(about 15 kcal per mole) is somewhat greater than the activation energy for ethylene and ethane formation (about 11 kcal per mole). If a distribution of site activity on the catalyst surface is assumed, it is possible for the most active sites to become poisoned initially by polymer formation. As the reaction proceeds and the most active sites are covered with polymer, the rate of polymer formation decreases because of a decrease in the number of sites with sufficient activity for polymer formation. A decrease in polymer formation will permit the ethylene previously used to form polymer to be available for ethane formation a t catalyst sites of lower activity. Accordingly, the quantity of ethane in the product stream should increase during this intermediate time period, as indicated in Figure 2. In the third time interval, a t long process times, the hydrogen and acetylene conversion and the ethylene and ethane formation approach a steady state. In this interval, polymer formation has subsided substantially, the poisoning effect approaching a maximum for the particular reaction temperature. Few catalyst sites with sufficient activity for polymer formation remain and thus the reaction of ethylene is biased toward the formation of ethane. Conclusions
The hydrogenation of acetylene in a bubble column slurry reactor is a function of the process variables: reactor temperature, feed ratio of reactant gases, catalyst loading, and reactant gas flow rate. The reaction is strongly dependent upon the length of a reaction run. The formation of ethane and ethylene in this type of reactor is believed to be affected by the formation of polymer of the form n(C2H4)on the Raney nickel catalyst. I t is believed that polymer forms only on the most active sites and a t long process times, when these sites are covered, polymerization is greatly reduced and the reaction is biased toward the
formation of ethane. All previous studies on the hydrogenation of acetylene fail to mention such a catalyst induction period. Acknowledgment
Raney nickel catalyst used in this study was donated by the W. R. Grace Co. Computer time was supplied by the Computer Science Center a t the University of Maryland under NASA Research Grant NSG-398. literature Cited
Bond, G. C., “Catalysis by Metals,” Academic Press, New York, 1962. Calderbank, P., Evans, F., Farley, R., Jepson, G., Poll, A., “Catalysis in Practice,” p. 66, Institute of Chemical Engineers, London, 1963. Dupont, G., Bull. SOC.Chim. Fr. 3; 1030 (1936). Farkas, E., Sc. D. thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1964. Farkas, A., Farkas, L., J . Amer. Chem. SOC.61, 3396 (1939). Kolbel, H., Chem. Eng. Sci. 14, 151 (1961). Kolbel, H., Hammer, H., Meisl, V., 3rd European Symposium on Chemical Reaction Kinetics, p. 115, 1964. Kolbel, H., Maennig, H., 2. Elektrochem. 66, 744 (1962). Mann, R., Safo, S., private communication, November 1968. Mars, P., Gorgels, M., 3rd European Symposium on Chemical Reaction Engineering, p. 55, 1964. Ozawa, Y., Bischoff, K. B., IND. ENG. CHEM.PROCESS DES. DEVELOP 7,67,72 (1968). Schlesinger, M., Crowell, J., Leva, M., Storch, H., Ind. Eng. Chem. 43, 1474 (1951). Sheridan, J., J . Chem. SOC.1944, 373. Slesser, C., Highet, J., Brit. Chem. Eng. 11 (4), 247 (1966).
RECEIVED for review February 12, 1969 ACCEPTED May 15, 1970
Photochemical Decomposition Rates of Potassium Ferrioxalate in Cone-Shaped Reactor
P. R. Harris, M. C. Hawley, and M. H. Chetrick Department of Chemical Engineering, Michigan State University, East Lansing, Mich. 48823
THE
study is based on earlier work (Harris, 1964) which suggested improvements in experimentation and theory for scale-up of photochemical reactions. In the previous research, a cylindrical annulus with a linear source a t the center, aligned with cylinder axis, was used. I t was assumed that all radiation from the source was radial, but actually radiation is skewed from a linear source. Jacob and Dranoff (1966) tried to remedy this problem by putting spaced mica disks around the source. 540
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970
Use of a point source in a spherical geometry eliminated the earlier problem with the linear source, since no line can be skew to a point. Another experimental advantage was the increase of volume and the strong decrease of radiation intensity with an increase of reactor radius. The decomposition of potassium ferrioxalate (Hatchard and Parker, 1956) was the photochemical reaction used. Composition and other quantities were accurately determined for this system. Analysis was based on a continuous
Decomposition rates of the photochemical reaction of 0.006M potassium ferrioxalate in 0.1N sulfuric acid were studied. A tungsten source was employed to emit radiation of sufficient intensity in the 300- to 600-mp wavelength region.
The reaction was
carried out in six cone-shaped reactors (about 20 t o 2600 cc), and batchwise experiments were conducted with the light source located a t the apex. Conversions were approximately 1.5% and the production rate increased by 23.5% from the smallest t o the largest reactor. The concentration dependence of the rate expression was not determined.
A unique feature is the use of a point light source in cone-shaped reactors to determine the reaction rate. This eliminated the problem of skewed light resulting from linear sources. Literature values of quantum efficiencies as a function of wavelength were used to predict results of experiments, and comparison was made for quantum efficiency of one. Use of wavelength dependence gave better predictability.
wavelength distribution, and a reaction rate was determined. Theory
Consider the following photochemical reaction
aA
+ bB + . . . . .
hu +
CC + dD
+ ....
occurring in a homogeneous system. The reactor contents are well mixed so the concentration of species and temperature is uniform throughout. Also, it is assumed that the concentrations of reaction intermediates are very small, the steady-state hypothesis is applied, and the light source gives off monochromatic light of uniform intensity. The polychromatic case will be treated later as an extension. The photochemical reaction rate, R , is related to the magnitude of the intensity, I TI, the absorption coefficient, p , of the reaction medium, and the quantum efficiency, $, according to the equation:
R = F IT14
(1)
Equation 1 does not describe the reaction rate if other photochemical reactions and dark reactions occur a t the same time as the considered reaction. Dark reactions may be accounted for by determining the rate in the dark and subtracting this from the total rate which gives the photochemical reaction rate. For the case of a single photochemical reaction, $I is just a constant, but if other photochemical reactions occur, it would probably be a complex function of reaction species concentration and intensity. Quantities R and P are the average reaction rate in the reactor and the total production rate, respectively, such that:
P=RV
(2)
and
R= ( l / V )
RdV
For the reaction system used in this study, 4 independent of 1 TI. The reactor is considered to be fectly stirred so that the absorption coefficient, p , is stant since it is a function of concentration and intensity varies through the reactor. Therefore, average reaction rate is
( 3) was perconthe the
Figure 1 . Geometry of the cone reactor system with a point source
The reactor geometry used in this investigation is shown in Figure 1. For spherical geometry with light being emitted from a source of radius p o , the relationship for the magnitude of the intensity at a radius, p , in the reactor is 2
I TI
=
I,
=
I,,
PO P
exp
[-P(P
-p0)]
Up to this point the light source has been considered monochromatic. To account for the polychromatic light source case one has to consider the variation of absorption coefficient and quantum efficiency with wavelength. Normally, the absorption coefficient is a decreasing function of wavelength. For many photochemical reactions the quantum efficiency has a maximum value as it varies with wavelength. Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970
541
The quantity a O Ais the monochromatic intensity a t wavelength h such that a,,h d h is the energy emitted per time between h and h + d h , and is defined as: > ap.x
= Np
,A
);(
exp
[-Px(p
-
~ J I
(6)
For polychromatic light the photochemical reaction rate equation a t each wavelength is
Rx
= PA cbx
Np.h
(7)
JA
The maximum production rate is found when
p
-
The total photochemical reaction rate, R , and the average rate, R, are given: and the dimensionless production rate is given by
The wavelength limits h 1 and hl are those for which the reaction rate becomes negligible a t low and high wavelengths: For the geometry of Figure 1, a p , his given by Equation 6 and d V is
d V = p' sin 4' dp d4f de
(10)
with
v = 44 rI(1 - cos 4f)(p3- pi)
(11)
Substituting for V and dV, Equations 8 and 9 reduce to
Experimental
Details of the reactor and experimentation are given by Harris (1967). Figure 2 is a drawing of the reactor, constructed in six different volumes. The sections of the reactors were of acrylic sheets of varying thickness, held together by rods threaded a t both ends and sealed by silicone grease. Larger or smaller reactors of the same shape were made by adding or taking away sections and changing the curved top section. The volume of each reactor was calculated and compared with the volume of
These equations can be put in dimensionless forms in the following way. The maximum reaction rate is found by setting p = po in Equation 12
The two dimensionless reaction rates are then defined as
o.i.2
SCALE - Inches Figure 2 . Scale drawing for a cross section view of reactor
542
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970
water t h a t filled the reactor: 19.35, 48.37, 117.7, 304.8, 894.6, and 2654.1 cc $' in Figure 1 is 15". The stirrer was driven a t moderate speed by an electric mixer (Lightnin' Model F). Qualitative step mixing tests showed that essentially perfect mixing was obtained with respect to macroscopic concentrations and temperature for all reactors. The light source (Model CM8-807 tungsten filament lamp) used in this investigation was manufactured by Chicago Miniature Lamp Works. I t was operated a t a constant power of 0.700 + 0.020 watt a t its nominal voltage of 6 volts. The radius of the source, p o , was 0.76 cm. A special circuit was designed to hold the lamp power constant (Harris, 1967). Relative intensities of the experimental source from 300 to 600 mp are tabulated in Table I. The reactant used was a 0.006M aqueous solution of potassium ferrioxalate, 0.1N in H2S04. I t has been used in the past for actinometric purposes (Baxendale and Bridge, 1955; Hatchard and Parker, 1956, 1959; Lee and Seliger, 1964; and Parker, 1953). Literature values for the monochromatic quantum efficiencies of potassium ferrioxalate in 0.1N H r S 0 4 are listed in Table 11. The absorption coefficients of the reaction medium as measured by a Beckman DK-2A spectrophotometer using cells with 0.1-, 1-. and 10-cm path lengths are given in Table I11 for the wavelength region 300- to 600-mp. Conversions in all runs were less than 1.5%, so that there was no appreciable difference between reactant and product absorption coefficients. The mechanism for the ferrioxalate decomposition is still not well understood, but it is known that the ferric ion is reduced stoichiometrically to ferrous iron according to the reaction: 2[Fe(C2O,)(]'
-
2 Fe ( C 2 0 4 )+ 3[C2O4]'
+ 2C02
This ferrous iron formation was measured by complexing
Table I. Relative Intensities of Experimental light Source Intensity,
Intensity, 12 I
Arbitrary Units
0.000 0.000 0.331 0.991 2.64 3.98 6.67 9.41 12.6 16.6 21..5 27.8 :14 1 41.1 18.5 j5.5 65.8 78.2 92.7 109 128
Wavelength,
u.
A. mg
Arbitrary Units
405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500
140 155 170 194 220 247 277 307 342 379 416 450 481 515 568 619 677 732 789 850
Intensity, Wavelength,
A. mic
505 510 515 ,520 525 530 535
540 545 550 555 560 565 570 575 580 58.5 ,590 595 600
the ferrous iron with 1,lO-phenanthroline and measurli p the amount of colored complex formed in a spectro photometer a t 510 mp. The exact procedure, similar to one given by Hatchard and Parker (1956), is given h> Harris (1967). Known amounts of ferrous iron were used to calibrate the equipment. Experiments were batch. Conversions were so low t ha1 concentration did not change significantly. This alloutti the reaction rate t o be given by the simple formula. R = X ' / A t , where AC is the concentration of ferrous Table II. literature Values for Monochromatic Quantum Efficiencies of Decomposition of Potassium Ferrioxalate in 0.1 N HeSOl
Wavelength, A, m g
Concn, C, Mole/L
254 254 297 313 334 358 36516 365 365/6 392 405 416 436 436 436 468 480 509 546 577'9
0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.005 0.006 0.006 0.006 0.006 0.006 0.005 0.15 0.15 0.15 0.15 0.15 0.15
Table Ill. Absorption Coefficients of 0.006N Potassium Ferrioxalate in 5-mp Intervals from 300 to 600 mal Wavelength,
Absorption Coeff
927 1000 1040 1120 1190 1270 1360 1460 1540 1640 1750
A, m i i
IL, cm
0I
2000 2140 2350 2610 2950 3270 3.540 3770
1.25' 1.2'2 1.24' 1.24' 1.23O 1.25 1- 0.01" 1.21" l.20b 1.26 =k 0.03' 1.13 z t 0.0ld 1.14c 1.12 1- 0.02" l.l1° 1.04" 1.0lb 0.99" 0.94" 0.86" 0.1st 0.013"
Baxendale and Bridge (1955). 'Hatchard and Parker 119561 'Lee and Seliger (1964). dWegner and Adamson 11966).
Arbitrary Units
1880
Quantum Efficiency, e, Moles Formed/ Einstein Absorbed
300 305 310 315 320 325 330 335 340 345 350 360 365 370 375 380 385 390 395 400
1
37.4 36.3 34.0 30.7 27.7 25.7 22.9 20.7 18.9 17.1 15.5 12.2 10.7 9.31 7.97 6.75 5.69 4.73 3.89 3.20
A, m i l
Absorption Coeff P , cm
405 410 415 420 425 430 435 440 445 450 455 46.5 470 47,s 480 485 490 495 500
2.41 2.11 174 1.40 1.12 0.896 0.724 0.541 0.443 0.347 0.263 0.149 0,113 0.08.56 0.0640 0.0477 0.0356 0.0251 0.01997
Wavelength
Wavelength
A,
505 510 515 520 525 5
