literature Cited
Alder, N., Promotionsarb., No. 3270, Zurich, 1962. Cadle, P. J., Sc.D. thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1966. Cadle. P. J.. Satterfield. c. N.. IND.END.CHEM.FUNDAMENTALS 7 , 192 (1968). Davies, B. R., Scott, D. S., “Symposium on Fundamentals of Heat and Mass Transfer,” 58th Annual Meeting, A.I.Ch.E., Philadelphia, 1965.
Hewitt, G. F., Morgan, J. R., “Progress in Applied Materials Research,” 5 , Gordon and Breach, New York, 1964. Johnson, M. F. L., Stewart, W.E., J . Catalysis 4, 248 (1965). Satterfield, C. N., Cadle, P. J., Ind. Eng. Chem. Process Design Develop. 7 , 256 (1968). Satterfield, C. N., Saraf, S. K., IND.ENG.CHEM.FUNDAMENTALS 4 451 .- - 11965’1 -FValker, P. L., Ruskino, F., Raats, E., *Vaature 146, 1167 (1955). -7
\-
~
RECEIVED for review February 20, 1967 ACCEPTED November 30, 1967
ANISOTROPIC DIFFUSIVITIES IN PRESSED BOEHMITE PELLETS P. J O H N C A D L E A N D C H A R L E S N . S A T T E R F I E L D Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass.
02139
The effective diffusivity in pellets pressed from powdered boehmite varied by a factor of as much as 3 or 4 with axial distance through the compact. Results are interpreted in terms of the density distribution pattern. Pellet shape and size significantly affect diffusivity in that they influence the porous structure; consequently, measurements made on one pellet size are not necessarily applicable to the same material in another pellet size or shape even when the pellets have the same density.
TUDIES
of diffusion in porous masses prepared by pressing
S a powder into a die have been reported by numerous investigators and in almost all cases the results have been analyzed assuming that the porous structure is uniform. This was supported by the results of Dye and Dallavalle (1958), who made unsteady-state diffusion measurements with large pellets (l’/s-inch diameter and lengths of 1, 2 , 4, and 8 inches) of potassium perchlorate and reported that the effective diffusion coefficient was invariant with length. However, the recent study of Satterfield and Saraf (1965) on pellets 3/8 or 1 inch in diameter made from a hard chromiaalumina catalyst powder revealed that pellet heterogeneity can cause the local effective gas diffusivity to vary with position by a factor of as much as 21/2. I t is frequently necessary to assume an isotropic structure in the absence of other information and the assumption of a constant effective diffusivity greatly simplifies analyses such as those of a catalyst effectiveness factoi. Nevertheless, several recent attempts to develop models for predicting diffusion in porous catalysts from measurements on pressed pellets seem overelaborate in view of the anisotropic structure found in most of these materials. Boehmite was studied here because it has been extensively used in these kinds of studies (Otani and Smith, 1965; Riverola and Smith, 1964; Robertson and Smith, 1963; Wakao and Smith, 1962) and, as a relatively soft material, its behavior is worth comparing to the relatively hard chromia-alumina powder. The general nature of density patterns in cylindrical pellets formed in unlubricated dies by pressing from one side only, called the top side, are well documented by Jones (1960), who was particularly concerned with applications to powder metallurgy. In general, the decsest region is the top outer periphery and the least dense region is the bottom outer periphery. The maximum density in an axial direction generally lies closer to the bottom than the top. 192
I&EC FUNDAMENTALS
Experimental
T h e boehmite was supplied by the American Cyanamid Co. and identified as “spray-dried alumina No. 1668.” I t is essentially the same as the boehmite studied by Smith and coworkers. A double latin square experimental design was used to investigate the influence of density level, time of pressing, and initial pellet thickness on the effective diffusivity of 1-inch diameter cylindrical boehmite pellets and of various sections of the pellets obtained by slicing and removal of plane surface layers. T h e design allowed study of: A. Four density levels. 0.65, 0.76, 0.87, and 0.99 gram per cc. B. Four times of pressing. 0, 1, 5, and 20 minutes. and ‘/4 inch. C. Two pellet thicknesses. D . Four pellet treatments 1. Removal of top and bottom surface layers. 2. Removal of top quarter of the pellet and the bottom surface layer. 3. Removal of the bottom quarter of the pellet and the top surface layer. 4. Removal of the top half of the pellet and the bottom surface layer. T h e surface layer removed from the plane surface was about 200 microns thick in each case. T o minimize the possibility of plugging of pores during the abrasion process, the pellet was inserted into Tygon tubing and a stream of oxygen under pressure \vas applied to the surface opposite that undergoing abrasion. Surface material was removed by folding a piece of finest grade emery paper and applying the edge gently to the surface. An air jet was also directed at the surface. Finally the pellet was placed in a vacuum flask and subjected to full vacuum for about 1 minute. T h e density levels essentially embrace pellets B, C, and D in the \Vakao and Smith study (1962) and the time of pressing refers to the length of time the pellets were held under load after the desired thickness had been obtained. Each latin square had four columns (density levels) and four ro\vs (time of pressing levels) and the four treatments were distributed
a t random, with the restriction that each treatment occurred once in each column and once in each row. Counterdiffusion measurements were made under zero pressure gradient with a Wicke-Kallenbach apparatus similar to that previously used 1:Satterfield and Saraf, 1965) and described by Henry et al. (1961). Hydrogen and nitrogen were the counterdiffusing gases. Flow rates were monitored by capillary flowmeters and measured by the soap bubble technique and their composition was determined by thermal conductivity cells (Gow-Mac Model 9454 with mechanical seal and tungsten filaments). Reference to Sherwood and Pigford (1952, page 82, Figure 26) suggests that the gas leaving the buret used in the soap bubble measurements was saturated with water vapor, but no correction for this has been applied to the measured flow rates. Diffusion measurements Lvere made on the untreated pellet and on the treated or sliced pellet. T h e order of experimentation was determined by the use of random digit tables. For each run an effective diffusion coefficient, defined by Equation 1, was calculated from the measured hydrogen flux.
U
x
MACROVOID
0.53
6-
5 -
This simplified approach to determining an effective diffusion coefficient is justified because the objective has been t o demonstrate the presence, if any, of density distributions and their effect on De. T h e bulk diffusion equation used here is strictly invalid for these pellets, since the macropores reside almost entirely in the transition region. Nevertheless, an effective diffusion coefficient defined by the bulk equation should be invariant for a given density, if pellet inhomogeneities do not exist. T h e effective diffusion coefficient-density relationships presented here are valid only for the hydrogen-nitrogen system a t room conditions.
3-
2-
1-
0.7 AVERAGE
I n general the molar flux ratio was close t o the theoretical value of 3.73, but a trend t o smaller values was discernible for the most dense half-inch, unsliced pellets, which appeared to be due t o desorption of adsorbed moisture. Although the rate of moisture desorption is :negligible compared with flow rate through each side of the diffusion cell, this may not be so relative to diffusion rates through the pellet. T h e thermal conductivity of water vapor is nearly that of nitrogen, so its presence in the nitrogen-rich stream will have a negligible influence on the apparent hydrogen concentration; however, in the hydrogen-rich stream, the presence of water vapor will cause a n inflated value :for the nitrogen concentration to be recorded. Of the previously reported studies on pressed boehmite pellets, only that of Riverola and Smith (1964) shows evidence of a decrease in flux ratio with increase in density. For pellets of density 0.79, 1.00, and 1.15 grams per cc., they observed flux ratios of 3.82, 3.59, and 3.56, respectively, with the hydrogen-nitrogen gas pair. However, their pellets were subjected to a rigorous pretreatment which precludes the possibility of adsorbed moisture being responsible for the decrease in flux ratio. T h e double latin squares were analyzed in two ways: first, with the effective diffusion coefficient, De, for the treated pellets as the variate, and second, with an effective diffusivity ratio, defined by Equation 2, as the variate.
1.o
0.0 0.9 PELLET DENSITY, g i c C
Effective diffusivity as a function of density
Figure 1 .
l/s-inch initial pellet thickness
c4-
€
0.53
0.45
I
I
7
NU.
X
:
6-
5-
0 29
I
I
OPEN SYMBOLS -UNSLICED PELLETS 0 SURFACE LAYER REMOVED TOP OUARTER R E M O V E D A BOTTOM OUARTER REMOVED T TOP HALF REMOVED
0
+
0 37
)%
w
0
U
4-
k 20LA
T
:+\
\
3-
n
w
mv\
2-
?
\-
0
Results and Discussion
0.29 I
I
4-
-0.6 Measurements were made at atmospheric pressure and temperature in the range 20" to 30' C. T h e per cent nitrogen in the hydrogen leaving the diffusion cell varied from about 0.7 to 3.9Yo and the hydrogen in nitrogen from about 2.5 to 127,. For each density level and pellet thickness the log term was a constant and for the entire series of experiments its value showed a maximum deviation of only about 57, from an average value. Consequently, values of D e are nearly proportional to the product of the flux and the pellet thickness.
0.37
OPEN SYMBOLS - UN SLI CE D PEL LETS 0 SURFACE LAYERS REMOVED TOP OUARTER REMOVED A BOTTOM OUARTER REMOVED T TOP HALF REMOVED
3
T
FRACTION
0.45 I
W
LL
%A\-
1-
L W
0 0.6
I
I
I
I
07
0.8
0.9
10
Effective diffusivity ratio =
De for treated pellet De for pellet prior to treatment (2)
In Equation 2, both the De values were corrected to 25' C. to eliminate the influence of temperature. T h e analysis of variance tables are given in the thesis of Cadle (1966). With De as variate, the pellet density and pellet thickness were very highly significant and the treatments and the time of pressing were significant a t the 95 and 90% levels, respectively. With the diffusivity ratio as variate only the treatments were significant (at the 90% level) and the time of pressing in this particular press had no significance. Figures 1 and 2 show that the effective diffusion coefficient is well correlated with the average density of the unsliced pellets for each of the two pellet thicknesses. Comparison of the two curves makes it evident that for the same average pellet density, VOL. 7
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193
1
-
1.01
individual unsliced pellets, but the diffusion results show that reproducible pore systems were obtained. T h e variation in density from pellet t o pellet is due in part to the different time of pressing to which each pellet of a given thickness and density level was subjected. These results suggest that the amount of pellet expansion or "springback" that takes place when the compressive load is removed decreases with a n increase in the time of compression. Figure 3 shows the pellet density ratio, defined by Equation 3, as a function of the time of pressing.
I
I
1.00
2
4
cc
-I:
>
t v)
1
Density ratio =
z
g
0.99
individual pellet density mean pellet density for all unsliced pellets a t that density level and thickness
(3) THE T I M E L E V E L
4
An interesting result of the two statistical analyses is that the time effects had no significance with the diffusivity ratio as the variate. This suggests that the influence of the time of pressing was uniformly dissipated throughout the pellet. T h e behavior of the cut pellets on diffusion can be discerned from Figures 1 and 2 , but a clearer presentation is provided in Figures 4 and 5 , where the effective diffusion coefficient has been plotted against a density deviation which is defined by:
0.9e
0
5
20
15
10
T I M E OF PRESSING, M I N .
Figure 3. Influence of time of pressing on pellet density ratio '/Z-inch and '/l-inch thick boehmile pellets
Density deviation = the effective diffusion coefficient decreases with decrease in pellet thickness-i.e., for a specified average pellet density there is a moderate effect of size and shape. This result is in agreement with the observations of Satterfield and Saraf (1965). De is seen to be very sensitive to density a t the lowest density level, but relatively insensitive at the highest density level. This observation might have been anticipated from the results of Otani and Smith (1965), who found that for boehmite the pore size distribution is very sensitive to density changes. At the lowest density level, small density deviations have a profound influence on the range of pore size distribution, but only a minor effect at high density levels. Since the flux in a porous solid is greatly influenced by the pore size distribution in the transition range, the observations noted here are readily explained. For each pellet density level and thickness there \vas a small spread in the densities of the
* O P E N S Y M B O L S FOR UNSLICED PELLETS
e4-
E
N2 c
A
TOP O U A R T E R R E M O V E D
The horizontal distance between a particular symbol in the open and the blocked form gives the change in average density caused by the particular treatment specified. I t is evident from all four figures that the D,-density relationship is well obeyed by the denser, sliced, half-inch pellets and to a lesser degree by the denser, sliced, quarter-inch pellets. The behavior at the lowest density levels is anomalous. For example, after removal of the top half of the pellet, the density of the portion of the pellet remaining after the slicing operation is less than that of the original pellet, but in spite of this a smaller De was observed. T h e reason for this is not clear, but it may be due to variations in
' "
-.05
-.04
-.03
DENSITY
Figure 4.
\ -
9ICC
BOTTOM QUARTER R E M O l E D 0 8 7 5 0
-.Ob
-.02
l&EC FUNDAMENTALS
-.01
DEVIATION, g
0
.01
.02
Icc
Effective diffusion coefficient as a function of density deviation '/*-inch thick pellets
194
pellets a t that density level
(4)
0x50
-.07
- mean density of all untreated
DENSITY AT ZERO ABSCISSA
0 SURFACE LAYERS ? € M O V E 3 0 6 5 2 5
6 -w
density of an individual treated or untreated pellet
D E N S I T Y AT ZERO ABSCISSA .SURFACE
I
1
:w
1
0.6525 g l c c
LAYERS REMOVED
\
v
3
I
i
1
c
o l
l
l
i
]
-,06
-.05
-.04
-.03
-.02
DENSITY
Figure 5.
l -D1
l
l
0 .01 DEVIATION, g l c c
l
l
02
.03
.04
Effective diffusion coefficient as a function of density deviation ‘/pinch ihick pellets
point densities in a radiarl direction which are not revealed by this approach. Satterfield and Saraf (1965) also observed anomalous results a t the lowest density levels, though not the same type as those reported here. They found that two pellets having the same average pellet density could have significantly different axial density distributions (see their Figure 4, pellet P). Finally, Figures 4 and 5 show that the range ofdensity deviation increases with increase in density level and pellet thickness, a n observation which is consistent with die-wall friction considerations. Treatment 1, the removal of the plane surface layers, was designed to demonstrate the possible presence of a skin effect. T h e results are not conclusive, for all four of the quarter-inch pellets but only two of ihe half-inch pellets subjected to this treatment had diffusiviliy ratios greater than unity. This result contrasts with that of Satterfield and Saraf (1965), who observed a marked skin effect, probably because they removed slices from the top and bottom surfaces equivalent t o 1 / 1 2 and of the initial pellet thickness, respectively, whereas in the present study only a total of 200 microns was removed. Treatments 2, 3, and 4,the removal of the top quarter, the bottom quarter, and the top half, respectively, were designed t o demonstrate the presence, if any, of density distributions within the pellets. The observed results were in general agreement with those predicted from density distribution patterns reported in the literature and showed that the average density of a slice taken across the pellet decreases with increase in distance of the slice from the top. However, as reported above, although after treatments 2 and 4 the portion of the pellet remaining always had a smaller density than the whole pellet, this is not always reflected by a corresponding increase in the value of the effective diffusion coefficient. Since the time of pressing had no statistical significant influence on the diffusivity ratio, the variation of the effective diffusion coefficient with axial position for a particular density level and pellet thickness can be estimated from all the measurements by the following procedure: Consider the pellet divided from top t o bottom into four slices of thicknesses X I , x2, x3, and x4. Then, under steady-state counterdiffusion conditions the following relations hold :
Here yo is the mole fraction of the diffusing gas a t the bottom of slice 1, y l that at the top of 1, and y L that a t the top of slice 4. Dividing through by D e / L , the diffusivity ratio can be formed and the values of the ratio of the individual slices can be expressed in terms of the measured diffusivity ratios
For example, for the bottom quarter
The calculated values of the diffusivity ratio for the individual slices as a function of their axial location, density level, and pellet thickness are sho\vn in Figures 6 and 7 . T h e important observations from these figures are: T h e degree of axial variation of the diffusivity ratio decreases with increase in average density level and decrease in original pellet thickness. I n extreme cases the diffusivity ratios for different slices differ by a factor of 3 to 4. I n the bottom middle quarter the diffusivity ratio tends to increase with increase in average pellet density, while the opposite trend was observed in the other slices. (The diffusivity ratios can be easily converted into the effective diffusion coefficient by multiplying by a mean D e for the unsliced pellets of the density level and pellet thickness of interest). T h e decrease in the axial variation of the diffusivity ratio through the pellet with increase in density level is due to the decreasing sensitivity of De to the pellet density with increase in VOL 7
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195
''O
ORIGINAL P E L L E T THICKNESS 0 OUARTER INCH 0 HALF INCH
:
%
DI
0.9
A
-
0
0.7600
'I 0.9900
"
L 4
L 4
0
" "
3L
-
L 3L 4 2 4 DISTANCE FROM BOTTOM
''I
0
L
4
1.0
Figure 6. Diffusivity ratio as a function of axial location
ORIGINAL P E L L E T
THICKNESS
1
I
L
3L
0 OUARTER I N C H H A L F INCH
L
DiSTANCE F R O M BOTTOM
Pellets initially
-
.L
Figure 8. Average density of pellet remaining after removing successive layers from the top, as a function of pellet thickness
9 Icc
W 0.0750
d
-
0
0.6525
I
I
-
U %
m
inch thick
'/2
v)
z
W
0
2.0
I
I
-
0.8
$8
I 0.7-
L I
1.5
-
I
0.6 0
L
4 2 4 DISTANCE FROM BOTTOM
1.0
Figure 9. Average density of individual slices as a function of the location of the slice
-
0.5 MEAN UNSLICED
PELLET D E N S I T Y
0 0.6525
A
0
g Icc
0.7600 00700
"
V 0.9750
"
I
0
I 4
I
L 4
"
I
3L
L
4
D I S T A N C E FROM BOTTOM
Figure 7. Diffusivity ratio as a function of axial location Pellets initially
'/4
inch thick
the density level, while the greater variation within the halfinch pellets is in agreement with the higher die-wall friction effectsassociated with the thicker pellets. The diffusibility behavior of the different slices within the pellets cannot be completely interpreted, because the average density values give no clues concerning the radial density distribution patterns within the slices. The axial density variations for the half-inch and quarter-inch diameter pellets are shown in Figures 8 and 9. I n Figure 8 each point represents the density of the pellet remaining after removal of successive layers from the top, and in Figure 9 each point represents 196
L
I&EC FUNDAMENTALS
the average density for an individual slice as a function of its location within the pellet. I t is evident from Figures 6 and 7 that a t lower density levels there is a high resistance to diffusion in the bottom middle quarter with which a relatively high density region can be associated from Figure 9. Furthermore, as the average density level increases this high resistance transfers t o the top middle quarter. Support for this inference is apparent from Figure 9, which shows that the density of the top middle quarter increases substantially in relation t o that of the bottom middle quarter as the average density level is increased. Equally apparent from Figures 6 through 9 is the fact that the bottom layer offers the least resistance to diffusion and is the region of lowest density. These results may be compared with the results of Satterfield and Saraf (1965). I n general, the density patterns appear to be similar, high density values being observed in the top middle region, and further, the high density region tends to be nearer the top as the density level is increased. Their data show a greater variability in the average density values than reported here, which is to be expected because larger die-wall friction X inch pellets. effects would be expected with their The D,P values for the different pellet slices for their pellet P shows qualitative agreement with the low density pellets used in this study. A more specific comparison on the basis of equivalent macropore void fraction (all pores > 100-A. radii designated as macropores) suggests that their pellet P(0, =
0.42) should be compared with the boehmite pellets of density 0.76 gram per cc. (e, = 0.45). T h e D,P value for the unsliced pellet P was about 15 sq. cm. atm./sec. and using this value to convert their Figure 7 t o a diffusivity ratio basis, it can be seen that the profile through the pellet is of the same form as that observed in this study, at least for the half-inch thick boehmite pellets, although the magnitude of the diffusivity ratio variation was greater in their case. Again, this is to be expected from die-wall friction considerations and probably explains the better agreement with the half-inch than quarter-inch pellets. The influence of pellei: heterogeneity on diffusion is poorly understood and it is an area which is in need of further investigation if a valid appraisal of predictive models for practical use is to be achieved. T h e extent to which anisotropic diffusivities occur in commercially manufactured, extruded, or pressed catalysts is unknown. T h e results of a study on a commercial nickel-base steam hydrocarbon reforming catalyst are described elsewhere (Cadle and Satterfield, 1968). I n that case the effective diffusivity was nearly isotropic. Acknowledgment
T h e authors appreciate the award of a N A T O Studentship to
P. J. Cadle by the Science Research Council (United Kingdom). Nomenclature
De L AT
= effective diffusivity, sq. cm./sec. = pellet thickness, cm. = diffusion flux, g. moles/sec. sq. cm.
P R
= pressure, atm. = gas constant, (cc.)(atm.)/g. mole T = temperature, O K.
x
y (Y
e,
= = = =
O
K.
distance through pellet, cm. mole fraction; y l = value at top of slice 1, Equation 5 molar flux ratio of nitrogen to hydrogen, plus one macropore void fraction, cc./cc.
SUBSCRIPTS
H
= hydrogen
L = limit, x = L 0 = limit, x = 0 literature Cited
Cadle, P. J., Sc. D. thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1966. Cadle, P. J., Satterfield, C. N., IND.ENG.CHEM.FUNDAMENTALS 7 . 189 11968). Dy;, R. F., Dailavalle, J. M., 2nd. Eng. Chem. 50, 1195 (1958). Henry, J. P., Chennakesvan, B., Smith, J. M., A.I.Ch.E. J . 7 , 10 (1961). Jones, LV. D., “Fundamental Principles of Powder Metallurgy,” Arnold, London, 1960. Otani, S., Smith, J . M.,A.Z.Ch.E. J . 11, 435 (1965). Riverola, J. B., Smith, J. M., IND.ENG.CHEM.FUNDAMENTALS 3, 308 (1964). Robertson, J. L., Smith, J. M., A.2.Ch.E. J . 9, 342 (1963). Satterfield, C. X., Saraf, S. K., IND.ENG.CmM. FUNDAMENTALS 4, 451 (1965). Sherwood, T. K., Pigford, R. L., “Absorption and Extraction,” 2nd ed., McGraw-Hill, New York, 1952. Wakao, N., Smith, J. M., Chem. Eng. Sci. 17, 825 (1962). RECEIVED for review April 25, 1967 ACCEPTED November 24, 1967
THERMAL EFFICIENCY OF T H E PRODUCTION OF ACETYLENE FROM CARBON AND HYDROGEN J . T. C L A R K E AND B. R. FOX
Brookhauen .VationaI Laboratory, Upton, Atr.Y. 7 1973 The effects of temperature and pressure on the heat requirements for forming acetylene from carbon and hydrogen were experimentally investigated using graphite filaments heated by timed a.c. pulses and in other experiments by condenser discharges. Acetylene is formed by the reaction of vaporized carbon and gaseous hydrogen, SO the minimum energy required is that of vaporization and the associated radiation. In the thermal reaction of graphite and H2, radiation, thermal conduction, and hydrogen dissociation dissipate most of the energy if the temperature is 95% acetylene. T h e purpose of the experiments reported herein was to analyze how the energy was utilized when a graphite filament is heated in hydrogen. If the rate of reaction to form acetylene is sufficiently rapid, the amount of energy going into this endothermic reaction could exceed that lost by radiation and the thermal conduction. T h e energy t o heat the carbon could then be supplied by the collision of alpha particles or fission fragments with small
graphite particles suspended in hydrogen, and this process could serve as a method of utilizing fission energy t o carry out endothermic chemical reactions such as the formation of acetylene or hydrocarbons. T h e heat of formation of acetylene is positive (endothermic) a t all temperatures. The free energy of formation is positive a t room temperature, but decreases with increased temperature; temperatures in excess of 3000’ K. are required before significant amounts are in equilibrium with carbon and hydrogen. Acetylene can be produced commercially by highVOL. 7
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197
