D,D
effective diffusivity for microporous particle. defined by Equation 18: sq. cm.,’sec. fi,, = mean Knudsen diffusivity of gas A in macropores: sq. cm.,’sec. Dk, = mean Knudsen diffusivity of gas A in micropores, sq. cm. Isec. E, = effectiveness factor of catalyst pellet E, = effectiveness factor defined for microporous powder particles hI,, h, = Thiele modulus defined by Equations 16 and 17, respectively = reaction rate constant defined per unit time per unit mass of catalI,st, g. mole/’g. sec. = half thickness of slab-shaped pellet. cm. = diffusion rate per unit time per unit area of pellet, g. mole,./sq. c m ~sec. = total pressure, atm. = average reaction rate per unit time per unit mass of catalyst pellet, g. mole/g. sec. = reaction rate (rate of conversion of reactant) per unit time per unit mass of powder particle, g. mole/ g. sec. = gas constant, cc. atm./’g. mole O K . = X “ 2 X/X, = temperature, K . = mean molecular velocity, cm./sec. = distance variable, cm. = mean radius of powder particles, cm. = mean radius of spherical pellet, cm. = reactant gas mole fraction in macropores of pellet = equilibrium mole fraction = reactant gas mole fraction at external surface of pellet = aiy - Je)/’!JoJ,) = 1 (1VR/lVA) = macrovoid fraction in pellet =
+
et
= rnicrovoid fraction in peliet
elp
=
e,
= = = =
X PB
pp
microvoid fraction in particle solid fraction in pellet reaction parameter defined by Equation 28 density of pellet, g I’cc. densit! of particle, g.;cc.
literature Cited
(1) Beek, John, A.I.Ch.E. J . 7 , 337 (1961). (2) Carberry. J. J.. Ibid., 7 , 351 (1961). (3) Evans, R. B., LVatson, G. M., Mason, E. .4.. “Gaseous Diffusion in Porous Media at Uniform Pressure,” IMP-AEC-15, Inst. for Molecular Phvsics. L’niv. of Marvland, June 1. 1961. (4) Henry, J. P.. Chennakesanan. B.. Smith. J. M.. A.Z.Ch.E. J . 7. 10 (1961) (5) ’Ho&sch&en, J., znd. Eng. Chem. 47, 906 (1955). (6) Masamune, S.. Smith. J. M., A.I.Ch.E. J . 8, 217 (1962). , , ( 7 ) Mingle, J. O., Smith. J. M., Ibid., 7, 243 (1961). (8) Rao: M. R., Wakao. Noriaki, Smith, J. M., IND.ENC.CHEM. FUKDAYESTALS 3, 127 (1964). (9) Rothfeld, I,. B., LVatson, C . C., “Gaseous Countrr Diffusion in Catalyst Pellets.” 54th ’4nnual Meeting: A.I.Ch.E., hTew York, Dec. 3-7. 1961. (10) Scott, I).S., Can. J . Chem. Ene., to br published. (11) Scott, I). S.. Cox. K. E., J . Chim. Phys. 57, 1010 (1960). (12) Scott. L). S.. Dullirn, F. A. L.. A.I.Ch.E. J.. to be published. (13) Thiele, E. i V . , Znd. Ene. Chem. 31, 916 (1939). (14) kl’akao. Noriaki, Smith, J. M., Chem. Erie. Sci. 17, 825 (1962). (15) Whmler, Alborn. “Catalysis,” Vol. 11, Reinhold, New York, 1955. (16) Weisz, P. B., Schwartz, A. B., J . Catalyris 1, 399 (1962) (17) Wicke, E., Kallenback, R., Kolloid Z. 97, 135 (1941). RECEIVED for review April 5, 1963 ACCEPTEDDecember 30, 1963 Project carried out with the financial assistance of the U. S. Army Research Office, Grant No. DA-ARO(D)-31-124-G191.
DIFFUSION AND REACTION RATES IN T H E ORTHO-HYDROGEN CONVERSION M. RAJA RAO, N O R l A K l WAKAO, AND J . M . S M I T H C’ni~ersityof Californza, Davis. Calif.
Rate studies were carried out for the ortho-para-hydrogen conversion using single-pellet catalysts of N i O on A1203. Measurements were also made with the powder particles of catalyst used to prepare the pellets, From these data the effectiveness factor, Ea, was evaluated for pellets of three different densities and, hence, different macropore properties.
Pore size distributions, void volumes, and particle sizes were also meas-
ured. This information was sufficient to apply the theory in the preceding paper to calculate theoretical effectiveness factors. The agreement between the experimental and predicted results indicated that the theory was satisfactory for the specific, bidisperse catalysts used in this study. The effectiveness factor, Et, for the microporous particles in the pellets was found to b e unity. It appears that E a will be close to 1.0 except for very rapid reactions using pellets prepared from unusually large catalyst particles.
effect of pole diffusion on rates of solid catalytic reacSince then a considerable volume of literature has accumulated-- for example (3. 5. 7, 72, 74. 75). However, no experimental work has been reported for diffusion measurements under reaction conditions Particularly the relation between diffusivity and pore geometrv. with simultaneous reaction, has not been studied I n a preceding paper, a model developed for diffusion in bidisperse pore systems (70) is applied to the reaction case. T h e object of the present study is to compare experimental results with the foregoing theory. HE
T tions was first analyzed by Thiele (6).
For the experimental proqram, reaction rates were measured for slab-type catalyst pellets under conditions analogous to those used to develop the diffusion theory. In addition. rate data were measured for the catalyst particles used to prepare the pellets. For these studies the ortho-para-hydrogen reaction was employed wing a 25% NiO on A1?03 catalyst. This reaction was chosen for several reasons: The diffusion process is equimolal and cquntercurrent. ’This simplifies the diffusivitv equations. because (Y = 0. Temperature gradients. even with large pellets. are negligible because of the low heat of reaction. VOL. 3
NO. 2
MAY
1964
127
I
I
/
5 0
Figure 1 .
Schematic flow diagram of apparatus
1. 2.
Electrolytic hydrogen cylinder Deoxo unit 3. Silica gel tuber 4. Precooler 59. Flow reactor 5b. Single pellet reactor
6. Liquid nitrogen bath 7. 8. 9. 10.
Reference gas Somple gar Thermal conductivity cell Soap-film meters
T h e rate equation for the S i 0 on A1?0$ catalyst has been studied and found to be first-order. a t constant pressure ( 7 7). ‘The rate measurements were made as a function of flow rate a t atmospheric pressure, liquid nitrogen temperature ( - 196’ C . ) , and with a feed composition of 25% para-hydrogen, corresponding to equilibrium a t room temperature. The following particle and pellet catalysts were studied : Powder particles. freshly prepared (approximate average size. 60 microns) supported on glass wool. Powder particles as above, but after 5 !.reeks’ storpge. 4-inch thickness), Cylindrical pellets (1 -inch diameter, with densities of 1.58. 1.33. and 1.09 grams per cc.
and Ni(XO3)* to Si0 are reported as 360’ and 400’ C.: respectively. Hence. the treatment given should ensure complete decomposition to the metallic oxides. Pellets were made by placing samples of the catalvst particles in a cylindrical mold. 1-inch i.d.. made of stainless inch steel. The material was then compressed to a pellet thick. The pellet. still encased in the mold. \vas inserted in the reactor. ‘Thus onlv one end face was exposed to the hydrogen mixture. creating a one-dimensional slab-geometry system for diffusion (see detail sketch in Figure 1). For the rate measurements with particles of catalyst, the particles of N i O on A1203 were supported in the glass reactor on glass wool. Preliminary runs with an empty reactor and separate experiments with dehydrated A1203 on glass wool, showed no activity. Evaluation of Rate Constants
Catalyst Particles. LYakao and colleagues (8, 7 7 ) have found that the ortho-hydroqen reaction a t constant pressure follows a first-order. reversible rate equation for many oxide and metal catalysts. including N i O on AI2O3. Hence for the catalyst particles the rate can be expressed as folloivs: Yp =
k,,E,(Y,’ - y’)
(1)
where Y ’ is the mole fraction of para-hydrogen in the gas stream. l’he specific reaction rate: k&, in general, is a function of external diffusion resistance as well as pore diffusion resistance within the particles. Using- a more active catalyst FVakao, Selwood. and Smith ( 8 ) found that the external diffusion resistance was negligible for particles as large as ’ 3 inch in the same range of velocities. Hence k,Ei.as determined in this ivork, should be a function only of pore diffusion resistance, temperature: and pressure. T h e rneasurements o n the particles \vere carried out in a continuous flow reactor, so that r,dlV
=
Fdy’
(2)
Combining Equations 1 and 2 , integrating, and solving for k,E, give
Experimental Rate Measurements
Apparatus. The apparatus used for the kinetic studies is shown in Figure 1. Electrol!-tic grade hydrogen was passed through a Deoxo unit. packed with palladium particles to remove oxygen. and then through two C-tubes filled with silica gel. The second silica gel tube and the reactor were immersed in a constant temperature bath of liquid nitrogen a t ?-inch i.d. and atmospheric pressure. A U-tube reactor. 5-inch length. constructed of borosilicate glass. was used for experiments \vith catalvst particles. A tank-type reactor (Figure 1) holding a single pellet \vas employed for studies with the pellets. The composition of hydrogen leaving the reactor was measured \vith a thermal conductivity cell (Gow-Mac tvpe \rith 30-S geometrv) as described by LVeitzel and LVhite (73). ‘The reference gas was normal hydrogen containing 2576 of the para form. Both reference and sample streams \\.ere passed through the cell. which \vas operated at a constant current of 180 ma. and \\-as maintained a t 25’ C . bvith a constant temperature bath. Flo\v rates through both sides of the cell \ v e x measured with soap-film meters. Calibration was effecled bv operating the reactor \vith catalyst particles at ]OW flow rates to obtain equilibrium composition [50.26y0 parah>-drogen a t -196’ C . (77)). hfeasurement a t successively lo\ver flo~v rates until the composition showed no further change was assumed to give the equilibrium value. Intermediate compositions were obtained bv mixing normal hydrogen and the equilibrium effluent from the reactor. Catalyst Preparation. .4 single batQh of 2iYc NiO on :\1203was prepared by soaking boehmite (.41203.H?O) poivder in S i ( N 0 3 ) ? solution. After impregnation. the material \vas dried a t 110’ C. for 2 hours and then heatfd a t 450’ C. for 4 hours. The catalvst \vas then lightly mixed to srparatc the aqglomerated material into particles of approximately the same si7e (60 microns) as those of the original hoehmite. The decomposition temperatures of A 1 2 0 3 . H20 128
l&EC
FUNDAMENTALS
(3) Table I summarizes the rate data for the powder particles. The k,Ei values from Equation 3 are given in the last column. T h e aged catalyst was the same as the fresh material except that it had been stored in a desiccator for 5 iveeks. T h e variation of 15% betlveen the two sets of data is a measure of the stability of the catalyst and reproducibility of the data. The results with the fresh catalyst were uqed in the analysis given in the next section. since these measurements Lvere made a t approximatelv the same time as thoce for the pellets. Catalvst Pellets. T h e single pellet reactor was designed to operate (Figure 1 ) with a constant gas composition on the face of the pellet that corresponded to the exit, J ? ’ , value. Hence the design equation is i T f ’ = F(y3’ - VI’)
(4)
where P is the average reaction rate for the pellet. This rate can be written also in terms of the pellet effectiveness factor. E,. I = (k,E,)E,(v.’ - y z ’ ) (5) Combining Equations 4 and 5 qives
Values of (k,,E,)E,: evaluated from Equation 6: are given for the three catalyst pellets in Table I . The numerical results for kWEi and (k,Et)Ea establish an experimental value for the macropore effectiveness factor for each pellet.
0 6 5 -
Table I.
I
Exparimento4 Rate Data ( 1 atm.,
- 196'
PELLET
C.) kw
__
0 60-
E,
cs:g/CC
ALUMINA
M.':F X 7 / T 5 , G. (Set.):
FLou Rate, cc . S e c . ( I
Hun
.Yo.
1 2 3 4
9.671 1. 0 0 1 .36 1 82 2.18 2.2' 2.78
3
6
5
(Sec.)
(C. Cot.) 1.26 Grams
0.500 0.492 0.480 0.464 0.449 0.44' 0.429
=
0.459 0.368 0.226 0.169 0.141 0.136 0,111
10.4 10.3 10 8 11.2 11 . 0 11 1 11.2
Av. 1 10 Grams
10.9
1.03 o3
,
BOEHMITE
~
m
I 2 0 I40
-___
3.50
8 0
CATALYST
c1
1'33 A
A
I 58
Aqrd 5 \leeks. Mass = 0 848 0 492 0 316 0 229 1 10 4'8 1 -2 0 446 0 156 2 25 0 418 0 119 2 -8 0 394 0 0965 3 22 0 381 0 0833
1 2 3 4 5 6
AV
I1
Density, 1 2 3
p~
=
1.05 1.09 1.31 pB
1
2 3
Densit!.
1.58 Grams C c . ; Mass = 5.08 Grams 0.420 1.18 1 .'4 1. i 2 0.417 1.14 0,407 0 95 1.72 Av. 1.73
=
1.09 Grams Cc.; Mass 0.83 0 445 1 03 1.06 0,426 0.81 0.71 1.22 0.415
p~
1 2 3
0.2 5
Catalyst Pellets
1.33 Grams 'Cc.; Mass 0 429 1.12 0.93 0.81 0,409 1.30 0 392 0.71 1.46
Density,
$2
-
0.55
(C. .\lolei
I?'
Catalpt T'a-tides, Mass
I.
G. .\4olk/
0
0.66 0 97
.x. 705.
=
=
=
0 . 10
0 .0 5
4.29 Grams 2.16 2.14 1 81 Av. 2 04
0 I
I
o3
I 0'
MACRO-PORE
3.52 Grams 3 27 2.85 2 . '0 .4v. 2.94
Figure 2. 2 400
.-It 2.1" C. and 1 atm.
Table II.
O2
RADIUS,
A.
0,.
Pore size distribution curves
1
I
0
ALUMINA
Properties of Alumina (Boehmite) Particles
Catalyst carrier. Solid density 2 . 6 8 g., cc. ( I ) . Surface a r e a 276 sq. m e t e r r / g . Pore volume (NL)0 . 9 0 cc.; g.
.\dicropm Pnrticie
Duttibiition Thiouzh, r C
..~~~~~ Sire. ~
.\firroni
90 60 45 20 10
~~~
61 . O 32.5 23 i 11 5.
70
--Porediam., A . 120 69 46 35 28
P
Sizt Distribution
Suitace aiea,
52
8 3 28 0
5- 1 -9 8 96 3
Port uoiume,
0;
31 1 5- 0 81 5 95 1 0.6
Pore Geometry Measurements
T o uhe the diffuiion theory of the preceding paper to evaluate diffu4virie. and ef-fectiveness factors requires geometrical propertic. of the catalyst pellets-. that is: mean pore radii and void fractions for calculating difTuqion rates and the poxvder particle yize for calculating the micropore effectiveness factor, E , . Thehe properties I\ ere determined from the follo\ving in for mat ion. Catalyst P o w d e r Particles. T h e boehmite powder used as a carrier \\-as a spray-dried marerial from the hmerican Cyanamid C o . Its properties. as dctermined by the company. are given i n Table 11. T h r average particle radius, I ~ evaluated . from he size distril~urioridata, is 30 niicrons. .After impregnaTion \\ ith S i N Q the particles had agglomerated. Folloiving
0.8
1.0
Boehmite
Figure
3.
1.2
1.4
density
16
of
2 0
18
P e Ilet
,
22
24
4ycc.
Average macropore radii
reduction to SiO. the material was subjected to a vex->-mild grinding operation to break the agglomeraiions into particles of approximately the same size as the original boehmite. .As seen in the follo\\ing section, an accurate kno\vledgc of ,tp is not needed to determine E,. Hence. wing a value of 30 micron< i q sati.,factory. .Macropore Characteristics. ?\lacropore L-oid volume and pore size distriburions \\-ere measured for the threc caralh-si pellets ivith an .kninco-\\-inslo\v porosirneter. Fig-ure 2 sho\vr the pore size distribution results for the three catalyst p r l l e ~ s , Table 111 gives the macropore void fracrion. e n . dr1ermined VOL. 3
NO. 2
M A Y
1964
129
from the total volume of the pellet and the macropore void volume. Also included in the table are diffusion-average values of the macropore radii. These latter quantities are necessary to evaluate Knudsen diffusion rates in the macropores. The expression for this averaging process, developed in the earlier diffusion paper (Q), is
6"
a&Va
an
=
- -
(7)
V,
From the pellet density, p R , and ea, the density, p p , of the microporous particles can he determined. These results are given also in Table 111. Such particle densities should be the same for any pellet density, provided particles are not crushed in the pelleting process. The values in Table I11 are about the same for each pellet. These average radii are higher than those normally encountered for this type of A1203 pellets. To verify this, pore size measurements were also made on pellets made from hoehmite particles and dehydrated A1203 particlm. 'The results for these two materials are also given in Table I11 and Figure 2. Figure 2 demonstrates that the pellets made from catalyst particles have larger radii and pore volumes than those for A1203, and that the A1203 results are larger than those for boehmite. Since the decomposition processes occurred before the powder was pelleted, the increases cannot be due to evolution of gas in the macropores. Presumably the differences are caused by changes in the particles which affect the pelletization process. Winslow ( 7 6 ) has found that decomposition, including dehydration, can lead to significant changes in powders and in materials formed from them. The differences in pore size distributions shown in Figure 2 are within the range of variations he ha#$observed for various types of alumina. Figure 3 shows the average macropore radiiis plotted against a common density, to provide a basis for comparison for the three materials. This common density is a hypothetical quantity for the dehydrated A1203 and catalyst materials. It is calculated by determining the mass of .41203.H?O corresponding to the A1203 in the pellet and assuming no change in volume. For example, for the A1203 pellets the hypothetical density \vould be (120/102)p~. This figure shows the increase in average pore radius of the catalyst over that for Al2O3or A 1 2 0 3 . H 2 0 . Hypothetical particle densities can be determined on a boehmite basis in a similar manner. Such quantities apply to the intercepts in Figure 3 shown by the dotted lines. The intersection of the lines for boehmite and A 1 2 0 3 suggests that the assumption of no volume change accompanying dehydration is valid. However, the hypothetical particle density for the catalyst is much larger, indicating Table 111.
giving, p t = 2 68
(' "?)
1 25 or 2.85 grams per cc Thiq 1.20 assumes there is no change in volume of the solid when N O is suhstituted for H20-a qirestionable assumption in general, hut accurate enough here in view of the small significance of micropore diffusion. Using an average value of p p the micropore void fraction, e i , was determined and is given in Table 111. Experimental and Theoretical Effectiveness Factors In the preceding paper it was shown for a = 0 that an ana-
lytical solution could be obtained for the pellet effectiveness factor. For pellets with slab geometry Equation 16 of the previous paper (70) determines Ea. Before these equations can be used, k,R, and the effective diffusivity, r ) , are needed. The former qiiantity is available from the experimental data on the powder particles (Table I ) . However, the micropore effectiveness factor, E,, must be determined before D can he evaluated. Micropore Effectiveness Factor, E,. Assuming spherical particles, E( is given by Equation 20 (70). The micropore diffusivity, Dip, can he evaluated from Equation 18 (70)that is,
nb
+-
Diih
At - 196" C. the molecular diffusivity of Hz, from the data of Jost ( 2 ) , is 0.14 sq. cm. per second. The Knudsen diffusivity, Dki. is 0.014 sq. cm. per second, as determined from the information in Table 111 and the expression
Physical Properties of Pellets
(Pellet diameter 1 inch. PB,
a shrinkage in volume. The effects of decomposition processes on the geometry of catalyst pores are just beginning to be studied and much remains to be done. Micropore Characteristics. Diffusion through the micropores is less than 10% of the total diffusion rate for the three catalyst pellets. For this reason relatively large errors in micropore characteristics, ei and d,? will not have a significant effect on the diffusion rate. Hence (z, was assumed to he the same as for the original hoehmite powder used to prepare the catalyst. This value is 23 A , , as reported by Wakao ( 9 ) . Similarly e t was estimated by assuming the true density of the solid material in the catalyst. The solid density of the boehmite was about 2.68 grams per cc., as measured by Johnson ( 7 ) . This value includes the effect of some water adsorbed on the solid surface. The value for the catalyst was estimated by accounting for the mass change in substituting NiO for H20,
Thickness
' / 4
inch.
Volume
3.22 cc.)
ai, A . U', G. G./CC. €i* e, 2 12 0 658 0 46 1940 1 22 Pi1 1 29 0 966 0 25 3 11 627 1 21 1 03 n 15 3 31 1 43 23 0 28 790 1 01 3 31 23 450 1 31 1 20 0 086 3 86 23 41 5 1 49 1 40 n 064 4 52 Catalyst, 25", NiO/A1208 3.51 1.09 n ,485d 2100d 0.10 23 6 0.20 0.13 1690 2.11 2 38 0 20 1 33 0 37 4.28 0 15 236 0 22 2 . 3 6 0 33 1270 1 58 5.08 a Density of mzctoporousparttcles calculated f r o m equation, p p = p ~ / I( - c c ) . Micropore void fraction in pellet obtained f r o m expresston e t = ( I / p , - 7 / p r ) p B : using 2.85 for solid deniitv and 2 2 1 / 0 0 ,mean particir denrlty. .Wirropore uoid fraction i n p o z d e r particle evaluated f r o m equation eip = Arsrtmed to be same as for boehmite. Extrapolated from data of other twopelletr. til( 7 - ea). Pellet Material
Dehydrated alumina, AlnOs
130
l&EC FUNDAMENTALS
Substituting these results in Equation 8 give1 a value of D,, for each catalyst pellet. Equation 20 then provides a relationship bet\veen k,. and E,. The product. k,.E,. is available from the raw measurementb on po\vder particles (Table I ) . so that E , can be evaluated by trial. ..\ctually the i i , value is so low ( h i = 0.16) that E , is unity. Examination of the relationship bet\veen h , and E , indicates that h , \vould have to increase to 0.8 in order for E , to be as lo\\-as 0.95. Hence effectiveness factor.; for the microporous particles in a pelleted catalyst are likely to be near unity except for exceptionally large particles and ver)- rapid reactions. Effective Diffusivity of Pellets. For (Y = 0 the effective diffusivity. D.for the pellei can be Lvritten. from Equation 9 ( 7 0 ) . as (hlacro) (hficro macro-micro)
+
D
..
1 ~~~
Dh
+ ct2(1
c a2 ~~~
~~~~
+
1 ~~
+ 3ca)
(l -
+
D/,.st. For high densit) plain alumina pellets this \ \ o d d not be true. For example. for the most dense .41?0,.H,O pellet described in Table 111. 0 , is 415 h. For thi, material the micro contribution to the diffusivity tvould be dominant. as illuctrated by the diffu.yion data for this material ( 9 ) . Kno\\-ing D and k,,E, = 10.9 X 1 0 - 5 grain mole (sec.) (gram.: of catalyTtl for the catalyst particles. Equation 16 ( 1 7 ) ~ v a qused to predict the effectivenesi factors. E,. for the three pellet.. A n experimental E , can be determined for comparison by ir\inq thr (/;,2,',)E~l data in Table I . T h e results sho\vn in the last columns of Table I\* substantiate the diffusion and reaction theory for the qystem studied. 'I'he relativel? large pellet thickness. I , = 0.25 inch. a n d the rapid reaction lead to large diffusional rrsistances in the mdcropo1.c.i. These conditions are especially suitable for analyzing the diffu>ion theory. for the)- correspond to small efyectivenesq factors (0.1' to 0.30'1. T h e decrease Ivith incr~aririgdensit!- of pellet i \ d u c primarily to the decrease in radius of the macropores. 'The hignificance of E , in the theory presented has not been verified in thiz experimental ivork. T h e pellets used in this study all sho\ved relatively large macropore contribution to the total diffuuon ratei (Table Predicted and experimental effrctiveneas factors for relatively small macropore contributions have recently been compared (41. I'he results again ahoived good agreement. However. all the pellets studied have had bidisperse pore distributions. 'This t)pe of material probably hzs man)- pore interconnec-
Table IV.
Acknowledgment
-
E
€ 0 )
tions --one of the assumptions in the prediction method. For other types of porous materials the theory may not be suitable.
0 16 0 19 0 2-
F k,, L h, hi.
= = = =
= =
= = =
P
I
=
= '
=
rp
=
z
=
1'"
=
TI7 , I
= = =
I
=
xp
mean macropore radius. cm. mean micropore radius. cm. effective diffusivity of hydrogen in catall.st pellet. sq. c m . sec. effective diffusivity of hydrogen in catalyst particle. sq. cm. sec. mean Knudsen diffusivity in macropores. sq. cm. sec. mean Knudsen diffusivity in micropores. sq. c m . sec. bulk ixnolecular) diffusivity of hvdrogen. s q . cni. sec. effectiveness factor (micropore) for catalyst particles effectiveness factor (macropore) for catalyst pellet flow rate. g. moles 'sec. specific reaction rate. (g. mole) (sec.)(g. c a t . ) thickness of catalyst pellet. cm. Thiele parameter for spherical particles Thiele parameter for catalyst pellet of slab geometr)total pressure. 1 a t m . average rate of rraction for catal!.st pellrt. ig. moles),' f s e c . ) lg. c a t . ) rate of production of para hydrogen. (6. moles) (sec.) i g . car.) for catal>-stparticles mean molecular velocit!. of h>-drogen at -196" C . cm. sec. macropore volnmr. cc. g . \\eight of c a t a l n t . g. mean radius of catalyst po\vder particles, c m . mole fraction of para-hydrogen in gas stream or in macropores equilibriurn value of para-h\.drogen concentration at -196" C . . 0.3026 (77)
GREEK
g. cc. particle density. g. cc. = solid densit>-.g. cc. = macropore void fraction in pellet = micropore void fraction in pellet = micropore void fraction in particle
PH
= pellet densit!-.
PP
=
P1 to 6,p
SVBSCRIPTS 1 = entrance of reactor 2
=
exit of reactor
literature Cited
(1) Johnson. M. F. L.. personal communication. ipril 1961, (2) .Tnst. \ V . . "Diffusion." L'erlag \.on Steinkopff. Darrnstadt. 1957. ( 3 ) Pctel-s(ln.1:. E.. .l.Z.C'/i.E. J . 3, 443 (19S7). (4) Hao. 41. l < . . Smith. J. M.. /bid.. 9, 485 (1963). (5) Scott. Jl. S..Cox. K . E...I. Chirn. Phys. 57, 1010 (1960). (6) Thiele. l , , \V.,Irid. Evq. C'hehPni.. .In,fii. EN'. 31, 0 1 6 (1939). (7) \\'acmi,r. I:. \ \ , , %. Phsiih. C h f m A193, 1 (1943). (8) IVakao. Noriaki. Se,l\vood. P.\V.,Smith. J. M.. .4./.Ch.E. J 8, 4-8 (l902) (9, \\.akao. S o r i a k i . Smith. .I. hi.. C h m Em>..+. li, 8? (10) \Vakan. Noriaki. Smith. J . kl.. I h n . E N G .C ~ t Fv( ~ 4 1 . s3, 123 (1064). ( 1 1 ) \Vakao. Soriaki. Smith. .J. M..Szlbvood. P. \ V . . J . C h / n / ) , i t 1, 6 2 (1962). (12) \Veisz. P. R.. Prater. C . D.. d d m n . C n f d y r i j 6 , 143 (1954). (13) \ V r i t z r l . D. H.. \Vhitr. L. E.. (14) !Vhrt-lri-. .4hlhorn, .Idton. Ciii (1 5 ) \\.heelrr. Ahlhorn. "Catalysi
S e \ v York. 1935. (1 6 ) IVinslo\v. N.M.. personal communication. .Tun? 1962 (1:) \\'oollry. H. \\-,. S r i i t t . K . H . . Brick\vedde. F. ( i . ~ ,/. K P I . .Vat/. Rut.. Ctd. 41, 3'9 (1948). RECEIVED for rc\-ic\n- April 5. 1063 :\C:(:F,PTEU 1)ecrmhcr 30. 1963
Financial support pro\-idd b!- V , S. .Arm\ I
