Molecular Sieve Zeolites-II - American Chemical Society

60 Diffusion in Granular Zeolites D. P. TIMOFEEV

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Institute of Physical Chemistry, Academy of Science of USSR, 31 Lenin Avenue, Moscow

Three modes of vapor diffusion in granular zeolites and some results are discussed. Thefirstmode involves diffusion of adsorbate through crystals and along secondary pores. On the basis of steady-state diffusion experiments, it was concluded that diffusion within the zeolite crystals is not significant as a contribution to total diffusion of organic vapors through the granule. In the second and the third modes, diffusion to the central parts of a granule is limited to secondary pores. For these modes which differ in the ratio of diffusion rates in the crystals and in the secondary pores, approximate equations of kinetics of adsorption are derived, and their agreement with experimental data is discussed.

C y n t h e t i c zeolites often are e m p l o y e d as s p h e r i c a l o r c y l i n d r i c a l pellets ^

c o m p o s i n g the aggregate o f e l e m e n t a r y crystals. Spaces b e t w e e n t h e

crystals f o r m t h e secondary p o r o u s structure w i t h p o r e d i m e n s i o n s o f a p p r o x i m a t e l y the same o r d e r as the d i m e n s i o n s o f the crystals. B o t h t h e first

( p o r o s i t y o f crystals) a n d t h e s e c o n d a r y p o r o s i t y a r e significant t o

k i n e t i c s of a d s o r p t i o n . D i f f u s i o n coefficients i n t h e crystals d e p e n d m a i n l y o n the t y p e a n d i o n i c f o r m o f the zeolite a n d o n the nature o f the a d s o r b i n g substance (2).

D e p e n d e n c e o f t h e d i f f u s i o n coefficients i n secondary

pores o n these factors is r e l a t i v e l y l i g h t ; together, t h e y a r e significantly d e p e n d e n t o n t h e c o n d i t i o n s of mass exchange w i t h t h e a m b i e n t gas media.

A q u a n t i t a t i v e d e s c r i p t i o n o f d i f f u s i o n i n a g r a n u l e is a r a t h e r

difficult task, t h e t o t a l d i f f u s i o n coefficient b e i n g a c o m p l e x f u n c t i o n o f m a n y variables. T h e q u a l i t a t i v e side o f the process is g i v e n b e l o w , w i t h some q u a n t i t a t i v e ratios o f use i n t h e e v a l u a t i o n assessments. T h r e e modes o f d i f f u s i o n i n a g r a n u l e , s c h e m a t i c a l l y r e p r e s e n t e d i n F i g u r e 1, are possible.

T h e first m o d e ( F i g u r e l a ) i n v o l v e s d i f f u s i o n o f

American Chemical Society Ubrary

In Molecular Sieve 1155Zeolites-II; 16th St,Flanigen, N.W. E., et al.; Advances in Chemistry; Wtehinfton. American Chemical Washington, DC, 1971. D.CSociety: xme

248

MOLECULAR

SIEVE

ZEOLITES

Π


I 1 I

a Figure

c 1.

Three modes of diffusion of adsorbate in a granule

adsorbate m o l e c u l e s t h r o u g h gaps b e t w e e n t h e crystals a n d t h r o u g h the crystals. I n t h e s e c o n d a n d t h i r d m o d e s , d i f f u s i o n to c e n t r a l parts of a g r a n u l e occurs o n l y t h r o u g h s e c o n d a r y pores.

A c c o r d i n g to t h e s e c o n d

m o d e , adsorbate m o l e c u l e s penetrate easily into t h e o p e n i n g s of a d s o r p t i o n cells a n d diffuse r a p i d l y i n t o t h e crystals ( F i g u r e l b ) . T h e a d s o r p t i o n c a p a c i t y of t h e crystals p a r t i c i p a t i n g i n t h e process is p r a c t i c a l l y exhausted as t h e d i f f u s i o n flow progresses i n t o the depths of the g r a n u l e . I n t h e t h i r d m o d e ( F i g u r e l c ) , d i f f u s i o n i n t o t h e crystals is s l o w a n d causes o n l y p a r t i a l

filling.

I n o r d e r to v e r i f y t h e d i f f u s i o n t h r o u g h t h e crystals, w e i n v e s t i g a t e d the steady-state d i f f u s i o n of a n u m b e r of o r g a n i c v a p o r s i n granules of zeolite C a A a n d N a X ( 12, 13 ). T h e experiments w e r e c a r r i e d o u t i n the presence of carrier gas at a t m o s p h e r i c pressure. G r a n u l e s of c o m m e r c i a l zeolite samples w e r e s e c u r e d w i t h h e r m e t i z i n g paste i n t o t h e orifice of a n a l u m i n u m m e m b r a n e , a n d p o w d e r e d c r y s t a l l i c zeolite w a s pressed i n t o t h e orifice. A p u r e c a r r i e r gas w a s streamed past one face of t h e m e m b r a n e as a gas m i x t u r e c o n t a i n i n g adsorbate v a p o r s w a s s t r e a m e d over t h e other face. W h e n a steady state w a s r e a c h e d , t h e c o n c e n t r a t i o n o n t h e granule's reverse side w a s d e t e r m i n e d , a n d t h e d i f f u s i o n coefficient w a s f o u n d a c c o r d i n g t o the e q u a t i o n

where C i a n d c

2

are t h e concentrations o n the f r o n t a n d reverse side of

the m e m b r a n e (c

2

0.1 C i ) , r e s p e c t i v e l y , ν is v e l o c i t y of c a r r i e r gas,

L a n d F are t h e l e n g t h a n d cross-sectional area of t h e sample. C u r v e s of the t e m p e r a t u r e d e p e n d e n c e of the d i f f u s i o n coefficient of e t h y l a l c o h o l a n d n i t r o g e n i n a g r a n u l e of zeolite C a A - I , g r a i n size

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

60.

Diffusion

TiMOFEEV

3 m m , are represented

in Granular

Zeolites

i n F i g u r e 2.

249

Helium

(curve 2) a n d nitrogen

( c u r v e 4 ) w e r e u s e d as carrier gas i n t h e experiments w i t h e t h y l a l c o h o l . T h e d o t t e d l i n e is c o m p u t e d f o r e t h y l a l c o h o l , as a n o n a d s o r b i n g gas, o n the basis of e x p e r i m e n t a l d a t a o b t a i n e d f o r n i t r o g e n a c c o r d i n g t o t h e equation

^C H OH 2

=

5

£>N

,

2


a

(2)

' l /mi S

i

m

8

2

where d + d x

σι,2 =

di + d

2

2

,

z

>

Σ Ι

'

3

2 — '

=

M

H

M

2

Y

M

3

'

,

, , A

are the masses a n d g a s - k i n e t i c diameters of the m o l e c u l e s h e l i u m , n i t r o gen, a n d e t h y l a l c o h o l , respectively. I n t h e temperature range 5 0 ° - 1 0 0 ° C , w e m a y i g n o r e a d s o r p t i o n of n i t r o g e n , a s s u m i n g i t as a first a p p r o x i m a t i o n to b e n o n a d s o r b i n g . F i g u r e 2 shows that t h e d i f f u s i o n coefficients of e t h y l a l c o h o l e v a l u a t e d a c c o r d i n g to E q u a t i o n 2 are w e l l i n a g r e e m e n t w i t h t h e e x p e r i m e n t a l values, i m p l y i n g that t r a n s p o r t t h r o u g h t h e a d s o r p t i o n phase is of n o c o n s p i c u o u s

consequence.

n\

Figure

1

25

2 also

1

1

1

50

75

SÛO

shows

the diffusion

°C Figure 2. Effect of temperature on diffusion coefficient of nitrogen (1) and ethyl alcohol (2-4) in the granule of zeolite CaA-I Carrier gas: 1,2,3 = helium, 4 = nitrogen Curve 3 is calculated according to Equation 2


250

M O L E C U L A R

SIEVE

ZEOLITES

II

coefficients to b e m a r k e d l y h i g h e r i n presence of h e l i u m as a c a r r i e r gas t h a n i n presence of n i t r o g e n . T h e b u l k of substance transport occurs i n the secondary pores, since t h e change of carrier gas does n o t i n f l u e n c e the transport of adsorbate i n t h e z e o l i t e crystal.

T h e same c o n c l u s i o n

f o l l o w s f r o m c o n s i d e r a t i o n of the t e m p e r a t u r e d e p e n d e n c e of t h e d i f f u s i o n coefficients. ('—' Τ

1 5

These

coefficients

increase

with

increasing

temperature

) w h i c h is characteristic of gas-in-gas d i f f u s i o n . S i m i l a r results

are o b t a i n e d w i t h zeolite N a X ( 1 3 ) . F ( E q u a t i o n 1 ) is t h e f u l l cross-sectional area of t h e sample. T a k i n g Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch060

a c c o u n t of t h e sample's p o r o s i t y , €, a n d of the tortuosity factor of t h e canals, k ( 5 ) , w e are able to find k u s i n g t h e e q u a t i o n

* = γ where D

g

Table

§

is t h e literature v a l u e of t h e gas-in-gas d i f f u s i o n coefficient. I d i s p l a y s values of k f o r g r a n u l a t e d zeolites

C a A - I I (12) a n d the pressed p o w d e r e d zeolite N a X Table I. Zeolite Substance

CaA-I Carrier Gas

Nitrogen

Helium

Ethyl Helium alcohol

Values of k

Zeolite k

Substance

2.6 B e n z o l

CaA-I and

(13).

Pressed Powdered Zeolite

CaA-II Carrier Gas

k

Substance

N i t r o g e n 2.2 B e n z o l

Carrier Gas

k

Helium

2.3

2.7 n - H e x a n e N i t r o g e n 2.0 n - H e x a n e H e l i u m

2.2

Ethyl N i t r o g e n 2.5 alcohol

n-Hexane H e l i u m

2.2

n - H e x a n e N i t r o g e n 2.5

Methyl alcohol

2.2

η-Heptane

Helium

N i t r o g e n 2.6

V a l u e s of k f o r the same zeolite s a m p l e i n experiments w i t h v a r i o u s substances p r a c t i c a l l y d o n o t differ—i.e., k is i n d e p e n d e n t of t h e n a t u r e of substance.

T h i s fact indicates t h e absence of a n y c o n s i d e r a b l e a m o u n t

of substance transport t h r o u g h crystals i n t h e i n v e s t i g a t e d systems. L e t us c o n s i d e r the second m o d e of d i f f u s i o n i n granules of zeolite. Zeolites are c h a r a c t e r i z e d b y h i g h values of a d s o r p t i o n at s m a l l values of e q u i l i b r i u m pressure, t h e c o n c e n t r a t i o n i n t h e a d s o r b e d phase b e i n g m u c h h i g h e r t h a n i n t h e gas phase. presents

a p i c t u r e of l a y e r - b y - l a y e r

filling

thus

T h e s e c o n d m o d e of d i f f u s i o n of t h e granule's a d s o r p t i o n


60.

Diffusion

TiMOFEEv

in Granular

251

Zeolites

c a p a c i t y , r u n n i n g f r o m the p e r i p h e r y to the center. I n the l i m i t i n g case ( a r e c t a n g u l a r i s o t h e r m ) , a s h a r p d i v i s i o n w i l l exist b e t w e e n the

filled

a n d the n o n f i l l e d parts of the g r a n u l e . F o r homogeneous a n d i s o t r o p i c g r a n u l e p o r o s i t y , the a d s o r p t i o n v a l u e is p r o p o r t i o n a l to the v o l u m e of the filled p a r t of the granule. I n this case, the r e l a t i v e a d s o r p t i o n v a l u e m a y b e expressed u s i n g the r a t i o of v o l u m e s . C o n s i d e r a s p h e r i c a l g r a n ule

of r a d i u s R, w h o s e a d s o r p t i o n f r o n t p e n e t r a t i o n is x; the r e l a t i v e

adsorption value w i l l be cited


γ

=

(14) = 3α -

°L

do

3α +

a

2

w h e r e a is the a d s o r p t i o n v a l u e at t i m e t, a

(4)

3

is the e q u i l i b r i u m v a l u e of

0

adsorption, and χ

W e h a v e s i m i l a r case for a c y l i n d e r .

γ

where k

x

k =

=

L/R,

=

2

(

1

+

^ )

" (

α

1

+

^ )

α

2

+

Ι

α

3

( 5 )

R a n d L are r a d i u s a n d l e n g t h of the c y l i n d e r .

If

2, t h e n E q u a t i o n 5 is the same as E q u a t i o n 4. S i n c e the m o v e m e n t of the a d s o r p t i o n f r o n t i n a g r a n u l e is r e l a t i v e l y

s m a l l , the adsorbate d i f f u s i o n i n t o the g r a n u l e m a y b e r e g a r d e d as a p s e u d o s t e a d y process. T h e a d s o r p t i o n f r o n t h a v i n g progressed for distance x, the

steady

d i f f u s i o n rate w i l l b e dt where c

0

=

R

4 x j D

(

~ χ

R

x

^

(6)

is the c o n c e n t r a t i o n o n the external surface of the granule.

The

c o n c e n t r a t i o n of adsorbate i n the n o n f i l l e d p a r t of the g r a n u l e is 0. T h e a d s o r p t i o n f r o n t w i l l t r a v e l a distance dx t o w a r d the center of the g r a n u l e i n a t i m e dt at this p a r t i c u l a r distance f r o m the center, the a d d i t i o n a l l y filled v o l u m e b e i n g

(R — x) dx. 2

4?r

t i o n a l to the a d s o r p t i o n increase dm,

T h i s v o l u m e is p r o p o r

i.e.,

dm = 4xz (R -

x) dx 2

(7)

w h e r e ζ is the c a p a c i t y of v o l u m e u n i t of adsorbent. F r o m E q u a t i o n s 6 a n d 7, w e

find

dx

dt

DRCQ z(R

— x)x


(8)

252

MOLECULAR

B y d i v i d i n g variables a n d i n t e g r a t i n g , w e SRx

-

2

SIEVE

ZEOLITES

II

find

2x* = K t

(9)

°

(10)

where κ

=

6

D

R

c

ζ

E q u a t i o n 9 assumes t h e f o r m


χ (3α -

2α ) = 2

ψ

(11)

2

a n d since 3α -

2α ^

3α -

2

3α + 2

α

(12)

3

w e have

Χ Ί

_

Kt

"

β

(13)

2

It f o l l o w s f r o m E q u a t i o n 13 that

χ ~

t -

(14)

Τ

and t α œ —— γίοο

(15)

w h e r e ί „ is the t i m e i n w h i c h the a d s o r p t i o n f r o n t is at the center of the granule. A f t e r i n s e r t i n g v a l u e of a i n E q u a t i o n 4, w e f i n d

ϊ — έ ~ ; ( έ ) '

+

Μ έ ) '

w h i c h approximates to

^ = έ- (έ) (έ) 2

the order of p r e c i s i o n b e i n g ^

3

3

2+

3

(17)

10%.

E q u a t i o n 17 enables us to find t i m e u s i n g o n l y 1 p o i n t of the e x p e r i m e n t a l c u r v e , e.g., y = 0.5. A c c o r d i n g to E q u a t i o n 17, a d s o r p t i o n v a l u e y = 0.5 is r e a c h e d i n the r e l a t i v e t i m e fo.eA» = 0.09; thus, the t i m e of c o m p l e t e filling of a granule ( s p h e r i c a l ) is = ίο.δ/0.09.



60.

Diffusion in Granular Zeolites

TIMOFEEV

253

y

Οβ

0,6 oh 0,2\ 20

40 60 80

iQ0 4&1'4C~16C •

*t

}

Figure 3.

m in

Experimental data plotted according to Equa tion 19; Zeolite CaA-II

a) n-Hexane (t, °C: 1 = 200°, 2 — 100% 3 = 20°; c = 10 mg/l) b) Ethyl alcohol (t, °C: 1 = 200°, 2 = 100°, 3 = 20°; c = 20 mg/l) c) n-Dodecane ft, °C, c mg/l: 1 = 195 and 7.1; 2 = 204 and 6.8; 3 = 111 and 9.8; 4 = 107 and 9.4; 5 = 110 and 8.9) If the d i f f u s i o n coefficient is k n o w n , t i m e t^ m a y b e f o u n d a c c o r d i n g to t h e e q u a t i o n zR

2

6Dc

(18) 0

w h i c h f o l l o w s f r o m E q u a t i o n 13 after u s i n g t h e assumptions a = γ =

1.

T h e reverse

experimental value i A

x

similar mode

1 and

is e q u a l l y possible—i.e., e v a l u a t i o n of D b y a n . of s h e l l p r o g r e s s i v e

combustion

d e s c r i b e d b y P . B . W e i s z a n d R . D . G o o d w i n (18)

coke

has

and W . J. Blinow

been (4).

E q u a t i o n 17 has b e e n c h e c k e d against e x p e r i m e n t a l d a t a i n a n u m b e r of investigations (1,16,17).

R e f . 17 dealt w i t h t h e k i n e t i c s of a d s o r p t i o n


254

MOLECULAR

of v a p o r s of n-hexane,

η - o c t a n e , n-decane,

SIEVE

ZEOLITES

Π

n-dodecane, ethyl alcohol,

p r o p y l a l c o h o l , a n d d i e t h y l ether f r o m a c a r r i e r gas flow ( n i t r o g e n ) zeolite C a A - I I w i t h i n the t e m p e r a t u r e range 2 0 ° - 2 0 0 ° C .

by

Measurements

w e r e c a r r i e d o u t w i t h single granules b y the g r a v i m e t r i c m e t h o d u n d e r d y n a m i c c o n d i t i o n s . T h e flow s p e e d w a s chosen so that the k i n e t i c w a s c o n t r o l l e d b y the rate of i n t e r n a l d i f f u s i o n . Z e o l i t e granules u s e d i n these experiments w e r e i n the f o r m of c y l i n d e r s w h o s e lengths a n d diameters were equal. Some results of experiments are s h o w n i n F i g u r e 3 a c c o r d i n g t o the Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch060

l i n e a r f o r m of E q u a t i o n 17.

(1 - 2)ΐ/3 Γ

χ_ A .

=

(19)

t

F i g u r e 3 shows that e x p e r i m e n t a l d a t a are i n satisfactory w i t h E q u a t i o n 19. F o r values ( 1 — γ ) 2

t i v e a d s o r p t i o n values γ >

1 / 3

t Assuming a =

~ , the a p p r o x i m a t e degree of filling of crystals

near the g r a n u l e surface w i l l b e

"

γ

= 3

τ Ϋπ, ' α'= M*{


(31)

258

M O L E C U L A R SIEVE ZEOLITES

II

whence a' y = 9A f

(a 1

a) (1 -

(32)

a) da 2

ο

B y i n t e g r a t i n g , w e find Y

9A ( 0 . 5 « * - I

(33)

+


or (34) where Β

and

β

(35)

2

It f o l l o w s f r o m E q u a t i o n 34 that the a d s o r p t i o n rate i s i n f l u e n c e d b y d i f f u s i o n coefficients i n t h e c r y s t a l a n d secondary p o r o s i t y b y t h e d i m e n -

15 , Ζ Kurve Figure 5.

Curves γ — τ for various values of Β according to Equation 34 Dotted lines represent experimental data Curves 1-5 as in Figure 4


60.

Diffusion

TiMOFEEV

in Granular

Zeolites

259

sions of crystals a n d granule. B y v i r t u e of assumptions 26 a n d 3 1 , E q u a t i o n 32 is v a l i d u p to γ «

0.1-0.2.

F i g u r e 5 d i s p l a y s curves, p l o t t e d i n a c c o r d a n c e w i t h E q u a t i o n 34 f o r v a r i o u s values of B. It also shows e x p e r i m e n t a l d a t a o b t a i n e d i n e v a c u a t e d systems a n d f r o m a d s o r p t i o n f r o m a carrier gas (15).

flow

(nitrogen)

T h e e x p e r i m e n t a l plots f o l l o w t h e same p a t t e r n as t h e c o m p u t e d

ones. A c c o r d i n g to E q u a t i o n 35, the d i f f u s i o n coefficient

i n crystals is

given b y Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch060

D

l

= ^

(36)

E q u a t i o n 36 p r o v i d e s a basis f o r assessing t h e v a l u e D i f r o m e x p e r i m e n t a l d a t a w i t h g r a n u l a t e d zeolites. V a l u e Β a n d ratio τ/t are f o u n d b y y — t plot. Assuming r =

2.10" c m , w e o b t a i n t h e f o l l o w i n g values of D i f o r 4

the d a t a of F i g u r e 5: η-heptane, 1 0 0 ° C - 1.5 Χ 3.7 χ

10" ; p r o p y l a l c o h o l , 0 ° C - 1.6 Χ 14

5 0 ° C - 6.9 χ 1 0 , 0 ° C - 3.4 χ 1 0 14

15

10"

14

10"

18

cm /sec, 20°C2

c m / s e c ; d i e t h y l ether, 2

c m / s e c . T h e s e values are a c c e p t a b l e 2

limits.

Literature Cited (1) Alekseeva, Ν. I., Timofeev, D. P., Sharifova, Ε. M., Zh. Fiz. Khim. 1966, 40, 238. (2) Barrer, R. M., Trans. Faraday Soc. 1949, 45, 358. (3) Barrer, R. M., Ibitson, D. Α., Trans. Faraday Soc. 1944, 40, 206. (4) Blinow, W. J., Dokl. Akad.Nauk1946, 52, 511. (5) Carman, P. C., "Flow of Gases through Porous Media," Butterworths, London, 1956. (6) Clarke, J. K., Ubbelohde, A. R.,J.Chem. Soc. 1957, 2050. (7) Cummings, G. Α., Ubbelohde, A. R.,J.Chem. Soc. 1953, 3751. (8) Fischer, J.C.,J.Appl. Phys. 1951, 22, 74. (9) Frischat, G. Η., Z. Angew. Phys. 1967, 22, 281. (10) Fuller, Ε. N., Schetter, P. D., Giddings, S. C., Ind. Eng. Chem. 1966, 5, (11) Le Claire, A. D., Phil. Mag. 1951, 42, 468. (12) Ponomarev, A. S., Sharifova, Ε. M., Timofeev, D. P., Dokl. Akad. Νauk 1967, 177, 395. (13) Ponomarev, A. S., Timofeev, D. P., Sbornik "Tseolity, ikh sintez, svoistva i primenenie". Izd. "Nauka", 1965. (14) Timofeev, D. P., Zh. Fiz. Khim. 1965, 39, 2735. (15) Timofeev, D. P., Tverdokhleb, Ν. Α., Sbornik Trudov 3-go Soveshchaniya po Adsorbentam, 1969 (in print). (16) Timofeev, D. P., Tverdokhleb, Ν. Α., Zh. Fiz. Khim. 1966, 40, 2351. (17) Timofeev, D. P., Tverdokhleb, Ν. Α., Sharifova, Ε. M., Zh. Fiz. Khim. 1968 42 2899. (18) Weisz, P. B., Goodwin, R. D.,J.Catalysis 1963, 2, 397. RECEIVED January 30,

1970.


Molecular Sieve Zeolites-II - American Chemical Society

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