3 X X d - k PICE-SURE
I
I
P.
JOHANNIN and B. VODAR
Laboratoire des Hautes Pressions 1, Place A Briand, Bellevue
(S.& 0.))France
Thermal Conductivity of Nitrogen at High Temperatures and Pressures T H E ONLY EXPERIMENTAL data on thermal conductivity of gases compressed to several hundred atmospheres are those of Stoliarov, Ipatiev, and Teodorovitch u p to 500 atm. and 300' C. ( 8 ) , of Lenoir and Comings up to 68' C. and 200 atm. ( 4 , 5 ) ,and of Michels and Botzen up to 2500 atm. and 75' C. (7, 6 ) . The final results of Keyes have not yet been published (3). Stoliarov used the hot-wire method; Michels employed parallel plates with guard ring; Lenoir, Comings, and Keyes the method of coaxial cylinders. I n these methods, the whole high pressure vessel was submitted to the temperature of the experiment; thus, stability and uniformity of the temperature is easily con trolled. T o obtain simultaneously both higher temperature and pressure, an internal heating method has been developed where difficulties arising from limited resistance of steels or other alloys at high temperature are completely removed. The whole measuring apparatus is in a n electric furnace placed inside the pressure vessel which is externally cooled. The furnace is thermally in-
d a t e d from the inside walls of the vessel. With the internal heating method, however, temperature stability and uniformity is more difficult. But in this work, temperatures were kept constant within 0.01' C. at 400' C. and within 0.05' C. a t 700' C. These figures refer to short time constancy-a slow temperature drift is sometimes observed, but this does not interfer seriously with measurements because temperature equilibrium is .reached quickly. The temperature-regulating element is the hot junction of a platinumplatinum-rhodium thermocouple which controls heating of the furnace through a potentiometer, a breaker-type amplifier, magnetic amplifier, and a phase shift device. Uniformity of temperature is difficult to obtain because of the enormous increase of convective heat transport under pressure. At the temperatures and pressures used, amount of heat transported by laminar convective phenomena increases by a factor of about 106 to 106 when going from normal pressure to the highest pressure obtained (1 600 atm.). Temperature uniformity that compared with temperature stability was obtained by using radiation shields, auxiliary heating windings, by filling with solid heat insulating substances most free space in the furnace, and by reducing the gap between the two cylinders of the cell. The coaxial cylinders method was used fm measurements. The method of parallel plates has been eliminated for obvious geometric reasons such as shape and dimensions of the furnace. Also, this method is not indispensable for reducing convective effects to a negligible value, and the cell has a large surface of thermal leakage between the hot plate and the guard ring and plate. Practically, the hot wire method could have been used-geometrically it is
This conductivity cell i s within the internal heating furnace a, auxiliary heating coilsi b, silver centering element;
6,
mobile silver centering
elementi
d , nickel-chromium ribbon that is the main heat-
ing winding; e, crosses indicating location of the thermocouples; f, silica insulator; g, high pressure vessel; h, outer cylinder; k, inner cylinder
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The thermoconductivity cell, partiully disassembled, showing auxiliary heating coils and external thermocouples
INDUSTRIAL A N D ENGINEERING CHEMISTRY
easy to employ in a cylindrical high pressure vessel of moderate inside diameter. It was discarded, however, not because of difficulties concerning the ends, but because it was thought doubtful that a uniform gas layer of known thickness could be obtained thin enough to keep convection within permissible limits. The apparatus used consists of two pure-silver coaxial cylinders. The outside cylinder is 150 mm. long, 20 mm. in external diameter, and 13.5 in internal diameter. Two silver elements center the internal cylinder, which is 88 mm. long by 13.1 mm. in diameter. Thickness of the cylindrical gas layer is cmsequently about 0.2 mm. Platinum-platinum-rhodium thermocouples, four set in the internal and eight in the external cylinder: measure the temperature difference between the cylinders and record the uniformity of temperature along the external one. A
This furnace, containing the thermal conductivity cell and mounted on the high pressure plug, is ready to be installed in the pressure vessel. The plug together with the screw is lifted with an air driven device
.
Therefore, variation of heat conductivity for the compressed gas is obtained, relative to heat conductivity at normal pressure which is known from other measurements (7). In principle, the true value of the conductivity can be obtained directly by making a measurement, not a t atmospheric pressure, but in a good vacuum. But this was abandoned because of the compact setup of the apparatus and the presence of very fine insulating powder which would make a good vacuum difficult to achieve in a reasonable time. An accurate determination of the geometric constant of the apparatus is necessary. Because of the small thickness and the shape of the gas layer, a mechanical determination would not have been sufficiently precise. The method used is based on the similarity between electric fields and temperature fields between two bodies at uniform voltages or temperatures. The cylinders are spaced with the help of very small alumina cylinders and thus are electrically insulated. Measurement of
Alumina conical sleeves supply insulation and these are insulated leads on a high pressure closure (2)
few watts are supplied at the center of the internal cylinder by a heater of platinum wire. The measuring cell composed of the two cylinders is entirely surrounded by a cylindrical electric furnace 320 mm. long and having an internal diameter of 21 mm. A silica cylinder is used as insulation for the furnace winding. The whole assembly of the thermal conductivity cell and the furnace is mounted on a head provided with 12 electrically insulated leads. Such a head is illustrated, with two high intensity leads used for the heating current of the furnace (2). The temperature difference between the two coaxial cylinders lies between 1' and 4' C. Because of the low value of this difference and thinness of the gas layer, the convective heat transport is reduced to a negligible value. This was checked by repeated measurements made with various temperature differences across the gas layer, which gave the same value for heat conductivity. Moreover, the thinness minimizes the radiative heat exchange compared with conductive heat transport. Heat conduction by the stands supporting the measuring cell and by the thermocouple wires, which is assumed to vary only slightly with pressure, and the heat conduction by radiation are compensated for by comparing the results for the same temperature under high pressure and at atmospheric pressure.
Figure 1. Thermal conductivity coefficient of nitrogen as a function of density for different temperatures
A Michels and Botzen a t 75' + Stoliarov, Ipatiev, and Teodorovitch, interpolated for 75' and 125' C.; thermal toef0 Johannin;
C.1
ficient in 1 O - b watt per cenfimeter per density in Amagat units
Table I. Thermal Conductivity of Nitrogen
c.
P
750
1
28.8 33.0 38.0 43.6 49.1 54.6 60.0 65.2 70.2 74.9 79.5
100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
125' C. 31.9 35.5 39.6 44.0 48.6 53.3 57.9 62.5 66.8 71.4 75.7 79.9
2000
c.
36.4 39.2 42.4 46.0 49.5 53.1 56.7 60.4 64.2 67.8 71.4 75.1 78.9
300' C. 42.3 44.6 47.1 49.8 52.6 55.5 58.4 61.5 64.5 67.5 70.5 73.4 76.2 79.0
C. and
the electrical capacity, which is accurate, gave the geometrical constant of the heat conductivity cell, including regions around the ends of the cylinders. This method does not require a guard ring, the main purpose of which is to suppress heat transport in regions where it is difficult to calculate the geometric constant. The apparatus has been operated u p to 700' C. and 1600 atm. This temperature is its approximate limit, but the pressure is far from the pressure limit of the vessel. Until now, measurements have been made only with nitrogen. Results are given for temperatures ranging from lsormal up to 300' C., which are presently the only data completely analyzed (Table I). X is expressed in 10-6 watt, cm.-', ' C.-I, P in international atmospheres, and T in ' C. The values given here are smoothed values. The maximum departure of the experimental from the smoothed values in this range is 0.470. Figure 1 compares data obtained in this work with those of other authors. The agreement with Stoliarov and others is satisfactory, considering the scattering of their data, but the discrepancy with the data of Michels and Botzen is obvious. At the highest pressures, this disagreement amounts to as much as 8%. As mentioned previously, it is believed that convection is not responsible for large errors in this workrepeated measurements with temperature differences varying from 1' to 4' C. furnish extremely consistent results within ag accuracy of a few thousandths. The final precision of these measurements is estimated to equal 1% for temperatures lower than 300' C. Consequently the disagreement with Michels and Botzen seems a serious problem. Direct experimental results u p to 700' C. have not yet been analyzed. These, however, along with the complete work, will be published in French. Literature Cited (1) Botzen, A., Thesis, Amsterdam, Holland. (2) Johannin, P., J. Recherches centre nat. recherche sci. L a b . Bellevue ( P a r i s ) 26.324 (1954). (3) Keyds, -F.'G., 'Trans. A m . Soc. Mech. Engrs. 1895 (1955). (4) Lenoir, J. M., Comings, P. W., Chem. E n e . Proer. 47. 223 (1951). (5) LenQir, J. M.,Jbnk, W. A;, Comings, P. W.. Ibid.. 49. 539-42 11953). ( 6 ) Michels,' A., 'Botzen, A.,' Phys'z'ca 19, 585-98 (1953). (7) Rothman, A. i., Bromley, L. A., IND. ENG. CHEM. 47, 899-906 (1955). (8) Stoliarov, Ipatiev, Teodorovitch, Zhur. F i t . K h i m . U.S.S.R. 24, 167-76 (1950). RECEIVED for review March 29, 1957 ACCEPTED October 11, 1957 Division of Industrial and Engineering Chemistry, High Pressure Symposium, 131st Meeting, ACS, Miami, Fla., April 1957. VOL. 49, NO. 12
DECEMBER 1957
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