles d o h a v e a s o m e w h a t l a r g e r average size. F o r analysis

of s o r p t i o n d a t a , the

particles

were represented

as

spheres w i t h r a d i u s e q u a l to the h y d r a u l i c r a d i u s of the particles.

For

c u b e s , this leads to a n e q u i v a l e n t s p h e r i c a l r a d i u s e q u a l to one-half

the

l e n g t h of the c u b e side or a.

T h e w e i g h t average r a d i u s m a y b e f o u n d

f r o m the p r e v i o u s d a t a a n d the r e l a t i o n a m o n g w e i g h t a n d n u m b e r aver age r a d i i a n d the s t a n d a r d d e v i a t i o n of the d i s t r i b u t i o n g i v e n b y H e r d a n (6).

In a

g

=

In a

}

g

— 3 (In σ ) 0

(1)

2

T h e results are l i s t e d i n T a b l e I. Sorption Kinetics.

T h e adsorption and desorption data were

l y z e d i n terms of a m o d e l b a s e d o n the f o l l o w i n g m a i n

ana

assumptions.

M i c r o p o r e d i f f u s i o n w i t h i n the sieve crystals is the r a t e - c o n t r o l l i n g p r o c ess.

D i f f u s i o n m a y be d e s c r i b e d b y F i c k ' s l a w f o r s p h e r i c a l

particle

g e o m e t r y w i t h a constant m i c r o p o r e d i f f u s i v i t y . T h e h e l i u m present i n the system is i n e r t a n d p l a y s no d i r e c t role i n the s o r p t i o n or d i f f u s i o n process.

S o r p t i o n occurs u n d e r i s o t h e r m a l c o n d i t i o n s .

Sorption equilib

r i u m is m a i n t a i n e d at the c r y s t a l surface, w h i c h is s u b j e c t e d to a step c h a n g e i n gas c o m p o s i t i o n . T h e s e assumptions l e a d to the f o l l o w i n g r e l a t i o n f o r the a m o u n t of ethane a d s o r b e d or d e s o r b e d b y a single p a r t i c l e as a f u n c t i o n of t i m e ( C r a n k , 4 ). Q

-

Qo

Qi -

Qo

=

1

- Ç ^v 6

n

1

exp

(2)

V""^"7

T h e c o r r e s p o n d i n g s o l u t i o n f o r a c u b i c p a r t i c l e w i t h sides 2a i n l e n g t h is i n v e r y close agreement w i t h E q u a t i o n 2, d e v i a t i n g at most b y a f e w p e r cent. Table I. Sample CPR, CPS ECPS

Average Crystal Particle Size Weight Average Radius

(Microns)

1.39 1.60



53.

KONDis

Kinetics

A N D DRANOFF

of Ethane

175

Sorption

E x p e r i m e n t s w e r e first p e r f o r m e d u s i n g sieve pellets c o n t a i n i n g a n i m b e d d e d t h e r m o c o u p l e a n d w i t h gas concentrations u p to 10%

ethane.

T h e s e s h o w e d t e m p e r a t u r e v a r i a t i o n s of less t h a n 0.5 ° C d u r i n g s o r p t i o n , thus c o n f i r m i n g t h e i s o t h e r m a l a s s u m p t i o n . Thereafter,

the experimental data were

fitted

equation b y a graphical superposition technique.

to t h e a b o v e m o d e l T h e data a n d model

c u r v e w e r e p l o t t e d separately as f r a c t i o n a d s o r b e d o r d e s o r b e d the l o g of the square root of t i m e .

against

T h e experimental curve was m o v e d

h o r i z o n a l l y u n t i l t h e best fit w a s o b t a i n e d , t h e r e b y d e t e r m i n i n g t h e a p p r o p r i a t e v a l u e at D /a . c

2

T h i s m e t h o d uses a l l of the d a t a , as o p p o s e d

to some approaches b a s e d o n t h e values at early times w h i c h h a v e b e e n u s e d b y others (1,2,5).

I t w a s a p p l i e d easily i n this w o r k because o f t h e

excellent agreement of t h e m o d e l w i t h the d a t a o b t a i n e d . F i g u r e 2 presents results f o r p u r e c r y s t a l pellets ( C P S ) at 7 3 . 8 ° C , w h i c h are t y p i c a l of a l l the d a t a o b t a i n e d .

C l e a r l y , the m o d e l provides

a n excellent fit t o these d a t a , w i t h the same d i f f u s i v i t y a p p l y i n g t o b o t h a d s o r p t i o n a n d d e s o r p t i o n runs. T h e r e is some slight d e v i a t i o n at e a r l y times, b u t this is w e l l w i t h i n l i m i t s of e x p e r i m e n t a l error.

Results at

other temperatures a n d w i t h a l l 3 adsorbent types s h o w t h e same k i n d of m o d e l fit. T h e c o r r e s p o n d i n g values of D /a c

p l o t t e d against t e m p e r a t u r e

2

are p r e s e n t e d i n T a b l e I I a n d are

o n t h e A r r h e n i u s p l o t i n F i g u r e 3.


Three

176

M O L E C U L A R

Table II.


Run

D /a c

2

Adsorbent

9 10 11 12 13 14 19 20 21 21A 30 31 33 34 36 37 38 39 44 45 53 54 55 56

CPS CPS CPS CPS CPS CPS CPS CPS CPS CPS CPS CPS CPR CPR CPR CPR CPR CPR ECPS ECPS ECPS ECPS ECPS ECPS

SIEVE

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II

Values Determined from Experimental Data

Temp.,

°C

Concentration? Vol. %

73.8 73.8 73.8 116.8 116.8 116.8 25.2 25.2 25.2 73.8 25.2 25.2 25.2 25.2 73.8 73.8 116.8 116.8 25.2 25.2 73.8 73.8 116.8 116.8

Adsorption Cycle

Desorption Cycle 7.84 7.84 7.84. 20.3 22.1 23.0 2.56 2.40 2.40

7.84 8.41 7.84 22.1 26.0 23.0 2.40 2.25 2.72 7.84 2.72 2.56 2.10 2.40 7.29 7.29 21.2 22.1 1.56 1.69 5.11 5.11 15.2 13.7

4 2 8 2 4 8 4 2 8 8 4 4 4 8 4 8 4 8 4 8 4 8 4 8

— — 2.56

2.40 2.40 7.29 8.40 22.1 22.1 1.56 1.69 5.11 5.3 15.2 13.7

° Concentration for adsorption cycle. For desorption cycle, concentration is zero. p r i n c i p l e results are a p p a r e n t f r o m these data. F i r s t , there is essentially n o difference b e t w e e n the values of D /a c

2

o b t a i n e d f r o m a d s o r p t i o n or

d e s o r p t i o n experiments, i n d i c a t i n g that the same m e c h a n i s m s are at w o r k i n b o t h processes. S e c o n d l y , the f a c t that i d e n t i c a l results are o b t a i n e d w i t h p u r e c r y s t a l p o w d e r a n d pellets m a d e f r o m that p o w d e r indicates that D /a c

2

is i n d e p e n d e n t of o v e r - a l l p a r t i c l e size a n d therefore

m i c r o p o r e or c r y s t a l d i f f u s i o n is the r a t e - c o n t r o l l i n g process.

that

F i n a l l y , the

values for the e l u t r i a t e d c r y s t a l pellets are l o w e r b y a factor of c o m p a r e d w i t h the other results. T h u s , the d i f f u s i o n measurements

1.44 imply

that the v a l u e of a f o r these pellets is 1.2 times the average r a d i u s f o r the p u r e crystals. r a d i u s r a t i o of 1.15

T h i s compares

q u i t e f a v o r a b l y w i t h the

measured

i n d i c a t e d b y the d a t a of T a b l e I, thus p r o v i d i n g

f u r t h e r c o n f i r m a t i o n of the m o d e l . T h e effect of the c r y s t a l size d i s t r i b u t i o n o n these results w a s i n v e s t i gated u s i n g the o b s e r v e d d i s t r i b u t i o n f u n c t i o n .

T h e p r e d i c t i o n of

the

m o d e l f o r the average p a r t i c l e r a d i u s w a s c o m p a r e d w i t h a p r e d i c t i o n


53.

KONDis

A N D

Kinetics

DRANOFF

of Ethane

177

Sorption

w e i g h t e d a c c o r d i n g t o t h e d i s t r i b u t i o n . T h e results s h o w e d n e g l i g i b l e difference over the entire r a n g e o f interest, thus v a l i d a t i n g the use o f a n average p a r t i c l e r a d i u s . T h e D values f o u n d i n this w o r k m a y b e c o m p a r e d w i t h t h e v a l u e C

of 4.8 χ 10"

cm /sec reported previously b y Brandt and Rudloff ( 3 ) ,

12

2

w h o s t u d i e d ethane s o r p t i o n b y 4 A crystals at 22.9 ° C b u t i n the absence of h e l i u m c a r r i e r gas. T h e present d a t a at 2 5 . 2 ° C i n d i c a t e ( f o r a n average r a d i u s o f 1.39 m i c r o n s ) that D is 4.6 Χ 10" C

m e n t w i t h t h e earlier w o r k .

12

c m / s e c , i n excellent agree 2

H o w e v e r , t h e a c t i v a t i o n energy r e p o r t e d


b y B r a n d t a n d R u d l o f f was 7.4 K c a l / m o l e , as c o m p a r e d w i t h the v a l u e of 5.66 K c a l / m o l e f o u n d here. E q u i l i b r i u m D a t a . F i n a l l y , e q u i l i b r i u m isotherms w e r e e s t a b l i s h e d f r o m the measurements m a d e i n this s t u d y . T h e s e are p l o t t e d i n F i g u r e 4. C l e a r l y , the results i n d i c a t e the isotherms to b e essentially l i n e a r except at 25.2 ° C .

S u b s e q u e n t w o r k at h i g h e r ethane concentrations h a s c o n -

20

2\

\

10

-

\

D . 3.22

\^°

c

exp(-5660/RT)

2

5

/RT)^\ -1 • 2.23 exp(-5660

N#

• CPR Ο CPS Δ ECPS 2.5

3.0 Ι/Τ

Figure 3.

χ I0

3

3.5 (°K)"

1

Arrhenius plot for experiments diffusivity data

micropore



178

M O L E C U L A R

firmed

SIEVE

ZEOLITES

II

that t h e isotherms f o l l o w the u s u a l L a n g m u i r f o r m . A s expected,

d a t a f o r a l l 3 adsorbents s h o w the same e q u i l i b r i u m b e h a v i o r . T h e heat of a d s o r p t i o n w a s d e t e r m i n e d f r o m these a n d m o r e c o m p l e t e e q u i l i b r i u m d a t a ( 7 ) a n d f o u n d to b e 7.04 K c a l / m o l e . Conclusions T h e results i n this s t u d y h a v e d e m o n s t r a t e d c l e a r l y that t h e rate of a d s o r p t i o n a n d d e s o r p t i o n of ethane at l o w concentrations o n 4 A m o l e c u l a r sieves i n t h e absence of b i n d e r is c o n t r o l l e d b y i n t r a c r y s t a l l i n e d i f f u sion of the ethane.

F u r t h e r m o r e , the d i f f u s i o n process m a y b e charac

t e r i z e d b y F i c k ' s l a w a n d a n effective

diffusivity dependent

only on

t e m p e r a t u r e , a n d a p p l i c a b l e to b o t h a d s o r p t i o n a n d d e s o r p t i o n . I t m a y b e expected, therefore, that s u c h m i c r o p o r e d i f f u s i o n also determines t h e rates of ethane s o r p t i o n w i t h

c o m m e r c i a l 4 A pellets

containing


clay

53.

KONDis A N D D R A N O F F

binders

since

the

Kinetics

of Ethane

same m i c r o p o r o u s

Sorption

structure

179

s h o u l d exist

in

these

adsorbents. Acknowledgment T h e authors t h a n k F . G . D w y e r of M o b i l O i l C o r p . f o r p r o v i d i n g the samples u s e d i n this w o r k , a n d D . L . J o h n s o n of N o r t h w e s t e r n U n i v e r s i t y f o r assistance i n c r y s t a l size measurement. the

Mobil

Oil

Corp.

Incentive

The

Fellowship

financial Program

assistance of is

gratefully


acknowledged. Nomenclature a

=

Effective crystal radius, c m

a

9

=

N u m b e r average p a r t i c l e size, c m

a'

=

W e i g h t average p a r t i c l e size, c m

D Q

= =

Intracrystalline diffusivity, c m / s e c A v e r a g e ethane content of adsorbent, g r a m s / g r a m of s o l i d

Ço

=

Çi t σ

= = =

I n i t i a l average ethane content of adsorbent, g r a m s / g r a m of solid F i n a l average ethane content, g r a m s / g r a m of s o l i d T i m e , sec S t a n d a r d d e v i a t i o n of size d i s t r i b u t i o n , c m

g

c

9

Literature

2

Cited

(1) (2) (3) (4)

Barrer, R. M . , Trans. Faraday Soc. 1949, 45, 358. Barrer, R. M . , Fender, B. E . F., J. Phys. Chem. Solids 1961, 21, 12. Brandt, W. W., Rudloff, W., J. Phys. Chem. Solids 1965, 26, 741. Crank, J., "The Mathematics of Diffusion", Oxford University Press, Ox ford, England, 1956. (5) Habgood, H . W., Can. J. Chem. 1958, 36, 1384. (6) Herdan, G., "Small Particle Statistics," Butterworths, London, England, 1960. (7) Kondis, E. F., Ph.D. Dissertation, Northwestern University, Evanston, Ill., 1968. RECEIVED February 13, 1970.

Discussion D . M . Ruthven a n d K . F . Loughlin ( U n i v e r s i t y of N e w B r u n s w i c k , F r e d e r i c t o n , Ν. B . , C a n a d a ) : T h e data of K o n d i s a n d D r a n o f f illustrate a n u m b e r of i m p o r t a n t points r e l a t i n g to the p r o b l e m of c a l c u l a t i n g d i f f u s i o n coefficients

f r o m s o r p t i o n curves.

F o r the analysis

of

sorption

curves, the c r y s t a l size d i s t r i b u t i o n s h o u l d be expressed o n a w e i g h t


(or

180

M O L E C U L A R

v o l u m e ) f r a c t i o n basis.

SIEVE

ZEOLITES

II

T h e t y p e A zeolite crystals are c u b i c a n d b y

p l o t t i n g the c u m u l a t i v e v o l u m e f r a c t i o n

\

di

Σ di

=

Ni 0

Σ

t

\di = 0

Nid-'

, I


against c r y s t a l d i a m e t e r di o n a r i t h m e t i c p r o b a b i l i t y p a p e r , i t m a y b e s h o w n that the c r y s t a l size d i s t r i b u t i o n d a t a of K o n d i s ( 1 ) are w e l l r e p r e sented b y a n o r m a l d i s t r i b u t i o n f u n c t i o n w i t h m e a n c r y s t a l size 2μ 2.70 m i c r o n a n d s t a n d a r d d e v i a t i o n 2σ =

1.08 m i c r o n ; s =

μ/σ =

= 2.5.

S i m i l a r c r y s t a l size d i s t r i b u t i o n d a t a w e r e o b t a i n e d b y R u t h v e n a n d L o u g h l i n (2) f o r L i n d e 5 A zeolite. F i g u r e 1 shows the t y p i c a l s o r p t i o n c u r v e p r e s e n t e d b y K o n d i s a n d D r a n o f f ( r u n 11) together w i t h the t h e o r e t i c a l c u r v e f o r u n i f o r m s p h e r i c a l p a r t i c l e s , c a l c u l a t e d f r o m E q u a t i o n 2 of the p r e c e d i n g p a p e r , u s i n g the v a l u e D/a

=

2

7.84 χ 10" sec" . T h e d e v i a t i o n of the e x p e r i m e n t a l points 4

1

f r o m the t h e o r e t i c a l c u r v e is c l e a r l y a p p a r e n t .

B y summing the contribu

tions of the i n d i v i d u a l size fractions of particles i t m a y b e s h o w n that, f o r a system of c u b i c particles w i t h a n a p p r o x i m a t e l y n o r m a l d i s t r i b u t i o n of size ( o n a w e i g h t o r v o l u m e f r a c t i o n b a s i s ) , the p r o p e r expression f o r the s o r p t i o n c u r v e is g i v e n b y ( 2 ) :

W

512s

= π

Σ

/7Γ~

κ

V2%

{ exp{-y s (y -

{

2

2

Σ

ΐ = ι

l)

m

s υ

η=\

= i

y

= o

τ*

2

Dt · — · [(2Z W μ (21 - l ) (2m -

l) + 2

(2m -

l) + 2

I

(2n

-

2

2

where W

=

l)

2

(2n - l )

2

I-SL

Q* = M a s s of sorbate a d s o r b e d or d e s o r b e d d u r i n g t i m e t M a s s of sorbate a d s o r b e d o r d e s o r b e d as t —> oo D i f f u s i o n coefficient

D -

M- = M e a n h a l f side of c u b i c p a r t i c l e S

=

σ


l)*]\dy J


53.

KONDIS

Kinetics

A N D DRANOFF

of Ethane

Sorption

181

TIME (seconds) Figure 1.

Sorption curve for ethane in 4A zeolite; data of Kondis (Run 11)

W h e n the v a l u e of s is k n o w n f r o m measurements of c r y s t a l size d i s t r i b u t i o n , this expression m a y b e e v a l u a t e d n u m e r i c a l l y to g i v e W as a f u n c t i o n of Dt/μ . 2

T h e v a l u e of D/μ

2

m a y then be obtained b y matching

the e x p e r i m e n t a l d a t a t o the t h e o r e t i c a l c u r v e . W h e n this analysis is a p p l i e d to the d a t a of r u n 11, w i t h s = v a l u e of Ό/μ

2

Ό/μ

2

=

=

2.5, a

10.7 Χ 10" sec" is o b t a i n e d , c o m p a r e d w i t h t h e v a l u e 4

1

7.84 X 10" sec" o b t a i n e d f r o m the e q u a t i o n f o r u n i f o r m s p h e r i 4

1

c a l particles. T h e c o r r e s p o n d i n g t h e o r e t i c a l c u r v e is s h o w n i n F i g u r e 1. a p p a r e n t that this c u r v e fits t h e e x p e r i m e n t a l d a t a w e l l , w h e r e a s

It is the

theoretical curve calculated assuming a mean equivalent spherical radius gives o n l y a rather p o o r fit. I n this t y p e o f system i n w h i c h t h e r e is present a significant r a n g e of c r y s t a l sizes, t h e a s s u m p t i o n of a m e a n e q u i v a l e n t s p h e r i c a l r a d i u s is a rather p o o r a p p r o x i m a t i o n w h i c h c a n l e a d to significant errors i n t h e c a l c u l a t e d diffusivities. Literature

Cited

(1) Kondis, E . F., P h . D . thesis, Northwestern University, 1969. (2) Ruthven, D. M., L o u g h l i n , K . F., Chem. Eng. Sci., i n press.


182

M O L E C U L A R

SIEVE

ZEOLITES

II

E . F . K o n d i s a n d J . S. D r a n o f f : W e agree w i t h L o u g h l i n a n d R u t h v e n that c r y s t a l shape a n d size d i s t r i b u t i o n are i m p o r t a n t considerations f o r a d s o r p t i o n o n zeolites. M o r e o v e r , w e h a v e p r e v i o u s l y e v a l u a t e d t h e i r effects i n o u r w o r k . D r . K o n d i s has p o i n t e d o u t at this s y m p o s i u m a n d elsewhere

( I ) that f o r o u r e x p e r i m e n t a l d a t a a n d f o r o u r m e t h o d o f

o b t a i n i n g t h e d i f f u s i o n coefficients, these t w o p a r a m e t e r s c a u s e d a 10 to 2 0 % v a r i a t i o n i n Ό Jo?.

about

W e a c c e p t e d this v a r i a t i o n as b e i n g

w i t h i n t h e a c c u r a c y o f o u r results. L o u g h l i n a n d R u t h v e n i n t h e i r F i g u r e 1 s h o w that b y a c c o u n t i n g f o r size d i s t r i b u t i o n a n d shape t h e y o b t a i n a v a r i a t i o n o f 3 5 % i n D /a . Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch053

c

H o w e v e r , t h e y u s e d a different t e c h n i q u e t o

2

o b t a i n t h e d i f f u s i o n coefficient.

M o r e o v e r , their m e t h o d of presentation

accents a m u c h different p o r t i o n o f t h e d a t a . I n F i g u r e 1 w e show a comparison of our data a n d m e t h o d of analy sis w i t h that o f L o u g h l i n a n d R u t h v e n u s i n g t h e same coordinate system as p r e s e n t e d i n o u r p a p e r at this s y m p o s i u m . I t is q u i t e o b v i o u s that t h e m o d e l u s e d b y L o u g h l i n a n d R u t h v e n gives a m u c h p o o r e r fit t o t h e e x p e r i m e n t a l d a t a over t h e first 5 0 - 6 0 % t h e i r m o d e l requires Ό J α

sorbed or desorbed.

I n fact,

7 Χ 10" sec" t o fit t h e d a t a i n this r e g i o n

2

4

1

( n o t 10.7 Χ 10" sec" as s h o w n i n t h e i r F i g u r e 1 ) . T h e i r m e t h o d gives a 4

1

1

2

3

4 t

1 / 2

5 (sec.

7 1 / 2

10

20

30

)

Figure 1. A comparison of the experimental data and model fit of Kondis and Dranoff with the proposed model of Loughlin and Ruthven Experimental Data of Kondis & Dranoff Ο Run 11 Adsorption Data φ Run 11 Desorption Data


53.

KONDIS

Kinetics

A N D DRANOFF

of Ethane

Sorption

183

better fit p r i m a r i l y o v e r the last 1 0 % of t h e s o r p t i o n o r d e s o r p t i o n c u r v e (see t h e i r F i g u r e 1 ) .

H o w e v e r , w e h a v e c a u t i o n e d against t h e use o f

the d a t a i n this r e g i o n ( I ) because s m a l l a m o u n t s of c o n t a m i n a t i o n i n the ethane gas c a n shift this p o r t i o n of the s o r p t i o n c u r v e q u i t e m a r k e d l y . W e h a v e also c a l c u l a t e d t h e v a l u e of D /a c

2

u s i n g the y/t

m e t h o d of

B a r r e r ( 2 ) as another c h e c k of o u r d a t a . B y this m e t h o d , D /a c

2

is a b o u t

7 X 10~ sec" , w h i c h is i n f a i r a g r e e m e n t w i t h o u r result of 7.84 Χ 10" 4

sec"

1

1

4

b u t also differs m a r k e d l y f r o m the L o u g h l i n a n d R u t h v e n result. I n

this case, i t is q u i t e o b v i o u s the m e t h o d of analysis b y L o u g h l i n a n d Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch053

R u t h v e n c o m p l e t e l y ignores t h e first 5 0 % of t h e a d s o r p t i o n or d e s o r p t i o n c u r v e . H a d t h e y c o n s i d e r e d this d a t a r e g i o n to b e e q u a l i n i m p o r t a n c e to the t a i l e n d of t h e a d s o r p t i o n o r d e s o r p t i o n c u r v e , they w o u l d h a v e o b t a i n e d a v a l u e of D /a c

Literature

2

w i t h i n 1 0 - 2 0 % of o u r v a l u e .

Cited

(1) Kondis, E. F., P h . D . dissertation, Northwestern University, 1969. (2) Barrer, R. M., Trans. Faraday Soc. 1949, 45, 358. J . D . Sherman ( U n i o n C a r b i d e , T a r r y t o w n , Ν. Y . 1 0 5 9 1 ) : H o w w e r e the p e l l e t e d c r y s t a l samples p r e p a r e d ?

In your introduction, y o u men

t i o n e d a desire to c o m p a r e y o u r results f o r binderless f o r m s w i t h results f o r c l a y - b o n d e d pellets.

H a v e y o u indeed made such comparisons, a n d

c o u l d y o u c o m m e n t o n y o u r results? E . F . Kondis: Samples w e r e c a r e f u l l y p r e p a r e d i n a single p e l l e t press. B i n d e r l e s s pellets s h o w values of D /a c

2

r o u g h l y 6 to 8 times greater t h a n

c o m m e r c i a l l y m a d e pellets w i t h b i n d e r . (to b e p u b l i s h e d i n Ind. Eng. Chem. reason f o r t h e change i n D /a c

crystals.

2

Detailed experimental

Proc. Design

Develop.)

results

attribute the

to h i g h - t e m p e r a t u r e s t e a m i n g of the 4 A

M i c r o p o r e d i f f u s i o n r e m a i n s the r a t e - c o n t r o l l i n g process.


Kinetics of Ethane Sorption on 4A Molecular Sieve Crystal Powder

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