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
NO. 2
M A Y 1968
197
temperature cracking of hydrocarbons or by high-temperature arc processing of hydrocarbons. I n these processes, acetylene is a significant fraction of the hydrocarbon product a t room temperature even though it is thermodynamically unstable. Thus acetylene can be stabilized by rapid cooling to a nonequilibrium composition. The authors have used resistively heated graphite filaments to determine the sublimation temperature of graphite as a function of the carbon-to-hydrogen ratio and the rate of reaction of graphite and hydrogen. A similar apparatus has been used in this work, but here the object has been t o determine the energy requirements for the production of acetylene as a function of pressure a t temperatures where the sublimation of graphite is a controlling factor. I n carrying out this work, two different methods were used. I n the first, short-but timed-high power energy bursts were used t o heat the filament. T h e temperature had t o be calculated from the rate of graphite sublimation. The energy required for the formation of acetylene was obtained by subtracting the amount needed for radiation, thermal conduction, and H ? dissociation from the total value. I n the second approach, the energy lost by radiation, thermal conduction, and surface reaction (including H ? dissociation) was minimized by using short reaction times ( = 1 msecond) obtained by discharging a condenser through the filament. Apparatus and Procedure
A schematic drawing of the filament reaction cell is shown in Figure 1. T h e graphite filament was mounted between two rhenium-lined stainless steel clamps attached to the electrodes and connected to the power supply. The reactor vessel was attached to the vacuum and gas handling systems. The product gas was mixed by operating the thermal siphon and drawing it into the sampling tubes; it was analyzed by a n Aerograph Model 6OOB vapor phase chromatograph having a hydrogen flame ionization detector. The graphite filaments were obtained from the Planchon Co.: Paris. I n carrying out the timed runs, the filaments were evacuated a t 2000’ K. for 15 minutes and then weighed. After remounting, the filaments were again heated to 2000’ K. and evacuated before adding a measured pressure of H?. I n carrying out a run, the filament was heated a t constant voltage for a predetermined time. The siphon heater was turned on and after 20 minutes of mixing, a gas sample was taken for analysis. The product gas was then pumped out of the cell and the run repeated a t an increased reaction time; in each experiment, three heating periods were used. I n the first, the
UUL Figure 1. Schematic of filament reaction cell 198
l&EC FUNDAMENTALS
filament was heated for a time sufficient to bring it to constant temperature. The second and third heating periods were of sufficient lengths to provide, respectively, 30 and 60 joules in excess of that required t o bring the filament to reaction temperature. The filament was taken out of the apparatus, reweighed, and the three gas samples were analyzed. T h e same reactor was used in the flash heating runs, but in this case the power was supplied by discharging a condenser across the filament. The condenser voltage was adjusted in the first flash to bring the filament to a temperature of = 3300’ K. This product was analyzed and after evacuating and filling with fresh H?, the condenser voltage was increased t o give a n additional quantity of heat. This additional heat had to be carefully controlled, for too much would burn out the filament or cause arcing. Experimental Results
Timed Runs. The timed runs reported herein were similar to the a.c. runs summarized by Clarke and Fox in their paper on the reaction rate of graphite and Hz, except that the present runs were carried out a t much higher power input and temperature. Under these conditions, the filament would have burned out in less than a second, so an electronic timer was used to turn the filament on and off. The temperature could not be measured with a n optical pyrometer, so it was calculated from the rate of vaporization of graphite. T h e rate of vaporization of graphite was determined experimentally from the filament weight loss and the run time and extrapolated to higher temperatures. The rate of vaporization of graphite as a function of temperature has been redetermined in the past year by using larger graphite filaments and a photoelectric pyrometer; the calculated temperatures are based on values given by Clarke and Fox (1967). The rate of vaporization of graphite depends t o some extent on the pressure of gas surrounding it as well as the temperature a t which it is vaporized. At high temperature where the carbon pressure is high, the rate of vaporization is much less dependent on the pressure of the surrounding gas. Above 3400’ K., the rate of vaporization is independent of H?pressure in the pressure range 76 t o 380 mm. The calculated temperatures are estimated to be correct to within 50’ to 100’ K. T h e results of the timed runs are summarized in Table I. The heating time is the total time a t reaction temperature. The product gas was analyzed for each heating period and the total micromoles of carbon as hydrocarbon formed is reported. The percentages of the carbon as CH,, CzH?, and C3Hs were reported. Later experiments show that these are the principal products, but in these analyses, the slight amount of CzH4 and CzHC formed are included in the C3Ha fraction. T h e last two columns of Table I are derived from an analysis of the power distribution and are discussed later. The power supplied t o the filament was determined by measuring the current and voltage on meters. Recent work using a n oscilloscope t o record the voltage, current, and a photoelectric pyrometer to measure the temperature shows that a t the power levels used, the 0.5-mm. filaments would rapidly approach a constant temperature and cool a t 4 X lo4’ C. per second a t 3500’ K. T h e temperature decreases slightly as the filament evaporates, since the resistance increases, but this amounts t o
