tions of p, and pB could not be obtained. The stoichiometric coefficients of 4.5 and 3 in Equation 2 appear as exponents on the partial pressures in the expressions for the equilibrium constants. Actually, either a nonnegative number or a function of pB could have been selected for psi as required to minimize the error between the calculated and experimental rates of reaction. I n view of the simplicity of the method for treating the particular system investigated, it is believed that this same general approach could be successfully applied to other catalytic reactions. T o apply it, only the stoichiometry of the reaction must be established experimentally. Additional postulates may be required to produce a n equality between the numbers of unknowns (the interfacial partial pressures) and the number of equations. The use of the mass transfer relationships requires far fewer postulates than does the usual approach of proposing a reaction mechanism. For example, a t the outset the five postulates, pAi = pA,psi = pB>pci = pcj Pni = pD, and pEi = p,, would have been required for a system such as the one considered herein. Sext, it is generally assumed that the rate of diffusion to and from the interior of the catalyst is fast. Finally, the assumption of a homogeneous catalytic surface is commonly employed. After all of these postulates have been made, the postulates pertaining to the reaction mechanism must be made and justified. The necessity for making this multiplicity of postulates is eliminated by use of the simple method employed herein.
In principle, this method of correlation may be employed for the correlation of integral reactor data. The corresponding procedure differs from the one shown only in the calculation of values for the rj’s. I n the case of a n integral reactor, r j a t any given W’/noT is the slope a t this value of the abscissa of a plot of nJnoT us. W/noT. literature Cited
(1) Andrianona, T. I., RoginshiY, S. C., Zhur. Obshchei. Khim. 24, 605 (1954). (2) Billingsley, D. S., Ph.D. Dissertation, A&M College of Texas, College Station, Tex., 1961. ( 3 ) Feigl, F., “Qualitative Analysis by Spot Tests,” 3rd ed., Elsevier, New York, 1946. (4) Goodings, E. P., Hadley, D. J. (to Distillers Co.: Ltd.), Brit. Patent 625,330 (June 27, 1949). (5) Zbid., 658,179 (Oct. 3, 1951). (6) Hearne, G. W., Adams, M. L. (to Shell Development Co.), U. S. Patent 2,486,842 (Nov. 1, 1949). (7) Hougen, 0. A,, Watson, K. M., “Chemical Process Principles,” p. 985, Wiley, New York, 1948. (8) Margolis, L. Ya., RoginshiY, S. Z., Gracheva, T. A., Zhur. Obshchei Khim. 26, 1368-71 (1956). (9) N. V. de Bataafsche Petroleum Maatschappij, Brit. Patent 640,383 (July 19, 1950). (10) Woodham, J. F., Holland, C. D., Ind. Eng. Chem. 52, 985 (1960). RECEIVED for review January 4, 1963 ACCEPTEDAugust 19, 1963 A.1.Ch.E. South Texas Section Meeting, Galveston, Tex., October 1962. Work supported by the Dow Chemical Co. and the Texas Engineering Experiment Station of the A & M College of Texas.
DIFFUSION AND HETEROGENEOUS REACTION IN A TUBULAR REACTOR Decomposition of Hydrogen Peroxide Vapor CHARLES N. SATTERFIELD A N D REGINALD S. C. YEUNG’ Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. The heterogeneous decomposition of HzOz vapor on platinum or 304 stainless steel was studied in a 1/4-inch i.d. tubular reactor a t temperatures of 130” to 460” C., Reynolds numbers of 370 to 41 00,H102 log mean concentrations up to 2.1 mole % H z 0 2 , and atmospheric pressure. Under most conditions mass transfer and surface reaction are both significant. Intrinsic surface rate constants are presented as a function of temperature for both catalysts. An unexpected finding is that the true surface rate goes through a maximum with increased temperature.
N STUDYING
a heterogeneous reaction under conditions in
I which diffusion and surface reaction may each be a significant rate-limiting step, it is necessary to choose a geometrical arrangement for which the mass transfer characteristics are known o r readily predictable. T h e packed bed may have uncertain temperature and concentration gradients axially and radially and the point mass transfer coefficient varies with position around each particle. I t was anticipated that the rotating cylinder, while useful for many investigations, would cause experimental difficulties in this case, a n d especially that undesired decomposition would occur on Present address, Cabot Gorp., Concord Road, Billerica, Mass.
the walls of the containing vessel. The tubular reactor having a smooth nonporous wall, chosen for these studies, provides a “uniformly accessible” geometry which is subject to fundamental theoretical analysis and for which a substantial amount of mass-transfer information is available. There is little difficulty in maintaining its surface essentially isothermal. T h e present investigation was concerned with a study of the heterogeneous decomposition of hydrogen peroxide vapor on two different catalyst surfaces, platinum and 304 stainless steel. The study was stimulated by a practical problem in the catalytic decomposition of concentrated hydrogen peroxide in catalyst beds. This is the basis of a method frequently used VOL. 2 N O . 4 N O V E M B E R 1 9 6 3
257
t
I'
-L
-_j
CONSTANT TEMPERATURE BATH
Figure 1 .
Apparatus
for generating auxiliary power or thrust in rockets, aircraft, space capsules, and other devices. Since the reaction is highly exothermic, the mixture of steam and oxygen formed by decomposition of 90 weight % H202 will leave under adiabatic conditions at a temperature of about 750' C. (23) and with some catalysts the exit portion of the catalyst bed has occasionally burned out. A possible method of avoiding such burnout is to pack the downstream portion of the catalyst bed with some material which is stable under the high temperature oxidizing conditions, even though it may be a relatively inactive catalyst to H232 decomposition. Since reaction rate usually increases exponentizlly with temperature while masstransfer rate increeses little more than linearly, one would anticipate that a t suffiziently high temperatures the heterogeneous decomposition rate might become mass transfer-controlled for all catalysts, active and relatively inactive; hence the observed rate would become the same for all the surfaces and no performance penalty would be incurred. Platinum was studied because it is the most active catalyst known that is completely stable under high temperature and oxidizing conditions. Stainless steel (304) was studied because, although less reactive a t ambient temperature, it is also stable and is a cheaper substitute. I t is also a structural material used in H202-manufacturing plant equipment, so that its vapor decomposition kinetics a t lower temperatures are of practical concern. Apparatus and Procedure
Nitrogen carrier gas was passed through layers of soda-lime and silica gel to remove oil droplets, COz, and dust and then forced through a fritted-glass bubbler into a standard "gaswashing" bottle containing concentrated unstabilized aqueous H 2 0 2of high purity. Two such devices, arranged in series (only one is shoivn in Figure 1) and submerged in a constant temperature bath, provided 80 to 98% saturation of the gas stream? depending upon the flow rate. A long superheater (36 inches) \cas used to evaporate entrained droplets and bring the gas up to reactor temperature. Following the sample tap was a 12-inch length of precision-bore borosilicate glass 0.250 =t0.002 inch in inside diameter, which acted as a calming section to reform a steady flow profile. This was insulated and wrapped with guard heaters to maintain the gas stream isothermal. The H209 decomposition in this calming section never exceeded 1 to 27, of that occurring in the platinum or stainless steel reactor. Each of the two reactors (Figure 2) consisted of metal tubing 0.250 inch in inside diameter and 36 inches long connected to the calming section by a stainless steel coupling carefully designed to cause the metal and glass tubing to line up exactly and without exposure of a third material to the H202 vapor (Figure 3). All contact areas between tubing and coupling \
0
l I l l ! l l l ' l l l
001 0 02 LOG MEAN MOLE FRACTION OF H ~ 0 2
Figure 6. Over-all decomposition rate of HzOz vapor on platinum
velocity profile is roughly one half to one third of that calculated if the parabolic velocity profile is assumed. This kind of difference would be expected in physical terms. For example, consider a fixed observed degree of conversion, which represents the mixed concentration of all fluid elements leaving the reactor. With a parabolic velocity distribution the reactant concentration in the elements nearest to the wall will be less than would occur in rodlike flow because of the longer residence time. Hence the calculated reaction rate constant, assuming the correct parabolic velocity distribution, will be higher than that obtained assuming rodlike flow. Figure 4 provides a rapid means of determining k'R,/D for a n intrinsic first-order reaction, from experimental values of inlet and exit mixed concentration and assuming Hoelscher's solution for the parabolic velocity distribution. Results are not shown for conversions of less than 50%, since a t low per cent conversions the mathematics deviate increasingly from reality.
Another method used here for analysis of data was to regard the surface rate and mass-transfer rate as additive resistances in series, which is equivalent to the so-called quasistationary state approach of Frank-Kamenetski1 (7). I t was assumed that the mass-transfer coefficient and the surface concentration could each be represented by a properly averaged value. Equating the mass-transfer and surface rates : 2
260
This contains two unknowns, n and k,. In principle these could be determined from a series of experimentally measured values of the over-all decomposition rate, r , corrected for homogeneous reaction, and corresponding bulk partial pressures of H202 combined with values of the mass-transfer coefficient, k,, obtained from correlations applicable to the prevailing flow rates and geometry. This method can be applied equally w7ell to data in laminar or turbulent flow conditions so long as the appropriate mass-transfer coefficients are employed. Ilrhen it was used for laminar flow conditions, the appropriate value ofp, and hence k , was calculated from the Graetz equation (27), @
!
P. -PI
= 1 - 8[0.12038e-14.6272 rr/4G,
+
0.0122 e-89.22~/4GS
Additive Resistances
YhR r - -=
Eliminating the unknown p , and simplifying :
klpsn =
I&EC F U N D A M E N T A L S
k,(p
- pe)
(12)
+ .] (14) , ,
For turbulent flow conditions the Sherwood-Gilliland equation (20) was used, which correlates a large range of experimental data.
Other correlations give substantially the same values of k , a t a Schmidt number ofabout unity, which holds for the present experimental conditions.
T h e accuracy of the additive resistance approach in reduction of data depends upon many factors, including the extent of conversion in the reactor, the accuracy with which the mass transfer coefficient can be predicted, and the extent to which mass transfer is controlling. A typical graph of data in the form of Equation 13 is shown on Figure 5. When the surface (intrinsic) reaction is first-order, as seems to be essentially true here, a n equivalent expression is:
200 x 10-6
I O 0 r10-E
(16)
' This is the additive resistance form as first proposed by Hottel (22) and Fischbeck ( 6 ) , but includes a n additional term to allow for homogeneous reaction. Under our conditions homogeneous reaction was negligible a t temperatures of about 400' C. and less and amounted to no more than 4% of the total a t 452' C., the highest temperature studied. Corrections, when necessary, were calculated using data as correlated by Hoare, Protheroe, and \Yalsh (70) (Figure 11). Equations 13 and 16 both assume isothermal operation, a uniform concentration profile in the core surrounded by a diffusion layer, negligible volume change due to reaction? constant diffusivity, and negligible axial molecular diffusion.
Results
Platinum. T h e platinum reactor was made from a bonded copper metal tubing with a n inner layer of platinum 0.0185 inch thick. Under the temperatures and duration operated, the total amount of copper diffused through the platinum layer should be small ( 7 4 , and serious contamination of the platinum surface seemed unlikely. The reactor showed a constant catalytic activity unaffected by time o r temperature of previous exposure to H202, even a t temperatures as high as 450' C. A total of 135 runs was made, from 19 to 24 a t each of six temperatures. Four flow rates were studied a t each temperature. Six runs a t 450' C. with 0 2 as the carrier gas showed no significant difference from comparable runs made with iX2. No effect of water concentration over the moderate variations here could be detected. There is only a moderate effect of temperature o n over-all reaction rate, so no temperature correction was made for slight deviations in desired temperature from run to run in evaluating the order of the over-all reaction, but partial pressures were corrected for variations in total pressure between runs. T h e order of the over-all rate was obtained by successive approximations from data obtained a t constant flou- rate and temperature. For a n integral reactor,
The over-all observed kinetics was found clearly to be firstorder with respect to HZ02 concentration and independent of the concentrations of Oe, Nz, and H20, a t each temperature studied over the entire range of 130' to 450' C. A typical graph is shown o n Figure 6 ; similar graphs were obtained a t each of the other temperatures studied. There was no effect of inlet Ha02 concentration or degree of conversion o n the over-all first-order rate constant. Figure 7 is a cross plot a t a constant H202 concentration of 0.01 atm. of the observed over-all rates as a function of Reynolds number, for each of several temperatures. For comparison, there are also plotted the mass-transfer rates (dashed
1
1000
'
'
'
2000 3200 ' 4000 R E Y N O L D S NUMBER
'
5000
Figure 7. Comparison of calculated mass-transfer rate to observed over-all decomposition rate on platinum
curves) as calculated from the Graetz equation for the laminar flow region and from the Sherwood-Gilliland equation for the turbulent flow region. In both cases the molecular diffusivity was calculated from the correlation of Hirschfelder (76). Under laminar flow conditions, the observed over-all rates amount to 60 to 807, of that predicted from the Graetz equation, indicating substantial mass-transfer limitation. In the turbulent flow region the observed rates amount to 43 to 67% of those predicted from the Sherwood-Gilliland equation. T h e increase in observed rate as Reynolds number is increased, plus the above comparisons between theory and experiment, shows that mass-transfer and surface rate are both significant over essentially all temperatures and flow conditions studied. This substantial mass-transfer limitation decreases the accuracy with which the order of the intrinsic reaction can be determined. Applying Equation 13 to the experimental over-all rate data for any one temperature showed first-order surface kinetics. A typical plot is shown in Figure 5, for 304' C. The straight line has a slope of unity and the fact that data from both laminar and turbulent flow conditions fit o n the same line lends confidence to the method of analysis. Elder and Rideal (5) also reported first-order kinetics for HzOz decomposition on platinum under conditions where presumably the intrinsic rate was being observed, and a first-order relationship is observed for H 2 0 2decomposition on most surfaces unless a large excess of water vapor is present, which may have a n inhibiting effect. O n the other hand, a completely diffusion-controlled mechanism will itself be first-order and this may hide some deviation of the true intrinsic kinetics from a first-order relationship. The order of the reaction may also change with temperature. An unexpected finding is that the first-order over-all rate constant goes through a maximum a t about 350' C., as shown by the Arrhenius plot in Figure 8, which means that the true heterogeneous decomposition rate constant also goes through a maximum. We were greatly concerned that this might be illusory rather than real and reflect some hidden bias in the way that the experiments were conducted or the data were analyzed. However. we could find none. Figure 8 sholvs that for a fixed Reynolds number in either the laminar or the turbulent flow region, the over-all rate constant goes through a maximum. Data plotted as in Figure 5 showed somewhat more scatter a t the highest temperatures. but matching pairs of runs having essentially the same inlet concentration and identical in every other respect showed higher exit concentrations a t reactor temperatures above 300' C. than a t 300' C. Perhaps most convincing, in the high temperature region in a run a t constant flow rate and with constant inlet conditions, VOL. 2 NO. 4 NOVEMBER 1 9 6 3
261
ESO
c
TEMPERATURE 200
~
d
'C.
430 300
I
z
I
,
100
I
I
I
I 1 26 1000 RECIPROCAL TEMPERATURE T'K l
I4
a
1
22
I8
Figure 8. Arrhenius plot of over-all rate constants on platinum
I
Lr
c a C
a 3 9'C 259°C
-
1
1
N R 1642 ~ t o 2305 N R ~~ 3 4 1 Io 958
-
-
-
L
cc W > 0
0
001
002
I
1
L O G M E A N MOLE FRACTION OF
H202
Figure 9. Over-all decomposition rate of laminar gas flow on 304 stainless steel
r 0-4-
-
SURFACE RATE CONTROLLING
RECIPROCAL
TEMPERATURE
003
HzOz in
1
-i
IO00 TOK.
Figure 10. Arrhenius plot for over-all decomposition rate constants on 304 stainless steel 262
I&EC FUNDAMENTALS
increasing the reactor wall temperature and inlet calming section to a higher isothermal level-for example, by about 50' C.-would significantly increase the exit HzOz concentration. The effect clearly occurred under high flow rate conditions, which would minimize mass-transfer resistance and it was repeated many times. No assumption concerning the order of reaction is involved nor the fact that we are dealing with an integral reactor. One can visualize the possibility of confusing results from operating in the transition region between laminar and turbulent flow regions: but we can see no way in which the masstransfer rate under flow conditions clearly in the turbulent region, for instance, could be decreased by a temperature increase. The intrinsic surface rate constants on platinum, as calculated by Equation 13 or Equation 16, assuming firstorder reaction, are sholvn as an Arrhenius plot on Figure 11, together with kinetic constants for other systems discussed later. Since mass-transfer increases with increased temperature, the intrinsic rate constant must decrease more rapidly with increased temperature than the over-all rate constant. Any explanation for this temperature maximum must be speculative a t present. The decomposition reaction is presumably preceded by chemisorption onto the metal surface, a process which is usually assumed to be much faster than the actual rezrrangement of bonds among adsorbed specie. IYith increased temperature, the amount of chemisorbed H202 could plausibly drop more rapidly than the rate of surface reaction could increase, thus leading to a maximum in the observed rate. This could be expressed in various quantitative ways, depending upon what assumptions one wished to make concerning the actual mechanism of the surface reaction, the extent to which the intrinsic reaction might depart from firstorder kinetics, and the variation of activity of catalytic sites with coverage and with temperature. Temperature maxima have been reported for but a few other catalytic systems. .4 temperature maximum a t about 150' C. is well established for the hydrogenation of ethylene on platinum foil and on many other catalysts (2). The kinetic order with respect to ethylene shifts from zero to first order as the temperature maximum is exceeded. Temperature maxima a t about 65' and 90' C., respectively, are also observed for the hydrogenation of maleic acid or crotonic acid on platinum black. The surface kinetic constants obtained here for platinum could not be compared to the only other published data (5) on this catalyst because of lack of experimental details on the latter. The data obtained on platinum in the laminar flow region were also analyzed by the solution to the diffusion equation, assuming first-order heterogeneous reaction 2nd rodlike flow, or Hoelscher's solution for the parabolic velocity profile. The intrinsic first-order reaction rate constants thus calculated by each of these two methods are shown on Figure 11. In both cases the constants thus calculated likeivise went through a maximum at 250' to 300' C. with increased temperature. The agreement between the rate constants calculated by the simple quasistationary state approach and those obtained via the method of Hoelscher is surprisingly close. The constants as calculated assuming a rodlike velocity profile are about one half to one third of the others and are clearly too low. for the reasons discussed above. Stainless Steel. T h e 304 stainless steel is one of the 18 : 8 austenitic stainless steels, stable in high temperature and oxidizing conditions. Kevertheless, the catalytic activity of its surface was found to depend on the maximum temperature to which the reactor surface had previously been subjected in contact with HzOz vapor.
A total of 76 runs was made with nitrogen as carrier gas, from 9 to 18 a t each of six temperatures ranging from 259' to 454' C., inclusive. Reynolds numbers varied from 340 to 3860. Four runs were also made a t 143' C. and . t ' ~=~437 and two a t 196' C. and X R ~ = 368. I n all these runs, the stainless steel surface temperature was equal to or greater than the maximum past temperature encountered. Twelve runs with oxygen as carrier gas, six a t about 259' C. and six a t 400' C., showed no significant change in over-all rate constant from those made with nitrogen. Twelve runs were made a t 259' C. after the stainless steel surface had been previously heated to 394' C. in thepresence of H202 vapor. and ten a t 259' C. after previous heating to 454' C. Analysis of the data indicated that heating to 394' C. increased the intrinsic rate constant a t 259' C. to a value about five times that otherwise obtained, and heating to 454' C. increased it to about seven times over that otherwise obtained a t 259" C. Electron micrographs of replicas of the reactor surface revealed no phase change or carbon deposition a t grain boundaries that could account for this increase in catalytic activity. The only surface change observed was development uf some pitting, but the increase in area could account for only a small portion of the increase in activity. All data obtained showed first-order over-all kinetics with iespect to H202. and results unaffected by moderate variations in the concentrations of 0 2 , N2, and HzO. Figure 9 shows data a t 259' and 319" C., respectively. In each case the temperature reported is the maximum to which the stainless steel had been subjected. For runs made with temperatures equal to o r greater than the maximum past temperature, rates were reproducible for any temperature. concentration, and flow rate.
61
I
2
4
6
8
20
2 2
2 4
9 F C P ? C C A - TEMPERA-LIRE "I(
.
Figure 1 1 Intrinsic decomposition rate of presence of Nz
H202 vapor
in
Total pressure 1 .O atm. Partial pressure of Hz02 0.01 a h . Sources 0 (8)
v
0 A
(9) (10)
(15) (18,19)
studies, onolyred b y additive resistance method tX Present Present studies on platinum, analyzed by solution to diffusion equation, assuming rodlike flow Present studies on platinum, assuming Hoelscher's solution for parabolic velocity profile
Figure 10 shows a n Arrhenius plot of the over-all first-order rate constants as determined under laminar and turbulent flow conditions ( N R ~ = 750 and N R e = 2500, respectively). At temperatures of 320' C. and below the observed rate is clearly that of the surface decomposition reaction, since the same kinetic constant is obtained under laminar and turbulent flow conditions and the slope is constant and equivalent to a n activation energy of 14.3 kcal. per gram mole. This Arrhenius plot was used in correcting for the effect of slight scattering of temperatures from run to run a t one temperature level. At temperatures of 350' C. and above the rate becomes a t least partly mass transfer-controlled under our flow conditions. If the flow is laminar, the rate becomes essentially mass transfercontrolled a t 350' C. and above, since the slope of the curve becomes almost zero, which is typical of mass-transfer control. Furthermore, the observed decomposition rate a t these temperatures was closely comparable to the mass-transfer rate as calculated by the Graetz equation for laminar flow. In turbulent flow a t 350' C. and above, the rate is a t least partly surface rate-controlled, since the over-all rate constants lie above those for laminar flow. The intrinsic surface rate constant was determined by the procedures described for the studies with platinum. The final set of intrinsic constants are shown on Figure 11 together with the results from the platinum reactor. The rate constant for stainless steel also goes through a maximum with increased temperature, as was observed with platinum. As with platinum, for fixed reactor inlet conditions, a n increase in wall temperature caused a n increase in exit H202 concentration. Figure 11 also shows heterogeneous decomposition rates previously reported for borosilicate glass after treatment with 4N phosphoric acid (78, 79) or with 40% H F (70). For comparative purposes, the homogeneous decomposition rate is also plotted. The relative position of the curves for heterogeneous and homogeneous reaction as shown here applies to a reactor vessel having a volume-surface ratio of 1 cm. T h e plot is for H 2 0 2partial pressure of 0.01 atm. in the presence of nitrogen, but since both homogeneous and heterogeneous reactions are essentially first order, the relative positions of the curves should not be substantially altered over large variations in HZ02 partial pressure. T h e activation energy of 14.3 kcal per gram mole falls within the range of 10 to 15 kcal. per gram moIe reported previously for H202 decomposition on various surfaces. The decomposition rates are about 30-fold less than those reported by Stein (78) for 304 stainless steel surfaces, but his had previously been pickled or electropolished and subsequent experience has shown that surfaces thus treated are substantially more active than a stainless steel surface that has been in contact with H202 vapor without any prior treatment. Wechsler (77) studied simultaneous diffusion and reaction in a porous reactor of 316 stainless steel, which is similar to 304 stainless steel in chemical composition, and which likewise had undergone no prior treatment. His experiments were not designed primarily for obtaining highly accurate data on the intrinsic surface kinetics, but his results obtained a t 100' and 152' C. showed, for H202 vapor in nitrogen, values of the intrinsic rate constant which agree with the present values within a factor of about 2. This is probably about the accuracy with which such data can be calculated from the porous tube studies. The data were also analyzed by Hoelscher's solution to the diffusion equation for the parabolic velocity profile. The resulting values of the intrinsic first-order rate constants (not shown on Figure 11) were about 50% higher than those calculated by the quasistationary state approach a t temperatures of VOL. 2
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NOVEMBER 1 9 6 3
263
400’ C. and above. At 260’ and 320’ C. there is no masstransfer limitation and over-all rate constants have the same value as the intrinsic surface rate constants. However, applying the parabolic velocity treatment to data taken a t these temperatures gave reaction rate constants too high by a factor of about 3. This illustrates the inadequacy of this parabolic velocity profile treatment a t low values of the dimensionless group k’R/D. Acknowledgment
We acknowledge helpful discussions with Benjamin Wood concerning some of the mathematical developments. Nomenclatare
C
D G.,f G,
J, J, k
k’ k, n
~ V .V,,
p ,/IB.M
R I
7
v w
264
= concentration,
gram moles per cc. Unsubscribed means local with respect to both x and r . C, for average (mixed) concentration a t any cross section at distance x from entrance. C, for entering composition (which is uniform with respect to r ) . Cz for local exit concentration, C, for concentration a t wall = molecular diffusivity, sq. cm. per min. = molal mass velocity of stream, gram moles/(min.) (sq. cm.) = Graetz group, w/Dpx = Bessel function of zero order and first kind = Bessel function of first order and first kind = first-order reaction rate constant, gram moles/(sq. cm.) (min.)(atm.). ko for over-all constant = r / p , k, for intrinsic (surface) rate constant, kh for first-order homo eneous reaction rate constant, gram moles/ cc ) min.)(atm.) = first-order surface reaction rate constant, gram moles/ (sq. cm.) (min.) (gram mole/cc.) = mass-transfer coefficient, gram moles/(min.) (sq. cm.) (atm.) = order of surface reaction kinetics, n’ for order ofover-all rate R = ~Reynoldsnumber, = D8p/p = Schmidt number, = p / p D = partial pressure in the gas bulk, atm. = log mean of p B a t surface and in bulk of fluid = inside radius of tubular reactor, cm. = observed (over-all) reaction rate, gram moles/(min.) (sq. cm.); rh for homogeneous reaction rate, gram moles/(min.) (cc.) = radial distance in reactor = linear velocity, cm. per min. 6 for average velocity (volumetric flow rate divided by cross-sectional area of tube) = mass flow rate, grams per min.
(’r
I&EC FUNDAMFNTALS
= distance from inlet in axial direction
x
GREEK
3
qn
= defined by Equation
p
= viscosity
p
= density, grams per cc.
Literature Cited
(1) Baron, T., Manning, W. R., Johnstone, H. F., Chem. Eng. Progr. 48, 125 (1952). (2) Bond, G. C., “Catalysis by Metals,” p. 242, Academic Press, New York, 1962. (3) Damkohler, G., in “Der Chemie-Ingenieur,” A. Euchen and M. Jacob, eds., Band 111, Teil 1, p. 414, Akademische Verlagsgesellschaft, Leipzig, 1937. (4) Damkohler. G.. Z. Electrochem. 42. 846 (1936). (5) Elder, L. LG.,Rideal, E. K., Tran;. Fariday Soc. 23, 545 1927). (6) Fischbeck, K., Z. Elektrochem. 39, 316 (1933); 40, 517 11934). (7) Frank-Kamenetskii, D. A., “Diffusion and Heat Exchange in ‘Chemical Kinetics,” tr. by N. Thon, Princeton University Press, Princeton, N. J., 1955. (8) Frost, W., Can. J . Chem. 36, 1308 (1958). (9) G i g u h , P. A,, Liu, I. D., J.Am. Chem. Soc. 7 7 , 6477 (1955). (10) Hoare, D. E., Protheroe, J. B., Walsh, D. A,, Trans. Faraday SOC.5 5 , 548 (1959). (11) Hoelscher, H. E., Chem. Eng. Progr. Symp. Ser. No. 10, 50, 45 (1954). (12) Honl, H., von TYolff, W.T. E., Z. Physik. Chem. 201, 278 (1952). (13) Johnstone, H. F., Houvouras, E. T., Schowalter, W. R., 2nd. Eng. Chem. 46,702 (1954). (14 Kubaschewski, O., Elbert, H., Z. Elektrochem. 50, 138 (1944). (151 McLane, C. K., J . Chem. Phys. 17, 379 (1949). (16) Reid. R. C.. Sherwood. T. K.. “ProDerties of Gases and Liauids:” McGraw-Hill. New York.‘1958. (17) ‘Satterfield, C. N., Reid, R. C., Wechsler, A. E., A.I.Ch.E. J . 9, 168 (1963). (18) Satterfield, C. N., Stein, T. W.,Ind. Eng. Chem. 49, 1173 A
/, “ C 7 \
( I Y J I ) .
(19) Satterfield, C. N., Stein, T. W., J . Phys. Chem. 61, 537 (1957). (20) Sherwood. T. K.. Pieford. R. L.. “AbsorDtion and Extraction,” 2nd ed:, p. 77,’Mc8raw’-Hill, New York; 1952. (21) Ibid., p. 81. (22) Tu, C. M., Davies, H., Hottel, H. C., Ind. Eng. Chem. 26, 749 (1934). (23) Williams, G. C., Satterfield, C. N., Isbin, H. S., J . A m . Rocket Soc., p. 70 (March-April 1952). \
I
RECEIVED for review December 14, 1962 ACCEPTEDJuly 16, 1963 Kinetics and Catalysis Symposium, Division of Industrial and Engineering Chemistry, ACS, Rice University, Houston, Tex., June 1963. Based on the Sc.D. thesis of R. S. C. Yeung, Department of Chemical Engineering, Massachusetts Institute of Technology. Work financially supported by the Office of Naval Research under Contract Nonr 1841(11).
