Nomenclature
literature Cited
floc-floc attractive force, dynes A, Bingham yield value coefficient, dynes/sq. cm. A, AS = true yield value coefficient, dynes/sq. cm. dF = floc diameter, cm. vol. flocs C F K= floc volume coefficient = -vel. clav in flocs G = shear rate. s e c . 3 K = Einstein coefficient AK = increment in Einstein coefficient due to electroviscous effect R = particle radius, cm. Z - = anionic site on kaolin surface e = dielectric constant of suspension medium 7 = apparent viscosity: dyne sec. 'sq. cm. qg? = apparent viscosity at G = 42 set.-' qB = Bingham viscosity, 7 q 8 a t large G X = specific conductivity of suspension medium, ohms 'cm. p, = viscosity of water. dyne sec./'sq. cm. E = electrokinetic potential, mv. T = shear stress, dynes, sq. cm. T~ = true yield value. T +. T~ as G +. 0 pp = floc volume concentration oFO= minimum floc volume concentration exhibiting finite yield value Q~ = kaolin volume concentration
(1) Georgia Kaolin Co., Elizabeth, N. J., Bull. TSBH-10 (1956). (2) Kuhn, it'., Kuhn, H., Helo. Chim. Acta 28, 97 (1945). (3) Michaels, A. S., Ind. En,c. Chem. 50, 951 (1958). (4) Michaels, A. S.. Bolger, J. C., IND.ENG.CHEM.FUNDAMENTALS 1, 24 (1962). (5) Ibid., p. 153. (6) Michaels, A . S., Tausch, F.. Ind. Enp. Chem. 52, 857 (1960). (7) Overbeek, J. Th. G., Bungenberg de Jong. H. G., in H. R . Kruyt, "Colloid Science, Vol. 11," p. 219, Elsevier, Amsterdam, 1949. (8) Schofield; R. K.. Samson, H. R.; Discussions Faraday Soc. 18, 135 (1954). (9) Strect, N.. .lustraizan J . Chem. 9, 467 (1956). (10) Street. X . , Buchanan. A. S..Ibid.. p. 450. (11) Thiessen. P. A , , 2'.Eit-ktrochm 48, 675 (1942). (12) Van Olphrn, H.. Discussions Faradq Soc. 11, 82 (1951). (13) Van Olphen. H., Proc. Fourth Natl. Conf. Clays and Clay Minerals. Tat]. Res. Council Publ. 456, 204-24 (1956). (14) Van Olphen H.; PYOC. T r a z ~ .Chim. Pays Bas 69, 1308 (1950). (15) Van \Vazer. ,J.> Besmertuk, J.: J . Phqs. Colioid Chfm. 54, 8 9 (1950), (16) Vyrwey. E. J. \V., Overbeek, J . Th. G . , "Theory of the Stability of Lyophobic Colloids." Elsevier, Amsterdam. 1948. (17) Von Smoluchowski, M., Kolioid-Z. 18, 194 (1916). RECEIVED for review November 19. 1962 ACCEPTED August 27. 1963 Division of Colloid and Surfacr Chemistry, 142nd Meeting, XCS, Atlantic City, N. J.. September 1962.
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RATE OF ISOMERIZATION OF CYCLOPROPANE IN A FLOW REACTOR B.
R . D A V I S A N D D . S. SCOTT
Drpartment of Chemical Enginpering. CTniversit~of British Columbia, Vancouaer. B C , Canada
Experimental studies planned to investigate combined diffusional and chemical effects in porous solids or packed beds might be simplified b y the use of a simple-order homogeneous gas phase reaction. The isomerization of cyclopropane to propylene appears to satisfy these requirements potentially, and to retain the simplicity of a binary system. However, the reaction behavior at fast reaction rates must be known if the reaciion i s to be used in a diffusion-controlled experiment. In the present work, the existing kinetic data for this isomerization, obtained in batch reactors at temperatures from 4 6 0 " to 550" C., were extended to 620" C. b y use of flow reactors constructed of borosilicate glass. The extent of secondary decomposition of propylene at these temperatures was investigated, as well as the effect of large surface-volume ratios. Kinetic behavior was measured at all conversion levels b y both integral and differential methods. At constant pressure, and temperatures to 620" C., this isomerization behaves as an ideal homogeneous first-order reaction in contact with borosilicate glass equipment.
HE mechanism of isomerization of cyclopropane has been 'carefully investigated by a number of \vorkers ( 7 : 3. 5-7) and found to be a homogeneous first-order gas phase reaction when carried out in borosilicate glass apparatus. Below 1atm. total pressure a dependence of the first-order rate constant on the pressure exists. Studies of the probable mechanism. both experimental and theoretical in nature. have indicated (after some controversy) that this isomerization is a molecular rearrangement dependent on a hydrogen shift in the cyclopropane molecule. and that the observed rate is not due to any extent to free radical processes. In many laboratory studies of catalyst or reactor behavior. particularly those in \yhich a diffusional step is significant, it is convenient to use a simple-order reaction of known behavior. For example. diffusional processes in the pore channels of a
20
I&EC FUNDAMENTALS
catalytic solid could be easily studied as a single phenomenon by using an ideal homogeneous reaction. Further. an isomerization reaction retains the simplicity of a binary system. HoLvever. the experimental study of diffusion-limited reactions requires relativelj- fast rates of chemical change. The majority of the kinetic studies of cyclopropane isomerization already mentioned have been done in static systems a t temperatures from 460' 10 550' C. Such batch techniques are usually not useful for the measurement of the rates of rapid reactions, and: therefore. results obtained at the higher temperatures by this method have been obtained at subatmospheric preszures to reduce reaction rates to a manageable level. In general. the entire range of conversion levels at different temperatures has not been fully investigated. Fast reaction rates can best be studied in a flow reactor.
I n rhe present work, three aspects of the cyclopropane isomerization reaction were investigated in this way. Rates of reaction at short residence timev-that is: a t high temperatures-over wide conversion ranges. and in reactors having a great variation in surface-to-volume ratio \yere measured to determine if any changes in kinetic behavior occurred compared to that observed a t lower temperatures and lo\ver conversions. Apparatus
A sketch of the apparatus is sho1.r.n in Figure 1. Either cyclopropane or propylene (both c. P . grades supplied by Matheson, Ltd.). or mixtures of the two. could be fed to the preheater and reactor coils. T h e flow rates of both gases were checked by a soap bubble flowmeter before and after reaction runs, and a small correction \vas made for the humidification occurring in the meter. Reactor size as well as reactant flow rate was varied in order to obtain desired residence times or conversion levels. The three reactors used were made of borosilicate glass tubing. and their principal characteristics are given in Table I . T h e reactor was contained in a n oven with forced air circulation, having a separate electrically powered air heating section. Thermocouple traverses within the oven showed variations of less than * l o C. with position, and of about 1 1 ' C. a t a given location over many control cycles. T h e outside walls of the flo\v reactors were heavily blackened before runs were made, to ensure that this wall temperature coincided with that read by thermocouples fastened to the outer reactor surface. At this temperature level (540' to 620' C.), the great majority of the heat transferred to the reactor was by radiation from the oven Lvalls. T h e reactor itself was designed on the basis of laminar plug flow to give a total radial temperature difference across the tube wall and the flowing gas stream of no more than 0.5' C. a t the highest reaction rate. C n d e r these conditions, and for the flo\v rates and reactor dimensions used in this work. Cleland and Lt'ilhelm (2) have shown that the effect on the conversion of a parabolic radial velocity gradient in the flobving gas is negligible. All reactors consisted of two sections in series, the first used as a reactant preheater, and the second the reaction volume itself. T h e outlet lines from the preheater and reactor Fections were made in a n identical fashion, so that the effect of the. variable reaction rate occurring in the outlet lines leaving the reactor \vas eliminated. Reactor and preheater volumes were determined by liquid filling and weighing. During a run, the multiple-port slide valve was set so that flow was through the preheater section only, and samples of the outlet gas stream were taken. T h e valve was then switched so that flow \vas through both the preheater and reactor sections, and the product was .again sampled. T h e concentrations of both cyclopropane and propylene were determined by gas chromatography. Pressure drop through reactors 1 and 2 was negligible, and in reactor 3 it amounted to about 0.05 a t m . Results
Reaction Order. Conversions were measured in an integral fashion in reactor 1 a t 570 C. by using a pure cyclopropane feed and allo\ving outlet concentrations of cyclopropane to vary from 86 to 377,. T h e first-order dependence plotted as the logarithm of the raKi0 of mole fractions against residence time is shown in Figure 2. T h e total pressure in these runs was essentially constant a t 1 atm. In addition, the reactor was operated differentially at cyclopropane levels in the feed varying from 1 to 95% a t two temperatures, 568 and 598.5' C. Again the resulting plots, shown in Figure 3, indicate an unmistakable first-order rate dependence-that is, the rate varies linearly \vith the average concentration. I n none of these tests was any significant amount of reaction product found other than propylene. However. the possibility of forming reaction products other than propylene was also checked by carrying out tests a t 565' C. using a reactor feed of pure propylene, the maximum reaction time
FLOW
Figure 1.
METER
Sketch of apparatus
T I M E , SEC.
Figure 2. behavior
Integral reactor data showing first-order
Table I .
Inside Diameter,
Characteristics of Flow Reactors Approximate Length,
Reaction Volume:
21 . 8
Reactor 1
Cm.
Cm .
0.325
240
2
0 168
150
3
2.20
9
cc .
3.45 23 2
Surface Volume Ratio.
Cm.-'
.Mater io1
12 . 3 Borosilicate glass tubing 29 Borosilicate glass tubing 1090 Borosilicateglass tubing pacAed with 42micron borosilicate glass beads
feasible Lvith the present apparatus, and reactor 3 \
