GASEOUS DIFFUSION AND FLOW I N COMMERCIAL CATALYSTS A T PRESSURE LEVELS ABOVE ATMOSPHERIC SIR: Satterfield and Cadle (1968) published data which are correlated on the basis that helium flow in a porous catalyst medium can be considered to be entirely in the gas phase. T o use this assumption they had to write off the findings reported by Hwang and Kammermeyer (1966a,b), who showed the existence of surface flow with helium even a t ambient temperatures and pressures. Satterfield and Cadle proceeded to d o this by making assertions in rather general terms which permitted them to overlook the problem of surface flow of helium. Generalized statements of this sort, which, in effect, discredit our findings, should not go unchallenged. T h e “possible” reasons put forth by Satterfield and Cadle can readily be shown to be untenable. The matter is, in our opinion, sufficiently serious that a rebuttal of their criticism is indicated, in order to point out the importance of the surface diffusion of helium in microporous media. (The statements in question appear on page 206 of their article.) The following points need discussion: Surface Diffusion. Satterfield and Cadle conclude that the surface flow of helium is negligible because of the very small degree of adsorption of helium a t room temperature, as reported by Steele and Halsey (1955). Helium shows very little adsorption on most adsorbents a t or above room temperature. Since surface diffusion is caused by the adsorbed molecules, it appears logical to assume that the rate of surface diffusion of helium is also negligible. But this is not necessarily true. Fick’s law for surface diffusion is
Paucity of Data. After their first publication, Hwang and Kammermeyer (1966a,b) provided additional data for D2, CH4, C2H6, and CZHs. The fifidings supported the previous theory. An even more forceful evidence of helium surface diffusion was reported in a cryogenic study by Hwang and Kammermeyer (1967). I t was also found that the parameter of surface diffusion can well be correlated with the critical properties and other molecular parameters of gases (Hwang, 1968). Additionally, systems of mixtures were investigated by Tock and Kammermeyer (1968) ; the resulting data further support the original findings for the pure component systems. The latter two investigations were available in reprint form a t the recent A.1.Ch.E. meeting in St. Louis. Standard Deviations. T h e standard deviations for the systems of D2, CHI, C2H6, and CaHg were reported in the previous publication (Hwang and Kammermeyer, 1966b). For the other gases, they will be found in the following table:
Standard Deuiation
Therefore, the surface diffusion flux, Fs, depends not only on the adsorption equilibrium constant (here, k,) but also on the surface diffusivity, D,. As temperature increases k, decreases but D, increases. The surface flux, which is proportional to the product (D,k,), decreases with increasing temperature at a slower rate than that of the gas phase flow. As a result, the fraction of the surface flow for most gases, including helium, is not negligible a t room temperature. (It is somewhat greater than 10% of the total flow.) The effect of temperature on the surface flow is well illustrated by Perry (1968). Technique of Measurements. Here one can only repeat what was described in the original article. The diffusion cell was constructed entirely from borosilicate glass in order to provide easy handling over a wide temperature range without the danger of leaks. The volume flow rate of the permeated gas stream (through the porous Vycor glass) was measured by a mercury displacement technique and with a bubble flowmeter. This description seems adequate and hardly open to criticism. Pressure Level. T h e downstream side was always kept a t atmospheric pressure; the upstream pressure was varied u p to 2 atm. to give the necessary pressure drop for each case. T h e important fact is that there was no indication of pressure dependency in the flow data. Since all the primary data could not be reported in the publication, they can be furnished upon request from the authors to those who need them.
0.0579 0.0314 0.0237 0.0617 0.0587 0,0743 0,0266
Hz Ar
Values f o r Q
If Henry’s law applies, this equation becomes
of Q m T X lo4
Gas He Ne
dzare given in the thesis (Hwang, 1965).
Here, the range of Q d E v a l u e s was 4.7 to 8.7 X low4for all gases. I t is believed that the standard deviations are within the range of the experimental errors-that is, less than 2%. Thermal Diffusion. Satterfield and Cadle then offered several possible explanations for the findings of Hwang and Kammermeyer. O n e is that thermal diffusion could be responsible for the observed effects. This is impossible for a n isothermal system. All runs were made a t constant temperature. Explanation through Change in Knudsen Number. T h e next suggestion was that “phenomena stemming from the sevenfold change in the Knudsen number, r / X , which means a sevenfold change in the collision frequency of the gas molecules with the wall,” could be responsible for the effect. This is a rather confusing statement; it seems to apply to the temperature range of Hwang and Kammermeyer’s investigation. The fact is that there was no sevenfold change in the Knudsen number for any of the runs. The maximum variation would be a doubling of Knudsen number owing to changes in the mean free path associated with the pressure drop. Slip Flow. Slip flow may exist a t the lowest temperature. But the importance of the surface diffusion of helium is expressed in the fact that the fraction of the surface diffusion increases with increasing temperature. T h e chances that slip flow may exist a t the higher temperatures are remote. Diffusion of Helium through Glass. This last suggestion has no merit. Norton (1953) published a comprehensive study of helium diffusion through various kinds of glasses over a wide temperature range. His data show that the permeability of helium through glasses is less than 10-9 (std. VOL. 7
NO. 4
NOVEMBER 1 9 6 8
671
cc.)(cm.)/(sec.)(sq. cm.)(cm. Hg) a t any temperature covered, while the smallest value for the porous Vycor glass is 10-5 in the same units. Besides, the porosity of the porous Vycor glass is 0.3 ; therefore, bulk flow thorugh nonporous glass must be negligible. Leiby and Chen (1960) also studied the permeation of helium through Vycor glass ; their findings verified Norton’s data. We are not in any way concerned with Satterfield and Cadle’s interpretation of their own data. The adequacy of such interpretation must be judged by the readers. We, howrever, feel that Satterfield and Cadle’s comments concerning our surface flow findings are incorrect and that their arguments are untenable. Nomenclature
C, = concentration of adsorbed phase D, = surface diffusivity, sq. cm./sec. F , = surface flow rate, std. cc./sec. G2 = geometric factor k, = Henry’s law constant M = molecular weight, g./g. mole. P = pressure, cm. H g
Q = permeability, (std. cc.)(cm.)/(sec.) (sq. cm.)(cm. Hg)
S
= cross-sectional area, sq. cm.
T = temperature,
OK.
literature Cited
Hwang, S.-T., Ph.D. thesis, University of Iowa, 1965. Hwang, S.-T., Kammermeyer, K., Can. J . Chem. Eng. 44, 8 2 (1966a). Hwang, S.-T., Kammermeyer, K., Separation Sci. 1 (5), 629 (1966b). Hwang, S.-T., Kammermeyer, K., Separation Sci. 2 (4), 555 (1967). Hwang, S.-T., A.Z.Ch.E. J., inpress, 1968. Leiby, C. C., Jr., Chen, C. L., J . Appl. Phys. 31,268 (1960). Norton, F. J., J . Am. Ceram. Sod. 36,90 (1953). Perry, E. S., “Progress in Separation and Purification,” Vol. 1, p. 335, Wiley, New York, 1968. Satterfield. C. N.. Cadle, P. J., IND.ENG.CHEM.FUNDAMENTALS 7, 202 (i968). . Steele, W. A., Halsey, G. D., Jr., J . Phys. Chem. 59, 57 (1955). Tack, R. W., Kammermeyer, K., A.I.Ch.E. J., in press, 1968. Sun-Tak Hwang Karl Kammermeyer
University of Iowa Iowa City,Iowa
Correction
GENERAL BALANCE EQUATION PHASE INTERFACE
FOR A
I n this article by John C. Slattery [IND.ENG.CHEM.FUNDA6, 108 (1967)], e should be replaced by e in Equations 5.21, 5.22, 5.232, 5.24, 6.2, 6.3, 6.4, 7.2. 7.3, 7.4, and 7.6. I n the Nomenclature, it is ea,&which is defined by Equation 5.22.
MENTALS
672
l&EC FUNDAMENTALS
