DIFFUSION STUDIES IN ZEOLITES RELATED SOLIDS B Y GAS CHROMATOGRAPHIC TECHNIQUES P . E. E B E R L Y , J R . ESSO Research Laboratories, Baton Rouge Rejinery, Humble Oil @ Refining Co., Baton Rouge, La. 70821 The diffusion of inert gases (Ar, Kr, SFs) in a series of zeolites including 3A and 5A Molecular Sieves, N a and H mordenites, N a faujasite, and amorphous silica-alumina catalyst was studied b y a gas chromatographic technique. Between 25' and 427" C., the flow is best described b y an activated diffusion process. Activation energies increase with molecular weight of the gas and range from 2.5 to 15 kcal. per mole. For gases which can readily enter the pores, the diffusion resistance for the various solids decreases in the order: Na mordenite H mordenite 5A N a faujasite silica-alumina. The effect of molecular weight on diffusivity is much more proneunced than that expected for Knudsen diffusion. A mathematical procedure for including the effects of adsorption on the diffusion constant is described. Heats of adsorption for the various gases varied from 3 to 6 kcal. per mole.
>
OR
>
>
>
many years, the principles of gas-solid chromatography
F have been used to measure heats of adsorption and the
initial slopes of adsorption isotherms (Eberly, 1962; Greene and Pust, 1958; Habgood and Hanlan, 1959; Ross et al., 1962). Only recently similar techniques have been applied to measuring the diffusivity of gases in porous solids (Davis and Scott, 1965; Leffler, 1966; Smith, 1967). Basically, the method consists in injecting a pulse of the gas under study into a carrier gas stream, transporting it through a packed column of solid, and measwin? the dispersion of the emergent pulse. By doing this at a series of flow rates, the effective diffusivity of the gas in the porous solid can be evaluated. This is an unsteady-state technique and, consequently, the effective diffusivity would be expected to reflect the "dead-end" as well as the continuous-pore structure. This method has the inherent advantage that a fairly large and representative sample of the solid can be studied at temperatures equivalent to those used in the commercial process. I n pelleted and extruded zeolites, the pore structure can be visualized as consisting of a macropore system connecting with the micropores in the individual crystallites, the latter having dimensions the same order of magnitude as the diffusing molecules. The effective diffusivity measured by gas chromatography would be expected to reflect both pore systems. Diffusion in the macropores would be fast and characterized by low activation energies. I n the micropores, however, the molecules are always very close to the pore walls and the flow would contain properties of both diffusion and adsorption. Thus, the diffusivity would be expected to show a stronger dependence on temperature and vary greatly with the nature of the diffusing molecule. Inert gases can be used to minimize the effects of adsorption. The present investigation concerns the diffusion of inert gases such as He, Ar, Kr, and SFGin type A zeolites, mordenites, and faujasites at 2 5 O to 427' C. as determined by gas chromatography. Comparative results are also included for an amorphous silica-alumina catalyst. Previous work on diffusion in zeolites has generally involved the measurement of adsorption or desorption rates under either constant-volume or constantpressure conditions (Barrer, 1949 ; Barrer and Peterson, 1964; Nelson and Walker, 1961 ; Satterfield and Frabetti, 1967 ; Satterfield and Shenvood, 1963).
Experimental
The solid (30 cc.) in the form of either 1/,6-inch extrudates or l/s-inch pellets was packed into nominal 3/s-inch aluminum tubing, resulting in a bed length of 76 cm. The column was immersed in a fluidized sand bath for constant temperature control and heated under helium flow at 427' C. for 16 hours to remove adsorbed impurities. The gas chromatographic measurements were then made at a series of descending temperatures. Attempts were made to minimize void volumes external to the packed bed by the insertion of solid rods. T o correct for wall effects, experiments were also made on similar columns containing nonporous glass beads. Characteristics of the columns are listed in Table I. The 3A and 5A Molecular Sieves were obtained from the Linde Co. Division, Union Carbide Corp. (lot numbers 35108 and 5253, respectively). The remaining materials were synthesized locally. The diameter, dp, of the particles was calculated for spheres of equal volume. The surface area and pore volume were evaluated by standard nitrogen adsorption techniques. T h e fraction of voids external to the particles was determined by saturating a separate portion of the particles with methanol, superficially drying them, and then measuring their displacement in methanol. Discussion of Results
Theory. I n gas chromatography, the height of a n equivavalent theoretical plate (HETP) can be obtained from the properties of the effluent pulse. I n our studies, the following equation listed by Purnell (1962) was used.
Van Deemter, Zuiderweg, and Klinkenberg (1956) have shown that H E T P can be related to the carrier gas interstitial velocity, U , by the relation: HETP = A
+ B-U + CU
where constants A and B are associated with the dispersion caused by eddy and molecular diffusion, respectively, in the gas phase. For our purposes, the most important constant is C, relating to the mass transfer effects of the porous pellets themselves. This can be determined experimentally by measuring H E T P as a function of U and evaluating the limiting slope a t high velocities. VOL. 8
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Table 1.
Characteristics of Columns
Internal cross section area = 0.388 sq. cm. Column length = 76 cm. Description
dp, Cm.
3A Mol. Sieve, extrudate, 0.16-cm. diam., 0.23 cm. long 5A Mol. Sieve, extrudate, 0.16-cm. diam., 0.26 cm. long Na mordenite, pellets, 0.32-cm. diam., 0.36 cm. high H mordenite, pellets, 0.32-cm. diam., 0.34 cm. high Na faujasite, pellets, 0.32-cm. diam., 0.41 cm. high 25% A1202-75% SiOz, pellets, 0.32-cm. diam., 0.25 cm. high ~
0,203
S.A., Sq. M./G. 0 . .
Pore Vol., Cc./G.
Bulk Density, G./Cc.
e
FI
(0.27)a
0.730
(0.42)o
0.53
0.211
47 8
0.34
0.843
0.63
0.54
0.382
322
0.24
0.833
0.42
0.53
0.375
45 5
0.34
0.757
0.53
0.51
0.395
711
0.39
0.620
0.52
0.54
0.340
378
0.58
0.617
0.78
0.54
Since this material does not adsorb nitrogen, values calculated from crystallographic dimensions.
This constant C is related to the diffusion constants in the gas and porous solid, DI and DII, respectively, by
C=
FI2dP2 FIK d p z 75(1 - F I ) 2D I+ 2 d ( 1 - F,) DIr FI
Substituting in Equation 7, we obtain
1-
(3)
The dependence of C upon particle diameter as given in this equation was confirmed by experiments on various mesh fractions. However, a severe loss in sensitivity of measurement was incurred when particles less than 0.15 cm. in diameter were used. Greater accuracy in evaluating DII is obtained with the larger particles. The distribution coefficient, K , deserves some further discussion, since it is sensitive to the extent of adsorption occurring on the solid. I t is defined as
P‘
z e + -
K
FII
(9)
However, it has been shown that
where t is the retention time of the adsorbed material and to the corresponding time for a completely nonadsorbable material (Eberly and Spencer, 1961). The latter was assumed to be the smallest time observed which occurred with the lightest inert gas at the highest temperature. Thus, we obtain
(4) where CI and CII are the concentrations in the mobile and immobile phases, respectively. Furthermore,
CII =
cp+ c a
(5)
The concentration, C,, represents the moles in the gas phase in the pores of the solid per unit pellet volume. C, is defined as the moles adsorbed per unit pellet volume. Hence, if no adsorption occurs, C, = 0, and if we assume that the concentration in the gas phase inside the pellets is equaI to that in the external gas phase, (6) ~,
e
c p
where e is the porosity of the pellet. This definition of K was used by Davis and Scott (1965). Even with inert gases, however, the concentration of adsorbed materials cannot always be neglected. Then, we can write: 1-
K
- + - c=ae + -- c, CI
CI
C, CI
(7)
The adsorption equilibrium constant, p’, expressed as the moles adsorbed per unit volume of column divided by the moles in the gas per unit volume of gas, can be defined as h
26
l&EC FUNDAMENTALS
I n our studies, this definition of K was used in Equation 3 to evaluate the diffusivity, DII. Habgood and Hanlan (1959) used a somewhat similar equation, but expressed the diffusivity as D I I / K . In general, the first term in the calculations and values of D Iwere determined by methods listed by Satterfield and Sherwood (1 963). Where adsorption occurred, heats of adsorption were evaluated from the variation of U ( t - to) with temperature according to established techniques (Eberly, 1961, 1962). 3A and 5A Molecular Sieves. T o illustrate the sensitivity of the G C technique to diffusion in the ultimate crystallites, experiments were done on a sample of 3A Molecular Sieve extrudate. With helium as the carrier gas, the H E T P values for argon pulses were obtained (bottom curve of Figure 1). Argon atoms are too large to enter the adsorption cages; hence, the curve and its corresponding limiting slope are equivalent to those observed with a nonporous glass bead column. If, however, argon is used as the carrier and helium as the pulsed gas, the upper curve is obtained, reflecting the ability of the helium atoms to diffuse through the adsorption cages in the ultimate crystallites. From the helium curve, the diffusivity, DII,was calculated to be 0.049 sq. cm. per second. These experiments demonstrate that a large part of the pulse dispersion is associated with diffusion in the micropores of the zeolite. The pores in 5A Molecular Sieve are large enough to accommodate both argon and krypton molecules. Data for
For these experiments, it appears to make little difference in the final values of DII. Heats of adsorption (AH) and energies of activation (4E)for diffusion are included in Table V. The activation energies are fairly high, amounting to 3.5 and 5.9 kcal. per mole for argon and krypton, respectively. The latter value is considerably higher than the corresponding heats of adsorption of k q p t o n evaluated from pulse retention time data alone. Too little adsorption of argon occurred to permit an accurate estimation of A H . Mordenite. I n contrast to zeolite A and the synthetic faujasite type zeolites (X and Y ) ,mordenite has a one-dimensional pore structure consisting of parallel nonintersecting pores. Experiments were done on both the Na and H forms of this material. The diffusivities obtained with the Na form are plotted in Figure 2. Corresponding values of K , the dis-
Table 11.
Results on SA Molecular Sieve Sq. Cm ./See. T , O C. K DII DIP 27 0.431 0.019 0.018 77 0.870 0.064 0.054 0 . 0.8.~ 2 113 1.50 0.089
Gar Argon
1.90 0.208 113 0.359 160 0.491 Calculated on assumption that K = I / E .
Krypton a
160
0.123
27
0.009
0.121 0.012
0.018
0.020
0.042
0.048
~~
these gases at various temperatures are listed in Table 11. Diffusivities were calculated, including the effects of adsorption; however, for comparative purposes, values of DII are also given assuming K = 1 / ~ ,neglecting the adsorption process. 0.1
0.5
0.:
0.I
t
Figure 1.
Results on 3A Molecular Sieve at
27°C. 0.:
0 0
0.:
Helium pulses injected into argon carrier gas Argon pulses using helium as carrier gas
- \
0.'
(
5
10
20
15
u,
25
30
35
40
cm./sec.
i I
i 7
Figure 2.
Diffusivities in
Na
mordenite
A
Values of D I I calculated on basis of no adsorp0 tion, K = 1 /e 0 A 0 Values of DII including adsorption effect
\>
\\.
0.002
t
h
1 VOL.
8
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FEBRUARY 1 9 6 9
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Table 111. Gas
Argon
Krypton
SFB
in a material of lowered diffusion resistance. Diffusivities and K values for H mordenite are plotted in Figures 4 and 5 , respectively. By using higher molecular weight gases, differences between the two forms of mordenite are more clearly distinguished. SFGis now able to enter most of the micropores in the crystallites. This is shown by a severe reduction on the value of the distribution coefficient K at 160' C.; it is nearly one order of magnitude less than that on Na mordenite. Similarly, this ability to enter the micropores reduces diffusivity to nearly one tenth. Faujasite. The results with inert gases on Na faujasite are listed in Tables I11 and V. T h e pores in this material easily accommodate the SFB molecules. Activation energies for
Results on Na Faujasite
T,
O
27 82 154 227 304 27 82 154 227 304 427 154 227 304 427
DII,
K
Sq. Cm./Sec.
0.598 1.18 1.68 1.92 1.92
0.039 0.077 0.180 0.267 0.776
0.149 0,305 0.592 0.886 1.12 0.910 0.0487 0.126 0.260 0.406
0.005 0.019 0.059 0.129 0.207 0.366 0.001 0.00s 0.016 0.055
C.
-
tribution coefficient, are shown in Figure 3. If one assumes = 1 / for ~ the calculation of the diffusivities (solid points in by increasing Figure 2), the the general values effect at low is to temperatures decrease the slope and decreasing of the line
K
0.5
them at higher temperatures. Hence, lower activation energies are obtained with this assumption. Activation energies using the proper value of K as well as heats of adsorption are listed in Table V. For argon and krypton, the K values observed on Na mordenite are lower than those found on the other solids. This increased adsorption is accompanied by higher heats of adsorption and energies of activation for diffusion. I t is known that SF6 is too large a molecule to enter the adsorption cages in 5A Molecular Sieve. Accordingly, we suspect that a large number of cylindrical pores in this sample of Na mordenite are also inaccessible to SF6. For example, as seen in Figure 3, the K values are nearly the same as those for krypton. This is not observed on other solids, even including
0.002
t
0.0011.4
1.e
1.8
I
2.0
Figure 4.
A H 0A 0 0
28
I&EC FUNDAMENTALS
I
2.2
E
0.2
!\\\\ \ J
KRYPTON
0.1
-
I
0.05
I
+
I
2.6
I 2.0
1.6
2.4
,
a .I8
3.0 I
( S K . ~ ) x 103
Diffusivities in H mordenite
Values of D I I calculated on basis of no adsorption, K = 1/e Values of DII including adsorption effect
,!,
,
2.4
2.8
1 3.2
I
3.4
3.2
3.6
Table IV.
Gas Argon
Krypton
SFe
Results on Silica-Alumina Pellet
T , C. 27 74 99 138 160 27 74 99 138 160 74 99 138 160
D I I ,Sq.
K 1.28 1.28 1.28 1.28 1.28 1.28 1.28 1.28 i .28 1.28 0.276 0.401 0.620 0.608
Cm ./Sec. 0.078 0.134 0.186 0.247 0.320 0.023 0.059 0.087 0.125 0.217 0.004 0.012 0.025 0.047
Gas Phase, D I , sq. Cm ./Sec. 0.73 0.95 1.06 1.25 1.37 0.63 0.83 0.93 1.11 1.20 0.54 0.61 0.70 0.78
c
I
I
1.8
2.2
I
I
I
Y
0.05
Table V.
Gas Argon
Krypton
Heats of Adsorption and Energies of Activation for Diffusion Kcal./Mole Solid AH AE
Na mordenite H mordenite 5A Na faujasite Silica-alumina Na mordenite H mordenite 5A Na faujasite Silica-alumina Na mordenite H mordenite Na faujasite Silica-alumina
4.1 3.6
... ... ...
4.3 4.1 3.6 3.7
*..
(3-4) 6.1
5.0 4.2
7.6 6.6 3.5 2.9 2.5 9.9 9.0 5.9 4.5 4.0 (11-15) 14.6 7.5 7.2
diffusion are considerably lower than observed for the mordenites. This reflects the increased ease of flow in the threedimensional porous network. The diffusion properties are similar to those for 5A Molecular Sieve at least with respect to argon and krypton. SFGis excluded from the pores in 5A. Amorphous 25% A1203-75% Si02 Catalyst. A wide range of pore sizes exists in silica-alumina catalysts, as shown, for instance, by Cranston and InkIey (1957). Also, most of the pores are considerably larger than those in the crystalline zeolites which have diameters the size of molecular dimensions, Consequently, the diffusion resistance is less, as shown by the data in Tables I V and V. The diffusion, however, is still governed by an activated type of process which distinguishes it from the diffusion in the bulk gas phase. Diffusivities for the latter (Table IV) show a considerably milder dependence on temperature. As the temperature is raised, and lower molecular weight gases are used, the diffusivity approaches values roughly 1 / 4 that of the bulk gas phase. The silica-alumina catalyst studied here consisted of pellets made by compressing fine powders and, hence, contained a macropore as well as a micropore structure. I n this sense, the material differed from the homogeneous spheres examined by Weisz and Schwartz (1962), which contained only a micropore structure. This accounts for the considerably higher values of diffusivity observed in the present investigation. Conclusions
The GC technique can be used to determine diffusion constants which cannot be conveniently measured by other unsteady-state techniques such as that involving analysis of ad-
b 0.02 1.4
Figure 5.
+
I 2.6
(oK-~)
I
I
3.0
3.4
x 103
Distribution coefficient K in
H
mordenite
sorption rates-for example, with inert gases, the amount of adsorption is generally too small for accurate measurement. Using the GC method, the flow of these materials in zeolites was found to be adequately described by an activated type of diffusion process over a wide temperature range. With large gas molecules at low temperatures, some adsorption can occur simultaneously with diffusion. This effect can be taken into account by using the proper value of K in the calculations. In doing this, activation energies are obtained which are higher than those calculated on the basis of no adsorption ( K = I/€). However, with zeolites the dividing line between adsorption and diffusion is not so clearly defined, since the molecules or atoms are always in close proximity to the pore walls. For gases which can readily enter the pores, the diffusion resistance is decreased in the order, Na mordenite > H mordenite > 5A > Na faujasite > silica-alumina. Heats of adsorption and energies of activation of diffusion decrease in the same order. The high diffusion resistance of mordenites is undoubtedly associated with their unique one-dimensional pore structure. The resistance in the remaining solids decreases as the pore size increases. Because of the pronounced effect of the surface on the nature of flow, it is difficult to predict the effect of molecular weight or type on the diffusivity. The dependence is certainly much greater than that predicted by Knudsen diffusion. For example, diffusion coefficients for C1-C4 hydrocarbons in Na mordenite were determined from adsorption rates and found to be to 1O-IO sq. cm. per second (Satterfield and Frabetti, 1967), several orders of magnitude below those reported here for the inert gases. Studies with larger molecules such as Decalin and toluene on H mordenite catalysts also indicate that these materials diffuse much more slowly than the inert gases (Beecher et al., 1968). Consequently, in attempting to relate diffusivity to reaction rate to determine catalyst effectiveness factors, it is highly important in the case of zeolite catalysts to use the actual compounds involved. Use of inert gas diffusivities can indicate no diffusional limitation where in reality one exists. VOL. 8
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29
I n investigating the use of gas chromatography in measuring diffusivities in porous particles, the question arises as to what extent the results agree with values obtained by more well established techniques. Davis and Scott (1965), using the GC method, found good agreement with steady-state results for solids which are reasonably homogeneous. However, for the solids studied in the present investigation, it would not be unreasonable to expect large differences in the results, since the zeolite pellets contain two distinct porous systems. The presence of the uniform micropore system having a pore dimension nearly the same size as the diffusing molecules would tend to make the unsteady-state diffusivities considerably lower than steady-state results wherein the micropore structure would contribute much less resistance to flow. Consequently, it is not too surprising that the G C technique yields activation energies considerably higher than those observed by steady-state methods. This is true even for the nonzeolitic silica-alumina catalyst which, although it does not have a uniform pore structure, still contains some pores of molecular dimensions. Evidently, more work remains to be done to explain fully the complex relationship between surface adsorption and diffusion in these heterogeneous pore systems. Acknowledgment
The author expresses his sincere appreciation to Dorothy Webb for her excellent work in the assembly and calculation of data. Nomenclature
A
B
C C, Cp CI CII dP
DI DII
30
= constant associated with longitudinal dispersion in
column due to eddy diffusion, cm. = constant associated with longitudinal dispersion in column due to molecular diffusion, sq. cm. per second = constant associated with longitudinal dispersion due to mass transfer in porous pellet, second = moles adsorbed per unit pellet volume, moles per cc. = moles in gas phase in pores of solid per unit pellet volume, moles per cc. = concentration in gas phase, moles per cc. = concentration in immobile phase, moles per cc. = diameter of particle, cm. = diffusivity in mobile gas phase, sq. cm. per second = diffusivity in porous solid (immobile phase), sq. cm. per second
IbEC FUNDAMENTALS
AE FI FII
= activation energy, kcal. per mole
fraction of voids in packed column volume fraction of pellets in packed column AH = heat of adsorption, kcal. per mole H E T P = height of an equivalent theoretical plate, cm. K = distribution coefficient L = length of column, cm. t = retention time of adsorbable material, second t* = retention time of pulse at a fraction l/e, 0.368 of pulse height, second tnl = retention time at maximum of pulse, second to = retention time of nonadsorbable material, second U = interstitial carrier gas velocity, cm. per second W, = width of pulse at a fraction l / e 0.368 of pulse height, second = =
GREEKLETTERS /3’
= moles adsorbed per cc. of column/moles in gas per
E
cc. of gas at equilibrium = pellet porosity
literature Cited
Barrer, R. M., T r a m . Faraday Sac. 45, 358 (1949). Barrer, R. M., Peterson, D. L., Prod. Roy. Sac. (London) Ser. A 280, 466 (1964). Beecher, R., Voorhies, A., Jr., Eberly, P. E., Jr., Znd. Eng. Chem. Prod. Res. Deoelop. 7, 203 (1968). Cranston, R. W., Inkley, F. -4., Advan. Catalysis 9, Chap. 17 (1957). Davis, B. R., Scott, D. S., “Measurement of the Effective Diffusivity of Porous Pellets,” Preprint 48D, 58th Annual Meeting, A.1.Ch.E. Philadelphia, Pa., December 1965. Deemter, J. J. van, Zuiderweg, F. J., Klinkenberg, A,, Chem. Eng. Sci.5. 271 11956). Eberly,’P. E.,‘Jr., j . Phys. Chem. 65, 68 (1961). Eberly, P. E., Jr., J.Phys. Chem. 66,812 (1962). Eberly, P. E., Jr., Spencer, E. H., T r a m . Faraday Sac. 57, 289 I1 O A 1 ,. ,. Z”.
Greene, S. A., Pust, H., J.Phys. Chem. 62,55 (1958). Habgood, H. W., Can. J . Chem. 36, 1384 (1958). Habgood, H. W., Hanlan, J. F., Can. J . Chem. 37,843 (1959). Leffler, A. J., J.Catalysis5,22 (1966). Nelson, E. T., Walker, P. L., Jr., J . Appl. Chem. 11, 358 (1961). Purnell, H., “Gas Chromatography,” Chap. 7, Wiley, New York, 1962. Ross, S., Saelens, J. K., Olivier, J. P., J . Phys. Chem. 66, 696 (1962). Satterfield, C. N., Frabetti, A. J., A.Z.CI1.E. J. 13,731 (1967). Satterfield, C. N., Sherwood, T. K., “The Role of Diffusion in Catalysis,” Chap. 1, Addison-Wesley, Reading, Mass., 1963. Smith, J. M., private communication, 1967. Weisz, P. B., Schwartz, A. B., J . Catalysis 1,399 (1962). RECEIVEDfor review December 7, 1967 ACCEPTED July 5, 1968
