membrane with a variable permeation flux and incomplete salt rejection. When these solutions are compared with the solutions for a constant flux membrane operating a t the same average permeation flux, it is found that the concentration polarization is greater for the variable flux case near the channel entrance and lower near the channel exit. The average polarization for the constant flux case is very nearly equal to that for the variable flux case, even under the relatively severe conditions examined in which the polarization caused the permeation flux to fall off by a factor of 5 from the channel entrance to the channel exit. This formed the basis of a simple design procrdure in which the constant flux solution can be used to predict i he effects of concentration polarization upon the required pressure drop and upon the product water salinity for a variable flux membrane. This simple procedure, together with generaliied graphs of the constant flux solution \vhich are presented, should be useful in the design and optimization of reverse osmosis processes. More accurate calculations of the concentration polarization can be performed by using the finite-difference method developed in this study, described in the appendix to (2). Acknowledgment
The machine computations were performed a t the Massachusetts Institute of Technology Computation Center, and the author is grateful for the use of the center’s facilities. This study is part of a research program on desalination supported by the Office of Saline LVater, U. S. Department of the Interior.
=
=
average value of u over channel a t a given value of x , cm./sec.
u
= u/a,
u
=
5,
y
= average value of urn over channel length, cm./sec. = u/uwo
x
=
Ve
X y Y
velocity component in y-direction, cm./sec.
average value of Vu over channel length longitudinal distance from channel inlet, cm. = (u~,/U,) (x/h) = transverse distance from channel midplane, cm. = yjh =
GREEK D,‘u,h for constant permeation flux D, Gw,h s = D,%,h P = R x o / ( 4 P - RT0) r = defined by Equation 22 Y = c, - 1 4 = defined by Equation 18 A = fractional water removal at a given longitudinal position AP = pressure drop across membrane, p.s.i. Air = difference in osmotic pressure across membrane, p.s.i. v = kinematic viscosity of solution, (sq. cm.)/sec. x = osmotic pressure, p.s.i. f f = ff, =
SUBSCRIPTS o = channel inlet-Le., x = 0 p = product water, mixed average over length of membrane w = channel wall-Le., membrane surface SUPERSCRIPT ’ = dummy variable in definite integral literature Cited (1) Berman, A. S., J . Appl. Phys. 24, 1232 (1953). (2) Brian, P. L. T., M.I.T. Desalination Research Laboratory, Rept. 295-7 (May 1965). (3) Merten, Ulrich, IND. END. CHEM. FUNDAMENTALS 2, 229
Nomenclature c
.ii
salt concentration, g./cc.
c = c c:,
D = molecular diffusion coefficient of salt, (sq. cm.)/sec. = half xvidth of channel, cm. K = membrane permeability constant, (cm./sec.)/p.s.i. v = hu,./u -.r Ts = salt flux through membrane, g./’(sq. cm.) (sec.) R = fractional salt rejection = 1 - iVs/ceu, u = velocity component in x-direction, cm./sec. h
(1963).
(4) Merten, Ulrich, Lonsdale, H. K., Riley, R. L., Ibid., 3, 210
(1964). (5) Sherwood, T. K., Brian, P. L. T., Fisher, R. E., Dresner, L., Ibid.,4, 113 (1965). RECEIVED for review May 7, 1965 ACCEPTED September 3, 1965
LIQUID P E R M E A T I O N T H R O U G H PLASTIC F I L M S R
. B.
L 0 N G , Central Basic Research Laboratory, Esso Research and Engineering Co., Linden, N . J.
Liquid permeaition i s apparently a special case of ordinary diffusion and can be explained by a classical diffusion model. The exponential concentration dependence of diffusivity leads to equations which are very sensitive to the concentration of liquid in the upstream side of the film. Furthermore, the liquid concentration gradient through the film shows that essentially all the resistance to diffusion i s at the downstream edge of the film. The imodel has been experimentally tested for permeation of hydrocarbons through polypropylene film and predicts the observed effect of downstream pressure as well as solvent absorption rate for bulk plastic. HE selective permeation of gases through plastic films has Tbeen \vel1 documented in the literature and the possibility of using this phenomenon to carry out practical separations More rehas frequently been suggested (2, 4, 77-73). cently Binning et al. ( 7 ) reported that permeating mixtures from the liquid phase on one side of the film to the vapor phase
on the other side has good commercial separation potential. He called this process liquid permeation. However, this process is not yet understood. Binning has suggested a liquid permeation model based on the existence of two zones in the polymer film, where the upstream zone exists as a highly swollen liquid solution and occupies the major portion of the VOL. 4
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445
film. T h e downstream zone is called the vapor-phase zone and corresponds more nearly to dry polymer film. Separation is believed to occur a t distinct interfaces in the film, largely because of the independence of selectivity from film thickness. O n the other hand, Michaels et al. (a),in discussing the separation of xylenes by permeation through preconditioned polyethylene films, presented a model based on the polymer acting as a simple Molecular Sieve or screen, wherein the amorphous regions constitute the holes and the interconnected crystalline regions constitute the mesh. Schrodt, Sweeney, and Rose (70) suggested that hydrogen bonding between the polymer film and solvent plays an important role. Apparently, no other mechanistic proposals have been advanced. This paper discusses a liquid permeation model based on classical diffusion concepts and the testing of this model for the explanation of the phenomenon encountered in liquid permeation through polypropylene film. Process
A schematic diagram of the liquid permeation process is shown in Figure 1.
LIQUID FEED+
PLASTIC FILM I
I
PERMEATE VAPOR PRODUCT
Figure 1.
90
80 70
60
Schematic flow plan for a permeation stage
-
1
I
5
-
1
-
\
1-
METHYLCYCLOHEXANE
\'
30
6
1
MISCIBILITY TEMP. FOPMCH
::t
The permeation cell is divided into two compartments by the plastic film. The liquid feed is introduced into the upper compartment and sufficient pressure is applied to maintain it in the liquid phase. The permeating product is removed as a vapor from the lower compartment, which is maintained a t reduced pressure. The permeation process is believed to involve solution of permeating molecules a t the film surface which is in contact with the liquid charge, diffusion of these molecules through the film, and evaporation of these molecules from the downstream face of the film ( 7 ) . The steady-state permeation process may then be described by a form of Fick's law,
STRIPPED PRODUCT
1
TEMPERATURE, OC.
;a
;1 2.7
2.5
Figure 2. propylene
, 'to , 2,9
4;
;2
3.1 3.3 ~Qoo/T.~K.
Solubility of
,
1
y, 3.7
3.5
3.9
liquid hydrocarbons in poly-
70
Crystallinity 74 Average crystal size 108 A.
where
q D C L
permeation rate, grams per sq. cm. per second diffusivity, sq. cm. per second = concentration, grams sorbed per cc. of swollen polymer = distance in direction of permeation, cm. = =
Unfortunately, the value of D depends very strongly on the concentration of solvents in the plastic film. Many expressions have been proposed to relate D to the solubility of solvent in the film and to a diffusivity, DO,obtained a t zero concentration of solvents. The equation most widely accepted (3, 6) is:
D
= DoeaC
in terms of the concentration of the permeating material in the plastic film a t the upstream, C1, and downstream, CZ, sides, the diffusivity, DO,the constant, a, and the film thickness, L. Complete evaluation of all the terms in this equation was undertaken for n-heptane, methylcyclohexane, and toluene in polypropylene film to see if it could predict liquid permeation phenomena. According to Binning et al. (7) any proposed mechanism I&EC FUNDAMENTALS
18
I
I
1
I
I
1
2
4
4
1
1
I
I
I
I
I
I
8
10
12
14
16
18
-
e
F 14
(2)
where Do and a are constants a t a given temperature. Substituting Equation 2 in Equation 1 gives the steady-state permeation rate for a single component
446
20
d
4
*r 0
0
1 20
TIME, HRS. x lo-*
Figure 3. Rate of approach to equilibrium at liquid solubility in polypropylene
0°C. for
30
t
WT. OF FILM = 0 . 2 2 8 SPRING CONSTANT = 34.2 MILLIGRAMS PER
-TOLUENE
PRESSURE, MM.HG.
CM.
n-HEPTANE METHYLCYCLOHWNE *TOLUENE
i
9
5z' P
,2
w z X
u 5 a v)
.05
TEMPERATURE,
"C,
Figure 4 . Vapoir solubility vs. temperature for toluene in polypropylene film
.02
-01
for liquid permeation must explain the rapid rate of liquid permeation compared with vapor permeation, linear relation between rate and film thickness, selectivity independent of film thickness, and permeation rate independent of downstream pressure over wide range. Therefore, the simple diffusion model of Equations 2 and 3 was tested against these facts. liquid Solubility in Polypropylene
Liquid hydrocarbon solubilities were determined by soaking duplicate disks of polypropylene 1.5 inches in diameter and 90 mils thick in the various liquid hydrocarbons in a constant temperature bath for sufficient time to reach equilibrium. Solubility was measured by the gain in weight of the sample. T h e solubility data in Figure 2 show a relatively small effect of temperature on solubility of these hydrocarbons in polypropylene. n-Heptane is the least soluble, toluene is intermediate, and methylcyclohexane has the highest solubility. T h e solubility determination a t 0" C. required about 1 month to reach equilibrium for n-heptane and toluene and over 2 months for methylcyclohexane. Therefore, data on solvent pickup us. time were al:;o obtained. These results, plotted in Figure 3, show that n-hesptane and toluene permeate faster than methylcyclohexane a t 0" C. and weight pickup is almost linear with time. X-ray crystallinity data were obtained on the dry polypropylene used in these solubility studies. and on the 0 ' C. swollen samples. T h e ,absolute crystal content of the sivollen samples a t 0" C. was essentially the same as for the dry polymer. Thus, the hydrocarbons dissolved only in the amorphous portion of the polymer. When one knows the percentage of crystallinity in the polymer, it is possible to correct the solubilities obtained on one sample of polymer to the values that lvould be obtained in a second sample of slightly different crystallinity. Vapor Solubility Data
Vapor solubilities were measured for the three hydrocarbons in the same sample of 1-mil polypropylene film over a range of temperatures and vapor pressures using a quartz spring balance enclosed in a constant temperature Lucite air bath. The balance case was evacuated to 0.1 mm. of Hg, and controlled pressures of the various hydrocarbons were introduced. When no further weight gain occurred in the films, the solu-
TIME, SECONDS x 10-3
Figure 5. Desorption of hydrocarbons from polypropylene
bility was measured by the extension of the quartz spring as measured with a cathetometer. Accuracy to 0.1% solubility could be obtained. T h e film was pre-annealed in n-heptane for 50 hours a t 75' C. and vacuum-dried before use. I n addition, several saturations and evacuations were made before taking data whenever changing t3 a new solvent. X-ray crystallinity was obtained on the film t o permit correlation of solubility between the film and the pads used for liquid measurements. T h e vapor solubility data show that for all three hydrocarbons the solubility decreases very rapidly as temperature is increased. This is illustrated for toluene in Figure 4. The other two hydrocarbons gave similar results. I n the region of downstream pressure normally used in liquid permeationLe., 0 to 30 mm. of mercury-vapor solubilities can vary from less than 1 to as high as 20 weight when temperature is changed 20' to 30" C. The solubilities are also very pressuresensitive. For example, a t 31' C. the solubility of toluene in polypropylene varies from less than 2 grams per 100 grams of dry film a t 5 mm. of H g to about 20 grams per 100 grams of film a t 30 mm. of Hg. Diffusivity at Zero Concentration
It is possible to mcasure D Ofrom a simple desorption experiment (71, in which a sample of film is saturated with vapor, the film is placed in a vacuum, and the weight loss with time is recorded. Our results using the spring balance to measure weight loss are illustrated for operation a t 25" C. in Figure 5. Since D = Doeac, Do is the diffusivity a t zero concentration. Hence, after a sufficiently long time in a desorption experiment, C becomes small and D approaches DO. Whether or not D is constant, after a short induction period a plot of 1nW against time has the slope n2D/L2,where FV is the total amount absorbed. Therefore, after a long enough wait, the slope of the plot \vi11 become linear and will equal r2Do/L2. T h e values of D o determined from the slopes for n-heptane, methylcyclohexane, and toluene are given in Figure 6. These data show that Do varies from less than sq. cm. per second a t about 0" C. to values on the order of 10-8 sq. cm. per second a t 50" C. VOL. 4
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NOVEMBER 1 9 6 5
447
10
n-HEPTANE METHYLCYCLOHEXANE
0
A
TOLUENE
A
i
SOLID POINTS ANNEALED FILM
5 Le r4
m2 2
Y
n-HEPTANE
J i
\
.
/\
.r
r
I
t 50
40
20
10
I
1
\
MCH
i TEMPERATbRE, 'C.
:8
"/,8
O:
2.9'
60 3.0
1000/TeK,
30 5;
3.1
4,"
3 2 1000/T°K,
20
10
I
3.3
3.4
3.5
Figure 6. Variation of diffusivity a t zero solvent concentration with temperature
Figure 7. Comparison of permeation rates for hydrocarbons through fresh and annealed polypropylene film
Thus, there is an extremely rapid increase in the zero concentration diffusivity as temperature is increased. Toluene shows about tenfold higher D O than methylcyclohexane, while nheptane values are about double those of methylcyclohexane. T h e activation energy for diffusion which is predicted from these slopes is about 18 kcal. per mole for toluene and methylcyclohexane and about 14 kcal. per mole for n-heptane. This corresponds closely to the activation energy for flow in very viscous liquids. Furthermore, the absolute values of Do are similar to those for gases and vapors in polyethylene (7).
hexane a t temperatures above room temperature. However, toluene shows only a small increase in permeation rate with temperature. Both n-heptane and methylcyclohexane show breaks in the curve of rate us. reciprocal temperature in the region of room temperature. The exact position of these breaks appears to depend on the previous history of the plastic film. These breaks are probably due to the onset of solventpolymer interaction as temperature is increased above the break temperature. Exponential Term
Steady-State Diffusion Rate
Steady-state permeation rates of the various hydrocarbons through the plastic film were obtained a t various temperatures using a permeation cell immersed in a constant temperature bath (Figure 7). Preliminary experiments with n-heptane and toluene showed that both solvents give similar curves of permeation rate us. reciprocal temperature when fresh film is used. However, as the film was used for a long time on toluene, the permeation rate a t high temperatures decreased markedly and the curve of permeation rate us. temperature for toluene became more nearly horizontal, whereas no change was detected in the n-heptane curve. Crystallinity measurements on the film after use indicated that the film was annealed during the permeation operation and went from the smectic or 0% crystallinity form for fresh film to a value of about 62 to 64% crystallinity for the film after it reached equilibrium. I t was then found that by annealing the film a t 75" to 80" C. for one day in the presence of either n-heptane or iso-octane, the crystallinity typical of the fully annealed film could be obtained. When this pre-annealed film was used for permeation experiments, the curve of toluene permeation rate us. temperature was exactly the same a t the start as had previously been obtained only after very long periods of time with unannealed film. All of the experiments were then made on pre-annealed film. With pre-annealed film, permeation rate increases rapidly as temperature is increased for n-heptane and methylcyclo448
l&EC FUNDAMENTALS
T h e values of a in the steady-state permeation equation were obtained from Equation 3 using experimental values for all the other terms. a is essentially a plasticizing constant, because it shows the magnitude of the effect of solvent concentration on the mobility of the solvent in the plastic film. If a is high, a small amount of solvent causes a large change in diffusivity. If it is low, a large amount of solvent is required to get a small change in diffusivity (Figure 8). The values of a obtained from these solvents vary from a low of 20 a t 50' C. to a high of 87 a t 0 ' C. These values increase with the calculated crystallinity as expected, but while n-heptane and toluene give a very similar relationship, methylcyclohexane shows a higher value of a for a given crystallinity and thus would be expected to be a better plasticizer or solvent for polypropylene. These a values indicate that the effect of concentration on diffusivity decreases rapidly as temperature is increased. This would be expected, since the DOvalues, or diffusivities a t zero concentration, increase very rapidly as temperature is increased and the effect of further plasticizing by the presence of solvent would be expected to be less. Concentration Protlle
From the value of a and DO,it is possible to calculate the effect of distance through the film on solvent concentration for steady-state permeation. Such calculations have been made for all the solvents a t temperatures of about O", 25', and 50' C.
and are shown in Figure 9 for n-heptane. T h e other solvents show similar curves. T h e solvent concentration on the upstream side of the film a t 0 ' C. is nearly the over-all bulk concentration of the solvent in the film. However, the concentration decreases very slowly with distance through the film to about goy0 of its upstream value a t a distance 75y0 of the way through the film. From there o n to the downstream side of the film, the concentration drops very rapidly to a value
90
I
1
D = Doeac
80 0
0
A
70
m
n-HEPTANE METHYLCYCLOHEXANE TOLUENE
I
60
d
+
0 0
2
50
-1
5
z + w
40
5 n
t: 30
depending on the downstream pressure. At higher temperatures the concentration profiles are similar but drop a little faster with distance through the film. I n contrast to the concentration, the point diffusivity, D, is very large compared to D Oover the upstream 90% of the film thickness. From then on to the downstream side of the film, this diffusivity drops very rapidly and almost linearly to the value of D Oor very near to it, depending on dc vvnstream concentration. Thus, essentially all the resistance to diffusion occurs near the downstream side of the film and the concentration profile resembles the two-zone process model proposed by Binning ( 7 ) . T h e slope of the concentration curve, AC/AL, is the driving force for permeation a t any point in the film and is thus inversely proportional to the diffusivity a t a given temperature. However, the shape of the curve is independent of film thickness if plotted on a basis of L = 0 to L = 1 where L = 1 is the distance to the downstream side of the film. Therefore, the point driving force for a film twice as thick as the reference film would be just one half that of the reference film and the permeation rate would correspondingly be one half that through the reference film. Thus, Equation 3 and the concentration profile predict the effect of film thickness observed by Binning. Finally, the calculated concentration profiles are very similar to those experimentally observed by Richman and Long (9) for the diffusion of methyl iodide into poly(viny1 acetate). Effect of Downstream Concentration on Rate
20
Using the values of DO,a, and concentrations obtained experimentally, the effect of downstream concentration on the permeation rate has been calculated and is illustrated for nheptane in Figure 10. The effect of downstream concentration is greatest a t high temperatures. O n the other hand, the pressure required on the downstream side to get a given downstream concentration is also greatly increased a t higher tem-
10 040
45
I
I
50
55
; c D:
P
0
4
a
u
0
80-
w' I-
d
60-
0 2
0.0
5
F
-
5
40-
S
P
20 -
I
I
1
10
15
20
25
Figure 9. Calculated concentration heptane through polypropylene film
gradient
20
0
40
60
80
DOWNSTREAM CONCENTRATION O F flC7 I N FILM,
DISTANCE THROUGH FILM, cm.x l o 4
for
n-
100
%
OF C 1
Figure 10. Effect of downstream concentration on permeation of n-heptane through polypropylene film VOL. 4
NO. 4
NOVEMBER 1 9 6 5
449
peratures. Therefore, as a first approximation, the effect of downstream pressure is nearly the same and almost negligible (7) over the range of temperatures of interest. For downstream concentrations up to 60% or more of the upstream concentrations, the permeation rate will be essentially unaffected-that is, reduced less than 1% a t 0 ' C . This has led to the general speculation that permeation rate is independent of downstream pressure. However, none of the experiments reported in the literature have covered downstream pressure close to saturation, where the effect would be most strongly felt. Thus, this diffusion model of permeation explains the observed effect of downstream pressure.
LIQUID TOLUENE AT ROOM TEMP. ON BOTH SIDES OF FILM FILM THICKNESS = 1 MIL. VOLUME INSIDE FILM = 363 CC. VOLUME OUTSIDE FILM = 57.5 CC. 50 J
Diffurivity Values
The form of Equation 3 predicts that the diffusivity would be very high for a film soaked on both sides with liquid. The prediction was tested experimentally using radioactive toluene. T o do this a permeation unit was built in which the film was covered on both sides with toluene but the radioactive toluene was initially on only one side of the film. Samples were then taken a t frequent intervals to follow the diffusion of toluene through the film. The data are given in Figure 11, From these data a diffusivity was calculated for comparison with the values predicted from the known concentration of toluene in the film. The results show a value of 3.0 X 10-6 sq. cm. per second, which compares to 1.3 X 10-6 sq. cm. per second predicted from Equation 2. This agreement is felt to be exceptional, since the diffusivity is so strongly dependent on the value of C because of the large values of a. T h e value of D that is obtained by this experiment is about sevenfold higher than would be calculated from a typical liquid-to-vapor permeation and 1000-fold higher than Dofor toluene a t this temperature. Thus, the radioactive toluene experiment tends to confirm the diffusion permeation model. T h e above diffusivities are about one tenth the values obtained for diffusion of toluene in various liquids a t 25' C. ( 5 ) . Exponential Concentration Dependence Model
The steady-state permeation equation given as Equation 3 explains many of the apparent peculiarities of liquid permeation. T h e lack of a downstream pressure effect is explained by this model. T h e sharpness of the front between the high concentration portion of the plastic film and the low concentration portion explains the linear weight gain with time found with thick pads of plastic. As the front moves into the plastic, the weight gain would be linear over the entire range from 0% dissohed u p to equilibrium. The exponential model also explains the frequently encountered difficulty in reproducing permeation data. For example, small changes in the crystallinity or conversely in the amorphous content of the polymer will have large effects on the concentration of solvent in the polymer and, thus, will have very large effects on the diffusivity. Since it is expected that a t equilibrium the upstream solubility in the polymer of solvents a t unit vapor activity-Le., saturated vapor-will be the same as for liquid solvent, Equation 3 predicts the same permeation rate for liquid or saturated vapor. However, if the permeation rate is rapid, it may be difficult to keep the upstream surface of the film in equilibrium with the unsaturated vapor. Thus, the diffusion model for permeation predicts large differences between liquid and saturated vapor permeation rates for solvents that give high liquid permeation rates, but small or no difference for materials which give low liquid permeation rates. 450
l&EC FUNDAMENTALS
Y 10
0
OUTSIDE FILM
0
I
I
I
I
5
10
15
20
i
TIME, HRS.
Figure 1 1 . Radiotracer diffusion of through polypropylene film
C14 toluene
Finally, the rapid decrease in solvent solubility as activity is reduced from 1.0, coupled with the high exponential effect of solvent concentration o n diffusion rates, would give a reasonably large rate reduction on going from saturated vapor to only slightly less than saturated vapor on the upstream side of the film. Summary
Liquid permeation is apparently a special case of ordinary diffusion and can be explained by a model using classical diffusion theory. T h e exponential concentration dependence of diffusivity leads to equations which are very sensitive to the concentration of liquid in the upstream side of the film and to the percentage of crystallinity in the film. Calculations of a concentration gradient of solvent through the film shows that essentially all the resistance to diffusion is a t the downstream edge of the film. Furthermore, the form of the equations predicts the results that have been experimentally observed with respect to the effect of downstream pressure and the rate of absorption of the plastic film for solvents. The breaks in the curve of permeation rate us. temperature indicate a phase transition in polypropylene near room temperature. Acknowledgment
The author thanks the Esso Research and Engineering C O G for permission to publish this work and F. A. Caruso, M. McKinley, and G. F. Shea for obtaining some of the data reported here. literature Cited
(1) Binning, R. C . , Lee, R. J., Jennings, J. F., Martin, E. C., Ind. Eng. Chem. 53, 45 (1961). (2) Brubaker, D. W., Kammermeyer, K., Ibid., 46, 733-72 (1954). (3) Chandler, H. W., Henley, E. J., A.I.Ch.E.J. 7, 295 (1961). (4) Dickey, F. H., J.Phys. Chem. 59, 635 (1955). (5) Holmes, J. T., Olander, D. R., Wilke, C. R., A.I.Ch.E.J. 8, '646 (1962). (6) McCall, D. W., J . Polymer Sci. 26, 151 (1957). I
(7) McCall, D. W., Slichter, W. P., J . Am. Chem. SOL.80, 1861 (1958). ( 8 ) Michaels, A. S., Bacldour, R. F., Bixler, H. F., Choo, C. Y . , 1, 1 4 (1962). IND.ENG.CHEM.PROCESS DESIGN DEVELOP. (9) Richman, D., Long, F. A., J . Am. Chem. SOC.82,509 (1960). (10). Schrodt, V. N., Sweeney, R. F., Rose, A., “Factors Determining Rate and Separation in Barrier Membrane Permeation,” Division of Industrial ,and Engineering Chemistry, 144th Meeting, ACS, Los Angeles. Calif., March 1963. (11) Tung, L. K., Buckscr, S., J . Phys. Chem. 62, 1530 (1958).
(12) Weller, S., Steiner, W. A., Chem. Eng. Progr. 46, 585-90 (1950). (13) FVeller, S., Steiner, W. A., J . Appl. Phys. 21, 279-83 (1950). RECEIVED for review July 29, 1964 ACCEPTED April 6, 1965 Division of Petroleum Chemistry, 148th Meeting, ACS, Chicago, Ill., September 1964.
ANISOTROPIC DIFFUSIVITIES IN P R E S S E D C A T A L Y S T PELLETS C H A R L E S N . S A T T E R F I E L D A N D S H A N T
K. S A R A F
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass.
The variation of effective diffusivity with depth in a catalyst pellet can be determined following careful removal of successive layers, as by a lathe. Studies with a powdered catalyst consisting of 2070 Crz03 on -y-A1203 lpressed into cylinders to various densities showed that the local diffusivity varied by a factor of as much as 2l/2 with axial distance through the pellet. The extensive use of diffusivity measurements on c:atalyst pellets prepared by pressing a powder into a die to analyze theoretical models for diffusion through porous structures i s suspect. Such pressed pellets must be made by special techniques to ensure uniforrnity of structure if diffusivity data are to be interpreted in a fundamental fashion.
has been much interest in recent years in developing T m e t h o d s of predicting the diffusion flux in porous catalysts. In many cases the predictions from various proposed models have been compared with diffusion measurements on catalysts or catalyst carriers prepared by pressing powdered material into a compact under various degrees of pressure in order to vary the pore size distribution. Workers in the fields of pharmaceuticals and powder metallurgy have long known that the usual pressing techniques produce density gradients in pellets, but the consequence, that diffusivities will also be nonuniform, seems to be unrecognized by many investigators in the field of catalysis. Hence many of the diffusivity data reported in the literature represent only averaged values through a pellet and their use to distinguish between alternative theoretical models for diffusion through porous structures is suspect. T h e nonuniform distribution of density is caused largely by die-wall friction and to some degree by interparticle friction. This study shows the nature and magnitude of the effects for one typical catalyst material. HERE
Experimental
Catalyst pellets were prepared by compressing a chromiaalumina catalyst powdcr (62 to 88 microns in diameter unless otherwise designated) into a stainless steel ring. Rings of inside diameter of 1 or 3/8 inch and thicknesses of ‘/8 to ‘/2 inch were studied. A plunger and die assembly was used in which several rings of the same inside diameter were stacked on top of one another and filled with catalyst powder and the powder was compressed into the bottom ring by a plunger, pressure being applied to the plunger by a hydraulic press. T h e bottom face of the powder in the ring was held stationary; compression came only from the top. T h e density of the final pellet was controlled by varying the amount of powder used. Diffusion measurements were made in a n apparatus similar t o that used and described by Smith and coworkers ( Z ) , which
is a modification of the original procedure of Wicke and Kallenbach ( 5 ) for measuring countercurrent diffusion rates through porous materials a t constant total pressure. Hydrogen and nitrogen were the counterdiffusing gases; rates of flow were measured by capillary flowmeters and the composition of exit gases from the diffusion cell by thermal conductivity cells (Gow-Mac Model 9454 with mechanical seal and tungsten filaments). T h e diffusion cell was carefully designed and tested to ensure that no transport occurred by leaks or by flow under a pressure gradient. From the measured flux of nitrogen from each run a n effective diffusion coefficient was calculated by the relationship :
where a is the measured molar ratio of flux of hydrogen to that of nitrogen, plus one. I n each case this flux ratio was close to the theoretical value of 3.72. Measurements were made at atmospheric pressure and temperatures of 20’ to 30’ C. T h e concentration of nitrogen in the hydrogen gas leaving the diffusion cell varied in different runs generally from about 1.5 to 2.5 mole %, the hydrogen in nitrogen usually from about 5 to 10 mole yo. Consequently the values of De reported herein are nearly proportional to the product of the flux and the catalyst pellet thickness. T h e catalyst was 207, Crz03 on y-alumina supplied by the Girdler Catalysts Department of Chemetron Corp. and designated as T-876. This was ground up and sized by us to produce the powder size fractions of interest. Pore size distributions were measured on two of the catalyst samples after they were pressed into rings 3/8-inch in i.d. and ”8 inch thick, using nitrogen adsorption and the Cranston-Inkley model for pores below 120-A. diameter and mercury porosimetry for the larger pores. Sample A had a pellet density of 1.277 grams per cc. and sample B, 1.571 grams per cc. T h e corresponding pore volumes are 0.509 and 0.369 cc. per gram and total void fractions are 65 and 58yob. T h e solid density was calculated to be 3.69 grams per cc. T h e pore size distribution is nearly bimodal VOL. 4
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