Air and Carbon

4 Apparent Surface Diffusion Effects for Carbon Dioxide/Air and Carbon Dioxide/Nitrogen Mixtures with Pelleted Zeolite Beds RICHARD T. MAURER

Downloaded by UNIV OF MELBOURNE on March 26, 2016 | http://pubs.acs.org Publication Date: August 15, 1980 | doi: 10.1021/bk-1980-0135.ch004

Union Carbide Corporation, Engineering Products & Processes Department, Tarrytown Technical Center, Tarrytown, NY 10591 As knowledge concerning diffusion processes in molecular sieve zeolites broadens, it becomes increasingly clear that development of a truly generalizable model for diffusivity prediction in such adsorbents is not likely in the immediate future. The complex electrical forces within and on the surface of the zeolitic crystals, the importance of geometric factors in adsorption of larger molecules, the possibility of diffusive resistances external to the crystals themselves, all conspire to make such a task extremely formidable, especially when it is realized that the predictive models ought to be applicable to adsorption processes involving heat transfer and multicomponent mixtures as well. When the sorbing (and/or desorbing) molecules are small, the situation becomes perhaps somewhat simpler from the standpoint of theoretical analysis, but more difficult experimentally because of the small time constants involved. Problems in analyzing such diffusion processes can arise due to limitations in the resolving ability of the timing device or when other diffusive resistances with larger time constants are present. Nonetheless, such systems can yield interesting information regarding certain features of zeolitic diffusion, and may perhaps be more amenable to successful correlation by means of theoretical or semi-empirical models. In this work, we investigate the diffusion rate of carbon dioxide, from a carrier stream of air or nitrogen, into pelleted forms of Linde types 4A, 5A, and 13X Molecular Sieves. The data are derived from the measurement of breakthrough curves in a uniformly packed column of pellets initially loaded with carrier gas alone, with the feed mixture introduced at constant pressure and flowrate. In selected cases, breakthrough runs were made for identical feed conditions but with different sized pellets, to permit an estimation of the contribution of zeolitic resistances to the overall mass transfer resistances in the system. Using this information, along with information regarding equilibrium loadings and effects of heat transfer, an attempt is made to correlate the mass transfer data over a wide range of feed 0-8412-0582-5/80/47-135-073$08.00/0 © 1980 American Chemical Society

Flank; Adsorption and Ion Exchange with Synthetic Zeolites ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

SYNTHETIC ZEOLITES

74

c o n d i t i o n s , based on standard d i f f u s i v i t y models (using constants derived from p h y s i c a l p r o p e r t i e s of the system), along with a model f o r c o r r e l a t i n g apparent e f f e c t s due to surface d i f f u s i o n w i t h i n the p a r t i c l e s (using a c o r r e l a t i o n constant of best f i t f o r each sorbate-sorbent system).


Theoretical Considerations The packed bed breakthrough method f o r i n v e s t i g a t i o n of mass t r a n s f e r phenomena i n sorbent systems can i n many instances o f f e r c e r t a i n advantages not found i n other experimental methods. The method i s e s p e c i a l l y u s e f u l when the adsorption isotherms f o r the p r i n c i p a l sorbate e x h i b i t favorable curvature (convex toward loading a x i s ) . In such a case, there i s the p o t e n t i a l f o r a port i o n of the s o r p t i o n f r o n t to approach a s t a b l e wave form (shape of the front i n v a r i a n t with time). Given the existence of a s t a b l e or " s t e a d y - s t a t e " mass t r a n s f e r zone (MTZ) and a d e t a i l e d knowledge of the e q u i l i b r i u m loading c h a r a c t e r i s t i c s w i t h i n that zone, one can e x t r a c t l o c a l values of the e f f e c t i v e mass t r a n s f e r r e s i s t a n c e at any c o n c e n t r a t i o n i n the zone. Another feature of the breakthrough method i s that the uniform geometry of the packed column permits f a i r l y s t r a i g h t forward a n a l y s i s o f the thermal waves produced due to heats of adsorption, and of t h e i r e f f e c t on the shape of the s o r p t i o n f r o n t s . The most obvious advantage of t h i s method, however, i s the f a c t that the r e s u l t s of the breakthrough experiments can be a p p l i e d r a t h e r d i r e c t l y to the design o f commercial adsorbers, with r e l a t i v e l y l i t t l e a n a l y s i s of the data. Except i n very simple systems (e.g., nonadsorbable c a r r i e r and n e g l i g i b l e thermal e f f e c t s ) , the a n a l y s i s of breakthrough data from the standpoint of mass t r a n s f e r phenomena r e q u i r e s f a i r l y s o p h i s t i c a t e d mathematical modeling techniques, as w e l l as p r e c i s e knowledge of the multicomponent loadings at e q u i l i b rium c o n d i t i o n s over the ranges of pressure, temperature, and c o n c e n t r a t i o n encountered i n the bed. The Linde D i v i s i o n of Union Carbide Corporation has spent many years developing the data and computer programs necessary f o r such a n a l y s i s , and continues expanding i t s data base to provide the c a p a b i l i t y f o r accurate design i n a wide range of adsorption systems. Among the models and mathematical t o o l s used to analyze the breakthrough data discussed below are the f o l l o w i n g , which w i l l be d i s c u s s e d b r i e f l y i n this section. (1) The l o a d i n g r a t i o c o r r e l a t i o n (LRC) method f o r c o r r e l a t i o n o f pure component s o r p t i o n therms and p r e d i c t i o n of m u l t i component s o r p t i o n therms. (2) The MASC ( f o r "multicomponent adsorption s i m u l a t i o n c a l c u l a t i o n s " ) computer program, which i d e n t i f i e s the regions of s t a b i l i t y and i n s t a b i l i t y w i t h i n the s o r p t i o n f r o n t s , the d i s tance which the f r o n t must t r a v e l through the bed f o r the potent i a l l y s t a b l e regions to a t t a i n t h e i r u l t i m a t e steady-state



4.

MAURER

75

Surface Diffusion Effects

shapes, and the axial temperature and loading profiles within the bed under conditions of adiabatic operation (no heat loss through the walls of the packed column). (3) The SSMTZ computer program, which uses the LRC c o e f f i cients and models for the various mass transfer resistances i n the system to predict the shape of the stable portions of the breakthrough curves in the multicomponent system under isothermal conditions. (4) The SSHTZ computer program, which is similar to the SSMTZ program, except that SSHTZ can predict the shape of the stable portions of the breakthrough curves for either isothermal or adiabatic operation. Due to the complexities involved in the solution, however, SSHTZ i s limited to predictions for binary mixtures only. The methods for correlating the breakthrough data using these tools w i l l be described later. F i r s t , let us briefly discuss the tools and models themselves. The Loading Ratio Correlation. The equilibrium sorption therms for the pure components are correlated to the LRC model (1 ), which can be stated in the following manner: _X_

=

(bP)

Vn

(1) Xo where

1/

1 + (bP) n

In b = Ai + A /T

(2)

η = A3 + A4/T

(3)

2

Thus, five constants (Αχ, A2, A3, A4, and XQ) are used to model the pure component loadings within the ranges of pressure and temperature required. The LRC model, as extended by the method of Markham and Benton (2.) > is also used to predict the loadings in the multicomponent system, based upon the correlation c o e f f i cients for the pure component loading data, v i z . ,

where

Xj

φ\

Xoi

1 + ?0j

(4)

1

1/n

0i - (biPi) *

1/n

- (b P) i iyi

(5)

The differential heat of adsorption for each component in the mixture i s estimated using the Clapeyron equation, extended to multicomponent mixtures and assuming ideal behavior of the gas phase (fugacity of i-th components pj.)> that i s ,


76

SYNTHETIC ZEOLITES

2/air/13X 1/16 p e l l e t systems, the runs c o n s i s t e d of two sets o f three breakthrough runs, with feed temperature being the only parameter v a r i e d i n the s e t , but with s l i g h t l y d i f f e r e n t conditions for either set. In Figure 13, three breakthrough runs i n v o l v i n g CC>2/air/4A 1/16" p e l l e t s with v a r i a t i o n s i n feed pressure alone are shown. Although the p r e d i c t i o n s using the surface d i f f u s i o n model are s l i g h t l y low, the f i t i s again much b e t t e r than that without t h i s model, e s p e c i a l l y i n the r a t i o s of MTZ lengths at high and low pressures. I n c i d e n t a l l y , not enough data were taken to permit s i m i l a r e v a l u a t i o n s of the dependence on temperature i n the 4A system or on pressure or temperature i n the 5A system. Figure 14 shows a p o r t i o n o f the breakthrough f r o n t s f o r the h i g h - c o n c e n t r a t i o n C02/5A 1/8" and 1/4" runs. As mentioned above, these cases r e q u i r e d extensive computer a n a l y s i s to i d e n t i f y the p o t e n t i a l l y s t a b l e p o r t i o n o f the front and the degree to which steady-state behavior of the f r o n t s was approached. I t was found that the o r i g i n a l pure-component LRC's provided a good f i t of the breakthrough loadings and were therefore used i n t h e i r unmodified form i n the multicomponent loading p r e d i c t i o n s . T h i s good f i t i s not s u p r i s i n g , since at the high feed concentrations used, the LRC s p r e d i c t e d that N2 and O2 account f o r l e s s than f i v e percent of the o v e r a l l loadings at bed s a t u r a t i o n . Based on the above-mentioned computer programs, i t was determined that the s t a b l e p o r t i o n of the f r o n t s had a t t a i n e d , at breakthrough, between e i g h t y - f i v e and n i n e t y percent o f t h e i r u l t i m a t e steady-state MTZ lengths, and that e x t r a p a r t i c u l a t e ( f i l m and a x i a l ) r e s i s t a n c e s cont r i b u t e d l e s s than twenty percent of the o v e r a l l mass t r a n s f e r r e s i s t a n c e i n e i t h e r run. M

1

Also presented i n Figure 14 are the computer p r e d i c t i o n s o f the breakthrough f r o n t s based on three separate assumptions. Curve 1 i s based on the assumption that the sole i n t r a p a r t i c l e r e s i s t a n c e s are due to Maxwell and Knudsen d i f f u s i o n . I t i s seen


SYNTHETIC ZEOLITES

96

4.5

PREDICTED USING D

O

S

= 0

2.5


S

ο ω 3

2.0

\ \ \

\

2.5

P R E D I C T E D U S I N G D ^ / T ^ 1.76

10

15

20

cm /HR 2

25

30

35

FEED PRESSURE (BAR)

Figure 11.

Experimental (%) vs. predicted ( ) variation of LUB/G feed pressure for selected CO /air/13X 1/16" runs

M

with

%

4.0 3.5 3.0

-PREDICTED USING D . = 0 ft

s

Ο m 3

2.5 2.0 h 1.5 1.0 PREDICTED USING

0.5

D

0

Figure 12.

220

OS S /T

=

176cm /HR 2

240 260 280 FEED TEMPERATURE (K)

Experimental (Φ,Μ) *· predicted ( ) variation of LUB/Gu with feed temperature for selected CO /air/13X 1/16" runs ν

t


MAURER


PREDICTED USING D

O

S

=0

1.5


1.0

PREDICTED USING D

10

20

30

40

Q S

/T

= 0.37cm /HR 2

s

_l I 50 60 70 80 90 Ρ (psia) FEED PRESSURE (BAR)

L_ 100 110

Figure 13. Experimental (Φ) vs. predicted ( ) variation of LUB/G feed pressure for selected CO Jair/4A 1/16" runs

M

Figure 14.

Y

with

Experimental vs. predicted values of [LUB] >/* for high concentration CO/5A breakthrough runs Ybt


SYNTHETIC ZEOLITES

98

that, as with the previous s e r i e s of runs, t h i s assumption tends to overestimate the s i z e of the MTZ. Curve 2 assumes that i n t r a p a r t i c l e r e s i s t a n c e i s s t i l l v i a the Knudsen and Maxwell d i f f u s i o n a l modes, but that the e f f e c t i v e r e s i s t a n c e due to these modes i s only seventeen percent of that p r e d i c t e d by the d i f f u s i o n models. Such an assumption gives f a i r l y reasonable MTZ length p r e d i c t i o n s down to about ten percent of the feed concent r a t i o n , but tends to o v e r p r e d i c t these lengths at lower concentrations. Curve 3 assumes that surface d i f f u s i o n i s present; the value of ( D /t ) assumed i n the model i s that derived from the runs shown i n Figure 6 f o r the case where micropore r e s i s t a n c e s are accounted f o r . However, since the r e s u l t s of Figure 6 suggest almost f u l l macropore c o n t r o l f o r the case of 1/8" and 1/4" p e l l e t s , the e f f e c t s of the micropore r e s i s t a n c e s were neglected for the current p r e d i c t i o n s . I t can be seen that curves 3A and 3B, for the C0 /N /5A 1/4 and C 0 / a i r / 5 A 1/8 cases, respect i v e l y , y i e l d very good f i t s of the breakthrough curves over the e n t i r e range of measurements shown i n Figure 14.


os

s

M

2

2

M

2

Using the computer programs discussed above, i t i s p o s s i b l e to e x t r a c t from these breakthrough curves the e f f e c t i v e l o c a l mass t r a n s f e r c o e f f i c i e n t s as a f u n c t i o n of C0 concentration w i t h i n the s t a b l e p o r t i o n of the wave. These mass t r a n s f e r c o e f f i c i e n t s are shown i n Figure 15, along with the p r e d i c t e d values with and without the i n c l u s i o n of the surface d i f f u s i o n model. I t i s seen that without the surface d i f f u s i o n model, very l i t t l e change i n the l o c a l mass t r a n s f e r c o e f f i c i e n t i s pred i c t e d , whereas with surface d i f f u s i o n e f f e c t s included, a more than s i x - f o l d increase i n d i f f u s i o n rates i s p r e d i c t e d over the concentrations measured and the p r e d i c t i o n s correspond very c l o s e l y to those a c t u a l l y encountered i n the breakthrough runs. Further, the experimentally derived r e s u l t s i n d i c a t e that, f o r these runs, the assumption that micropore ( i n t r a c r y s t a l l i n e ) r e s i s t a n c e s are small r e l a t i v e to o v e r a l l mass t r a n s f e r r e s i s t ance i s j u s t i f i e d , since the e f f e c t i v e mass t r a n s f e r c o e f f i c i e n t s f o r the two (1/8" and 1/4" p e l l e t s ) runs s c a l e approximately to the inverse of the square of the p a r t i c l e diameter, as would be expected when d i f f u s i v e r e s i s t a n c e s i n the p a r t i c l e macropores predominate. 2

Conclusions The preceding analyses of f i x e d bed breakthrough curves i n v o l v i n g C 0 / a i r or N /4A, 5A or 13X Linde Molecular Sieve p e l l e t s s t r o n g l y suggest the presence of some b e n e f i c i a t i n g mode of mass t r a n s p o r t , which appears to e f f e c t a reduction i n the r e s i s t a n c e s to mass t r a n s f e r w i t h i n the macropore spaces of the zeolite pellets. The author a t t r i b u t e s these e f f e c t s to the presence of surface d i f f u s i o n along the faces of the z e o l i t e c r y s t a l s , which form the w a l l s of the macropores. Equation (21) of the t e x t , based on the S l a d e c k - G i l l i l a n d model f o r surface 2

2



MAURER


Figure 15. Predicted vs. experimentally obtained mass transfer coefficients as functions of breakthrough concentration for the high concentration C0 /5A runs of Figure 14. 2


100

SYNTHETIC ZEOLITES

d i f f u s i o n on nonporous or s o l e l y macroporous sorbent media, appears to provide an e x c e l l e n t means for c o r r e l a t i n g t h i s e f f e c t , at l e a s t w i t h i n a given sorbate-sorbent system. Although the systems i n v e s t i g a t e d here e x h i b i t e d predominantly macropore c o n t r o l (at l e a s t those with p e l l e t diameters exceeding 1/8 or 0.32 cm), there i s no reason to b e l i e v e that surface d i f f u s i o n e f f e c t s would not be e x h i b i t e d i n systems i n which micropore ( i n t r a c r y s t a l l i n e ) r e s i s t a n c e s are important as well. In f a c t , t h i s apparent surface d i f f u s i o n e f f e c t may be r e s p o n s i b l e for the d i f f e r e n c e s i n z e o l i t i c d i f f u s i o n coeff i c i e n t s obtained by d i f f e r e n t methods of a n a l y s i s (13). However, due to the complex i n t e r a c t i o n of various f a c t o r s i n the a n l a y s i s of mass t r a n s p o r t i n z e o l i t i c media, i n c l u d i n g i n s t a b i l i t i e s due to heat e f f e c t s , the presence of multimodal pore s i z e d i s t r i b u t i o n i n p e l l e t e d media, and the u n c e r t a i n t i e s involved i n the measurement of d i f f u s i o n c o e f f i c i e n t s i n m u l t i component systems, f u r t h e r research i s necessary to e f f e c t a r e s o l u t i o n of these d i s c r e p a n c i e s .


M

Nomenclature a

=

Outer p a r t i c l e surface area per column, cm/cm-*

volume of

2

Ajj

=

C r o s s - s e c t i o n a l area of packed column, cm 2

A^, A3, b

A, A4 2

=

C o e f f i c i e n t s i n loading r a t i o c o r r e l a t i o n (LRC), defined by equations (2) and (3)

=

Parameter i n LRC

equation, equal

exp

(-A1-A2/T) phase c o n c e n t r a t i o n , gmol/cm^

to

Cg

=

Gas

c

s

=

Sorbed phase c o n c e n t r a t i o n , gmol/cm

Cpg

=

Heat c a p a c i t y of gas

Cp

=

Heat c a p a c i t y of s o l i d phase, cal/g-K

dp

=

P a r t i c l e diameter,

cm

D

=

Axial d i f f u s i v i t y ,

cm /hr

=

Surface d i f f u s i v i t y along the w a l l s of p a r t i c l e macropores, cm /hr

a x

Dg

S

2

phase, cal/gmol-K

2

the

2

D

os

=

Preexponential f a c t o r i n G i l l i l a n d - S l a d e c k model f o r surface d i f f u s i o n , cm /hr 2


4.

MAURER

101


Nomenclature (Cont'd) G l

'

Molar v e l o c i t y of f l u i d phase i n moving bed a n a l y s i s of steady-state wave, defined by equation (15), gmol/hr/cm 2

G

Molar v e l o c i t y o f feed gas,

M

ΔΗ


^ax

gmol/hr/cm

D i f f e r e n t i a l heat of adsorption,

=

2

cal/gmol

E f f e c t i v e bed thermal c o n d u c t i v i t y i n a x i a l d i r e c t i o n , cal/hr/cm/K Mass t r a n s f e r c o e f f i c i e n t , expressed as e q u i v a l e n t f i l m c o e f f i c i e n t , cm/hr

Κ

P a r t i c l e length, cm L

A x i a l distance measured from feed end o f bed, cm

Lb

O v e r a l l length of bed, cm

LUB

Length o f unused bed i n s o r p t i o n f r o n t , f t .

m

=

Parameter i n a c t i v a t i o n energy term of G i l l i l a n d - S l a d e c k model f o r surface d i f f u s i o n = 1 , 2 or 3 depending on type o f sorbate-sorbent i n t e r a c t i o n

η

=

Parameter i n LRC equation = A3 + A4/T

Ρ

Pressure, Bar (1 Bar = 100 kPa)

Pi

P a r t i a l pressure of component i i n mixture, Bar

ο r

pore

=

Mean radius of macropore channels, A R Gas

constant

I n t r a p a r t i c l e s p e c i f i c surface area, cm /g of sorbent 2

t

Temperature i n mass t r a n s f e r f r o n t , °C

T

Temperature, Κ

TUB

Time of unused bed,

hr = (LUB)/uf


102

SYNTHETIC ZEOLITES

Nomenclature (Cont'd) uf

=

Mass t r a n s f e r front speed, defined by equation (16), cm/hr

V

=

Superficial velocity

0

column = X


X

0

through unpacked

G^lp

gm

=

Loading

of sorbate, gmol/g of sorbent

=

Maximum achievable loading, gmol/g o f sorbent

y

=

Gas phase mole

fraction

yj

=

Mole f r a c t i o n o f i n e r t c a r r i e r gas

Y

=

Gas phase molar r a t i o , gmol/gmol c a r r i e r

Greek L e t t e r s ε

=

ρ

=

8j

Void f r a c t i o n o f p a r t i c l e macropores, cm-Vcm^ p a r t i c l e T o t a l v o i d f r a c t i o n of bed, excluding i n t r a c r y s t a l l i n e (micropore) voids = 1 - (ρ /Ρ )(ΐ-ε ) 0

ρ

ρ

θ

=

Time, h r

Pb

=

P a r t i c l e bulk (packed) d e n s i t y , g/cm^

Pgm

=

Molar d e n s i t y o f gas phase, gmol/cm^

Pp

=

P a r t i c l e piece d e n s i t y , g/cm^

=

T o r t u o s i t y f a c t o r f o r Maxwell and surface diffusion, respectively

=

( b i p i ) / ! i n LRC equation

bt

=

Conditions at breakthrough c o n c e n t r a t i o n

eff

=

Effective

f

=

Conditions at feed concentration

r

=

Residual bed c o n d i t i o n s (at beginning of each s o r p t i o n run)

T

S

*i

1

1 1

Subscripts

value


4.

MAURER

103


Nomenclature (Cont'd) 1/2

Conditions at the point at h a l f the sorbate feed concentration

ι

1, 2,

η component

Superscript E q u i l i b r i u m value


Abstract Breakthrough runs for CO /N and CO /Air mixtures on Linde 4A, 5A, and 13X pellets of three different diameters were carried out in fixed bed columns designed to simulate nearly adiabatic behavior. The sorption fronts were analyzed to sepa rate effects of intraparticle mass transfer from those due to heat transfer and extraparticle (film and axial) mass transfer phenomena. Although the dependence of mass transfer zone (MTZ) length upon pellet size indicated that mass transfer rates for pellets with diameters of 1/8" and larger are essentially con trolled by macropore resistances, the observed MTZ lengths were consistently less (sometimes by nearly an order of magnitude) than those predicted by macropore Maxwell and Knudsen dif fusional modes alone. Such predictions were also unable to account for variations in MTZ length with different feed con ditions. Inclusion of a surface diffusion model, however, gave excellent correlations of the data over wide ranges of pressure, temperature, and concentration. The author suggests that such a surface effect and/or heat transfer effects discussed in the paper could conceivably account for past discrepancies in the values of zeolitic (micropore) diffusion coefficients as ob served through different experimental techniques. 2

2

2


104

SYNTHETIC ZEOLITES


Literature Cited 1. Yon, C.M.; Turnock, P.H. AICHE Symposium Ser. No. 117, 1971, 67, 75. 2. Markham, E.D.; Benton, A.F. J. Am. Chem. Soc., 1931, 53, 497. 3. Michaels, A.S. Ind. Eng. Chem., 1952, 44, 1922. 4. Leavitt, F.W. Chem. Engr. Progr., 1962, 58, 54. 5. Lightfoot, E.N.; Sanchez-Palma, R.J.; Edwards, D.O., in "New Chemical Engineering Separation Techniques" (Schoen, H.M., Ed.); Interscience: New York, 1962, p. 99. 6. Perry, R.H.; Chilton, C.H.; Kirkpatrick, S.D. "Chemical Engineers' Handbook", 4th ed.; McGraw-Hill: New York, 1962; pp. 13-16. 7. Treybal, R.E. "Mass Transfer Operations"; McGraw-Hill: New York, 1955; pp. 54-55. 8. Hirschfelder, J.O.; Curtiss, C.F.; Bird, R.B. "Molecular Theory of Grases and Liquids"; John Wiley & Sons: New York, 1954. 9. Satterfield, C.N. "Mass Transfer in Heterogeneous Catalysis"; MIT Press: Cambridge, Mass., 1970; pp. 33-42. 10. Gilliland, E.R.; Baddour, R.F.; Perkinson, G.P.; Sladeck, K.J. Ind. Eng. Chem. Fundamentals, 1974, 13, 95. 11. Sladeck, K.J.; Gilliland, E.R.; Baddour, R.F. Ind. Eng. Chem. Fundamentals, 1974, 13, 100. 12. Breck, D.W. "Zeolite Molecular Sieves"; John Wiley & Sons: New York, 1974; p. 384. 13. Ruthven, D.M., in "Molecular Sieves - II" (Katzer, J.R., Ed.); ACS Symposium Ser. No. 40; American Chemical Society: Washington, D.C., 1977; p. 330. RECEIVED

April 24, 1980.


Air and Carbon

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