Butane in Zeolite NaX

34 Kinetics of Sorption, Desorption, and Diffusion of n-Butane in Zeolite N a X H.-J.

DOELLE and L . RIEKERT

Downloaded by UNIV OF PITTSBURGH on May 10, 2016 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0040.ch034

Institut für Chemische Verfahrenstechnik, der Universität Karlsruhe, Karlsruhe, West Germany

ABSTRACT The kinetics of sorption and desorption of n-butane in single crystals of zeolite X (crystal diameter = 80/μm) has been studied at 25°C, using a rapid gravimetric apparatus. Intracrystalline diffusion coefficients for sorption and desorption are of the order of 10 sq.cm sec and indepen dent of the direction of flux. The temperature of the zeo lite sample changes significantly in a sorption or desorp tion run, due to the heat of sorption. Heat transfer is rate limiting in the final approach to equilibrium in unsteady sorption or desorption experiments. -7

-1

Introduction D i f f u s i o n c o e f f i c i e n t s o f substances sorbed i n z e o l i t e s have been obtained from rates o f sorption and desorption f o r many systems under the assumption that i n t r a c r y s t a l l i n e d i f f u s i o n i s rate determining i n these processes* Three pecu l i a r i t i e s o f the pattern o f d i f f u s i v i t i e s i n z e o l i t e s , ob tained i n t h i s way, however, are not e a s i l y explained by a random movement o f guest molecules i n the host l a t t i c e as the basic mechanism of d i f f u s i o n : (1) D i f f u s i o n c o e f f i c i e n t s have sometimes been found t o depend very s t r o n g l y on the degree o f loading ( o r con c e n t r a t i o n o f the sorbate) — with some systems a v a r i a t i o n by several orders o f magnitude has been ob served (1, 2 ) * (2) In some cases i t f o l l o w s from the k i n e t i c s o f sorption 401 Katzer; Molecular Sieves—II ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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and o f desorption that the d i f f u s i o n c o e f f i c i e n t depends rather on the degree o f advancement o f the process i n e i t h e r d i r e c t i o n than on the concentration of the sorbate ( 3 4 ) , a r e l a t i v e l y high r a t e (or d i f f u s i v i t y ) always being observed a t the beginning of s o r p t i o n o r desorption. I f the d i f f u s i v i t y decreases with concentration o f the sorbate, then the r a t e o f desorption should increase with the advancement o f the process, a behaviour that was never observed to our knowledge. (3) I t was observed i n some cases that the d i f f u s i v i t y depends on the d i r e c t i o n o f the f l u x , the d i f f u s i v i t y i n s o r p t i o n being much higher than i n desorption (5, 6). These observations taken together can not be explained on the b a s i s o f any mechanism o f random walk d i f f u s i o n i n a z e o l i t e - c r y s t a l (or an ensemble o f c r y s t a l s whose p r o p e r t i e s and a c c e s s i b i l i t y f o r the sorbate are i d e n t i c a l ) , even i f the d i f f u s i v i t y changes with concentration. I t was the purpose o f the work described here to i n v e s t i g a t e the r a t e o f s o r p t i o n and desorption o f η-butane i n z e o l i t e X as an example, d i f f e r e n t v a r i a b l e s i n the e x p e r i ment being c a r e f u l l y c o n t r o l l e d i n order t o e s t a b l i s h which f a c t o r s o r processes i n f l u e n c e the observed r a t e .


#

Experimental procedure, m a t e r i a l s Sorption e q u i l i b r i a and k i n e t i c s o f s o r p t i o n and de s o r p t i o n were observed with the apparatus shown schemati c a l l y i n f i g u r e 1. The basic equipment o f the g r a v i m e t r i c system was a Cahn R 100 electrobalance which proved t o be s a t i s f a c t o r y a f t e r i n i t i a l d i f f i c u l t i e s had been overcome. The time constant o f the balance and i t s recording c i r c u i t r y i s o f the order o f 10-1 sec. Temperature o f the g l a s s tube with the sample l e g was kept constant a t (25+0,1)°C by c i r c u l a t i n g water. Pressure i n the s o r p t i o n volume (V =2,79 l ) was monitored by a d i f f e r e n t i a l pressure t r a n s ducer (MKS Baratron Type 77) with \% accuracy. Step f u n c t i o n s o f pressure (symmetrical i n s o r p t i o n and desorption) could be obtained with t h i s apparatus, the time constant o f pressure change (0,3 sec) being short compared to the time constant o f the r e s u l t i n g mass t r a n s f e r i n t o or out o f the s o l i d . In separate experiments the change i n s

Katzer; Molecular Sieves—II ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


34.

D O E L L E A N D RiEKERT

η-Butane

in Zeolite NaX

403

temperature o f the z e o l i t e sample was measured with a t h i n thermocouple (Pt/PtRh; 0,1 mm 0) during s o r p t i o n runs being e x a c t l y i d e n t i c a l t o those o f the g r a v i m e t r i c studies* Z e o l i t e X was synthesized according to C h a r n e l l ( 7 ) , c r y s t a l s ranging i n s i z e from 10>um t o 100/urn were obtained and a f r a c t i o n c o n t a i n i n g only c r y s t a l s i n the diameter range (80 + 10) /jm was separated by wet s i e v i n g and used i n the present experiments* The dry composition o f the zeo l i t e corresponded to Na2Û · AI2O3 · 2,25 S1O2; i t s c r y s t a l s t r u c t u r e was v e r i f i e d by X-ray d i f f r a c t i o n * jj-Butane (CH3-CH2-CH2-CH3) 99,5 vol% pure an no i n e r t c a r r i e r gas was used as a sorbate* A c t i v a t i o n o f the z e o l i t e c r y s t a l s i n the sample pan was accomplished by evacuating the sample a t 300°C t o ρ < 1 0 - t o r r u n t i l a constant weight reading was recorded by the balance (about 2 hours)* Sorption and desorption runs were performed w i t h i n an approximately l i n e a r range o f the isotherm, i t ' s slope being given as 4

dn (?) f

—5 dp

0)

= K m ζ

I f k i n e t i c s are c o n t r o l l e d by d i f f u s i o n i n t o or out of the sample then the e v a l u a t i o n o f s o r p t i o n and desorption experiments should be represented by the appropriate s o l u t i o n o f the d i f f u s i o n equation f o r the case o f " d i f f u s i o n from a s t i r r e d s o l u t i o n o f l i m i t e d volume" (8,9,10), the time dependent boundary c o n d i t i o n f o r t h i s case being i d e n t i c a l t o the boundary c o n d i t i o n f o r the present case (11, 12X

Results and d i s c u s s i o n s Sorption isotherms obtained f o r η-butane i n the z e o l i t e (Identical i n s o r p t i o n and desorption) are shown i n f i q u r e 2. An i s o s t e r i c heat o f s o r p t i o n ^ H = - 4 0 k J mol~^ f o l l o w s from these data* Results o f k i n e t i c measurements a r e presented i n f i g u r e 3d-3c, where the dimensionsless r a t i o ùn/ànf [ f r a c t i o n o f f i n a l ( p o s i t i v e o r negative) uptake J i s p l o t t e d as a f u n c t i o n o f YF. Conditions o f the experiments are s p e c i f i e d i n Table I ; the r e p r o d u c i b i l i t y o f a l l these r e s u l t s was v e r i f i e d s



3,97· ΙΟ"

92

Sorption

Sorption

8

9

-

2

8,17·10"

91

Desorption

7

92

2

2

6,74·ΙΟ"

6,74·ΊΟ"

91

Sorption

6

8,19·10"

2

2

8,22·ΙΟ"

2

2

8,18·10"

2 2

0,9·ΙΟ"

1,47·1θ"

5

1,47·10"

2

0,667·ΙΟ"

0,72

0,472

0,186

0,327

0,075

0,256

0,165

0,215

0,217

0,234

0,278

0,127

0,198

0,097

0,108

0,205

2

2

0,112

f mm Hg

P

F i n a l pressure

0,35

18

Sorption

4

18

ο

mm Hg

ρ

I n i t i a l pressure

2

1,63·10"

3.97·10"

m mol

F i n a l amount of sorbate

Desorption

Sorption

3

39,5

-

0 m mol

n

I n i t i a l amount of sorbate

2

Sorption

2

92

weight

0,88·ΙΟ"

Sorption

1

m ζ mg

Zeolite

18

Type

No

Table I.-Conditions o f experiments presented i n f i g u r e 3a-3c


34.

DOELLE AND

RIEKERT

n-Dutane in Zeolite

NaX

405


Figure 1. Schematic of the apparatus. B, electrohdlance; P, pressure trans ducer; T, turbomolecular pump.

.1

.2

.3 Ρ torr

Figure 2.

Sorption isotherms of n-hutane in NaX: mass ratio of butane and zeolite at equilibrium



406 MOLECULAB SIEVES—II



Figure 3. (a,b; left, c; above) Kinetics of sorption (O) and desorption (Φ) of n-butane in NaX. Numbers on curves refer to Table 1.


MOLECULAR


408

SIEVES—II

repeatedly* Three general observations about the r a t e behaviour are immediately obvious from f i g u r e 3a-3c: a) The amount Δ η of uptake or desorption i s i n i t i a l l y p r o p o r t i o n a l to A f t , the slope being independent of the d i r e c t i o n of the f l u x ; b) The i n i t i a l r a t e of s o r p t i o n or desorption, resp*, decreases with sample-weight; c) The r a t e of s o r p t i o n or desorption slows down con s i d e r a b l y a f t e r about 5QJS of the process i s completed: i n a l l cases there i s a pronounced bend i n the curve of Δ η vs. ~\JT. Observation (a) i n d i c a t e s t h a t a process of d i f f u s i v e mass t r a n s f e r c o n t r o l s the r a t e of s o r p t i o n or desorption, resp. The z e o l i t e sample c o n s i s t e d of a loose p i l e (height h) of i n d i v i d u a l c r y s t a l s (with diameter d ) , there are there fore two l i m i t i n g cases of r a t e law which can be expected: (1) The d i f f u s i o n of sorbate i n the c r y s t a l s i s rate con t r o l l i n g and there i s no concentration gradient i n the gas phase between the c r y s t a l s along the height h of the p i l e * In t h i s case the r e l a t i v e change of the amount of sorbate i n the sample must be a f u n c t i o n of the dimenionless group D t / d * where D i s the c o e f f i c i e n t of d i f f u s i o n i n the z e o l i t e c r y s t a l s and t i s the time c

An Δη^

=

f

4-

(2)

η

(2)

c

ν δ

the i n i t i a l slope of Δ η / Δ ί · being pro p o r t i o n a l to Y ^ c / d ; independent of the sample height h. E q u i l i b r i u m between i n d i v i d u a l c r y s t a l s and the gas phase contingent to any c r y s t a l i s e s t a b l i s h e d , depen ding on gas phase concentration along sample height h. There i s then no concentration gradient i n the i n d i v i dual c r y s t a l s , the r a t e of d i f f u s i v e mass t r a n s f e r i n the voids between c r y s t a l s i s r a t e c o n t r o l l i n g and we must have ' D_ · t


34.


η-Butane

in Zeolite

409

NaX

the i n i t i a l slope of Δ η / Δ η ^ v s . ~\fV being propor t i o n a l to \ Dapp/h» dependent on sample height h. app

D

w i l 1

b e

a l v e n

D

D app

KRT

b v

eff

(4)

Q

, + 6 * sample

, /

where D f f i s the e f f e c t i v e d i f f u s i v i t y i n the void spaces of the sample, Κ the slope of the isotherm (equ. (1)) and 6 the void f r a c t i o n i n the sample p i l e


e

03)· As can be seen from f i g u r e 3a, the slope of Δ η / Δ nf vs. "^ΊΓ decreases almost l i n e a r l y with the i n v e r s e of the weight m of the sample z

Expt. ηο· m

z

1 92 1.1

2

3 39,5

(18)

mg

2.0

(4.3)

min" /

1

2

I t can thus be concluded that the second case, equ. ( 3 ) , was approximated, mass t r a n s f e r i n the voids between c r y s t a l l i t e s s t r o n g l y i n f l u e n c i n g the r a t e i n experiments no. 1 and 2 with the l a r g e r samples. In order to o b t a i n the d i f f u s i v i t y D of η-butane i n the z e o l i t e - c r y s t a l s the mass t r a n s f e r r e s i s t a n c e i n the voids between the c r y s t a l s had t h e r e f o r e to be avoided. This was achieved by using a small sample (m =18 mg) spxead evenly over a surface of 2 cm^ on a s p e c i a l sample-pan made from aluminum f o i l . The sample consisted thus of l e s s than a monolayer o f c r y s t a l s (about 65%); no r e s i s t a n c e to mass t r a n s f e r i n the gas phase i s p o s s i b l e with t h i s arrangement, whereas i n experiments no 1 and 2 a smaller sample pan and thus a p i l e of approximately 16 or 37 monolayers of c r y s t a l s was used. Rate data f o r the monolayer-case are shown as runs no 3,4,5 i n f i g u r e 3b. I t can be seen that the amount of up take or desorption i s i n i t i a l l y p r o p o r t i o n a l to Λ^Τ* a l s o i n t h i s case where i t then must be represented by equ. (2)· c

2


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410

SIEVES—II

From the s o l u t i o n of the d i f f u s i o n equation f o r s p h e r i c a l geometry f o l l o w s a lower l i m i t f o r the d i f f u s i o n c o e f f i c i e n t D of η-butane i n NaX a t 300 Κ of c

D

c

^

2· 10""^ cm

2

sec~\

This value i s given as a lower l i m i t since i n t h i s case 50% o f Δ η / Δ nf was reached at t «*0.75 sec. which i s close to the response-time of the equipment. I n t e r e s t i n g l y t h i s value of D comes close t o i n t r a c r y s t a l l i n e d i f f u s i o n c o e f f i c i e n t s that have been observed i n z e o l i t e s by NMR spin-echo techniques (14, 15). The v a r i a t i o n of Δ η / Δ η { with time i s independent of the d i r e c t i o n of the f l u x , the d i f f u s i v i t y D obtained f o r s o r p t i o n i s equal t o the value which c h a r a c t e r i z e s desorption. T h i s r e s u l t was obtained by observing the r e l a x a t i o n of sample weight and pressure i n a closed system a f t e r the volume of the system had been expanded a t t = 0 i n a s t e p - l i k e f a s h i o n . The desorbing gas was not removed from the system by pumping, because i n that case the r a t e of desorption would have been i n f l u e n c e d by the pumping-rate, which i s always f i n i t e . The change of Δ η / Δ n^ was always linear i n "^~Fup to Δ η/Δ nf 0.5, afterwards a decrease i n the slope was observed i n a l l cases which i s much more pronounced than


c

c

could possibly be explained on the basis of the diffusionequation. T h i s bend can a l s o not be due to a concentration dependent d i f f u s i o n c o e f f i c i e n t since i t occurs i n desorption i n e x a c t l y the same way as i n s o r p t i o n . Furthermore i t was a l s o observed i n experiments no. 1 , 8 , 9 where the rate was mainly c o n t r o l l e d by gas-phase d i f f u s i o n between c r y s t a l s , the apparent d i f f u s i o n c o e f f i c i e n t Dgpp being constant i n the l i n e a r range o f the isotherm according to equ. ( 3 ) . The phenomenon can therefore not be explained by any p e c u l i a r i t y of d i f f u s i v e mass-transfer. However, since the s o r p t i o n of η-butane i s exothermic (AHs=-40kJ mol-1), the sample can not remain a t s t r i c t l y constant temperature i n any s o r p t i o n or desorption run, as has been pointed out by Wicke (16). I t ' s average temperature Τ w i l l be given by a heat balance


34.


η-Butane

in Zeolite

NaX

411

s

where hy=m ( c ) + η (cpis+^pCcp)* * "the combined heat capacity o f z e o l i t e ( z ) , sorbate As) and sample-pan ( p ) , and IT Τ i the time-constant o f temperature-equilibration with the surroundings a t T Q * Since sorption o r desorption i s very r a p i d i n i t i a l l y - f o l l o w i n g "^"T - the f i r s t term on the r i g h t hand side o f equ* (5) w i l l be more important than the second i n the e a r l y stages o f a run, the sample being then approximately a d i a b a t i c . The amount η of sorbate at e q u i l i b r i u m decreases with pressure and with temperature, the e q u i l i b r i u m point w i l l therefore be reached e a r l i e r un der a d i a b a t i c than under isothermal conditions* The combi nation o f the mass and heat balances i s i l l u s t r a t e d schema t i c a l l y for the case o f sorption ( Δ η > 0) i n f i g u r e 4, assuming .that the sample i s a d i a b a t i c up t o point B, where the a c t u a l uptake Δ η becomes equal t o the e q u i l i b r i u m value Δη*· At t h i s point the system i s i n e q u i l i b r i u m with respect to mass t r a n s f e r , but not with respect t o heat trans f e r * A f t e r point Β has been reached the temperature d i f f e rence T - T Q w i l l decrease e x p o n e n t i a l l y with timeconstant *Xj. The e q u i l i b r i u m uptake Δ η * (Τ, ρ) w i l l now increase accordingly and so w i l l the a c t u a l uptake Δ η i f the sample remains close t o e q u i l i b r i u m with respect t o mass t r a n s f e r * This rather simple model p r e d i c t s a change o f the rate law at point Β (ηβ , b ) ; i t ' s l o c a t i o n can be c a l c u l a t e d from the heat balance and from the e q u i l i b r i u m data presented i n f i g u r e 2* E* g* f o r the conditions of experiment no* 1 point Β should be reached before Δ η / Δ η ^ equals 0*7; the change o f the rate law being more gradual i n the a c t u a l system than i n the s i m p l i f i e d model which neglects gradients of temperature o r concentration i n the sample* 2

p

z


s

7

The v a r i a t i o n o f temperature with i j ' t obtained by T-measurements i n the z e o l i t e sample i s shown i n f i g u r e 5 together with the sorption k i n e t i c s under i d e n t i c a l con d i t i o n s ; the maximum o f Τ occurs a t the same time as the bend i n Δ η/Δ nf* A f t e r t h i s point the temperature i n c r e ment T - T Q decreases e x p o n e n t i a l l y with time and so does the distance (nf-n) o f the amount η o f butane i n the z e o l i t e from the amount nf a t f i n a l e q u i l i b r i u m , the time constant being 1 j=1*8 min i n both cases as shown i n f i g u r e 6. We may thus s a f e l y conclude that the rate o f sorption or de sorption a f t e r the bend i n the curves o f Δ n / ^ n f i s e s s e n t i a l l y c o n t r o l l e d by heat t r a n s f e r and not relevant with respect to d i f f u s i o n i n the z e o l i t e *



MOLECULAR

Figure 4. Variation of Δ η, temperature, and Δ η * (ρ,Τ) with \ / t if sample behaves nearly adiabatic up to point (n *, b) (sche matic); (- · -), isothermal case b

Figure 5. Variation of sample temperature from thermo couple measurements and sorption kinetics under identical conditions


SIEVES—Π

DOELLE

A N D RIEKERT

η-Butane

in Zeolite

NaX


34.


413

414

MOLECULAR

SIEVES—II

I t a l s o f o l l o w s that s o r p t i o n during the i n i t i a l uptake does not take place i n a s t r i c t l y isothermal system* The c o e f f i c i e n t o f i n t r a c r i s t a l l i n e d i f f u s i o n obtained from the i n i t i a l r a t e o f s o r p t i o n o r desorption i n a monolayer o f c r y s t a l s has hence t o be considered as an average f o r the r e s p e c t i v e temperature i n t e r v a l o f approximately 10 K.


Conclusions Three conclusions can be drawn from these r e s u l t s : a)

b)

Sorption and desorption o f η-butane i n i n d i v i d u a l c r y s t a l s o f NaX i s c o n t r o l l e d by d i f f u s i o n , the d i f f u s i v i t y being a t l e a s t 2·10-7 cm* sec-1 a t 300 K, inde pendent o f the d i r e c t i o n o f the f l u x . The time constant o f d i f f u s i o n i n the c r y s t a l s T d = A D 7T2 i s o f the order o f magnitude o f o n l y 8 sec with the r e l a t i v e l y l a r g e c r y s t a l s (d=80/jra) used here and i t w i l l be shorter f o r smaller c r y s t a l s . D i f f u s i o n i n the gas phase between c r y s t a l s w i l l then be l i k e l y t o c o n t r o l the r a t e o f s o r p t i o n o r desorption i n agglomerates. Unsteady s o r p t i o n or desorption can never be s t r i c t l y i s o t h e r m a l ; the f i n a l approach t o e q u i l i b r i u m i s con t r o l l e d by heat t r a n s f e r . D2

C

c)

Acknowledgement We are indebted t o H. Pdtow who synthesized z e o l i t e NaX i n l a r g e c r y s t a l s . F i n a n c i a l support o f our work from the Fonds der Chemie i s g r a t e f u l l y acknowledged.

Notation Cp D

Heat c a p a c i t y a t constant pressure, J g~1 Κ D i f f u s i o n c o e f f i c i e n t o f butane i n z e o l i t e c r y s t a l s , c«2 sec-1 D f f E f f e c t i v e d i f f u s i o n c o e f f i c i e n t o f butane i n the voids between c r y s t a l s , cm2 sec-1 c

e


34.


D pp Δ Hs Κ m η ρ R Τ t Q


z

η-Butane

in Zeolite

NaX

415

Apparent d i f f u s i v i t y , cm^ sec"^ Heat o f s o r p t i o n , J raol""^ Slope o f the e q u i l i b r i u m isotherm, mol Pa"^ g' Mass o f the z e o l i t e sample, g Amount o f sorbate i n the sample, mol Pressure, Pa Gas constant = 8.32 J mol-^KAbsolute temperature, Κ Time, sec 1

Subscripts ο * f

Value a t the beginning o f experiment (t=0) Value a t e q u i l i b r i u m with respect t o mass t r a n s f e r F i n a l value a t e q u i l i b r i u m with respect t o mass and heat t r a n s f e r

Literature Cited 1 2 3 4 5 6 7 8 9 10 11 12 13

Loughlin, K . F . , Derrah, R . J . , Ruthven, D.M., Can.J.Chem. Eng. (1971) 49, 66 Ruthven, D.M., Loughlin, K . F . , Derrah, R . I . , Advan.Chem. Ser. (1973) 121, 330 Satterfield, C . N . , Margetts, W.G., A . I . C h . E . J . (1971) 17, 295 Brandt, W.W., Rudloff, W., J. Phys.Chem.Solids (1964) 26, 741 Satterfield, C . N . , Frabetti, A . S . , Α . I . C h . E . J . (1967) 13, 731 Karge, H . G . , Klose, K . , Ber.Bunsenges.phys.Chem. (1975) 79, 454 Chamell, J.F., J.Cryst.Growth (1971) 8, 291 Berthier, G . , J.Chim.Phys. (1952) 49, 527 Carman, P . C . , Haul, R.A.W., Proc.Roy.Soc.A (1954) 222, 109 Crank, J., The Mathematics of Diffusion, Oxford Univ. Press 1970 Barrer, R.M., Trans. Faraday Soc. (1949) 45, 358 Riekert, L., A . I . C h . E . J . (1971) 17, 446 Weisz, P . B . , Trans. Faraday Soc.(1967) 63, 1801


416

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SIEVES—II

Resing, H . A . , Murday, J.S., Advan.Chem.Ser. (1973) 121, 414 P f e i f e r , H., Schirmer, W., Winkler, H., Advan.Chem. Ser. (1973) 121, 430 Wicke, E., K o l l o i d - Z e i t s c h r i f t (1939) 86, 167


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Butane in Zeolite NaX

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