606
INDUSTRIAL AND ENGINEERING CHEMISTRY
tion factors described by Livingston (Q)in his studies of octane number. The factors he used-for calculating octane numbers would seem to also apply to low-pressure open flames of the type studied here. He devised a series of rules to calculate the effects of various structures on the oxidation rates of hydrocarbons according to the location of the group in the molecule; methyl, tert-alkyl, vinyl, cyclic methylene, and phenyl radicals are oxidation-retarding groups, and of these the phenyl group has the strongest influence. Certain parallels and extensions of Livingston’s work can be drawn from the present study. Particularly noticeable is the change in smoke point noted on the addition of a methyl branch. On the basis that an oxidation-retarding group lowers the smoke point, sec-alkyl and isoalkyl groups should be added to Livingston’s list. The very low smoke points of the aromatic hydrocarbons would be explained by the strong retarding influence of the phenyl radical. According to the theory of oxidation-retardation and as demonstrated in the present work, the n-alkyl structure is the easiest to oxidize, and any substitution on the molecule causes i t to resist oxidation in accordance with the position and type of substitution.
Vol. 45, No. 3
ACKNOWLEDGMENT
The author wishes to acknowledge the valuable assistance of George Hajduk in obtaining the data reported in this study. LITERATURE CITED (1) Clark, A. E., Hunter, T. G., and Garner, P. H., J . Inst. Petroleum, 32, 627 (1946). ( 2 ) Institute o f Petroleum, London, “Standard Methods for Testing Petroleum and Its Products,” p. 456, 1951. (3) Kewley, J., and Jackson, J. S., J . Znst. Petroleum Technol., 13, 364 (1927). (4) Livingston, H. K., IND. ENQ.CHEM.,4 3 , 2 8 3 4 (1951). ( 5 ) Minohen, S. T., J . Znst. Petroleum Technol., 17, 102 (1931). ( G ) Terry, J. B., and Field, E., IND. Esr,. CHEM..Ax.4~.Eo., 8 , 293 (1936). (7) Woodrow, W. A., Secorid World Petroleum Congr., London 1@SS, Proc., 2 , 7 3 2 . RECEIVED for review July 21, 1952. ACCEPTEDOctober 10, 1952. Presented before the Division of Petroleum Chemistry a t the 122nd Meeting of the + x E R I C A N C H E M I C A L S o C I s r Y , .&tlantic City, N. J.
PVT Relations of Nitrogen and ixtures at High Pressure WILLIAM P. HAGENBACH’ AND EDWARD W. COMINGS2 University of Illinois, Urbunu, I l l .
A
LARGE amount of compressibility data covering a significant range of temperatures and pressures is available for pure gases. The amount of data on mixtures of gases is rather meager but has increased considerably in recent years. A knowledge of the compressibilities of mixtures is important in the design of high pressure equipment. Accurate compressibility measurements also provide a basis for calculating the thermodynamic properties. I n the absence o’f PVT data for gas mixtures, their compressibility factors must be estimated from the factors for the component gases. The methods of Kay ( 7 ) and Gilliland ( 5 ) are useful in this respect. The apparatus and procedure used in this investigation were similar to those employed by Michels ( 1 1 ) who obtained very high precision in his measurements. DESCRIPTION OF APPARATUS
The apparatus consists of four main parts: a dead-weight gage, a glass piezometer, a steel pressure bomb, and a constant temperature bath. Auxiliary apparatus includes oil injectors, Bourdon pressure gages, mercury manometers, steel sample bombs, and high pressure valves and fitting. The dead-weight gage is similar to that described by Keyes (8) and is fitted with five different piston and cylinder combinations to cover a pressure range up to 50,000 pounds per square inch. The piston diameters were measured accurately a t 20” C. by comparing them with standard Johansson blocks in a Pratt and Whitney Electrolimit gage. The gage constants for the various pistons were calculated by using the empirical formula developed by Beattie and Bridgeman ( 3 ) which indicates that the effectivediameter of the piston is equal t o the actual diameter plus 0.00025 cm. This relation gives gage constants accurate within 0.04%. 1 Present address, Yerkes Research Laboratory, E. I. du Pont de Nemours & Co., Ino., Buffalo, N. Y. 2 Present address, Purdue University, Lafayette, Ind.
A glass piezometer similar to those employed by Michels (10) was used to measure the gas volumes. It was made from soft glass and consists ot a series of glass bulbs of ---O 5 MM. v a r y i n g size sepaC A P ILLAR rated by l-mm. capilRESISTANCE METER lary tubing. A 3.8CC. 10-mil platinum wire was fused into each piece of c a p i l l a r y tubing. The total 0.5 C.C. volume of the pir1.1 cc. zometer is a b o u t 68 cc., and the smallest volume measured is about 4 cc. Each successive platinum contact was joined by a small coil of No. 30 Chrome14 wire having a resistance / \\ of a p p r o x i m a t el y 5 ohms. The piezometer is illustrated in Figure 1. The 52.6 CC v o l u m e from each contact to the top of the piezometer was found by weighing the mercury required t o occupy this volume a t constant t e m p e r a t u r e . The calibration was Figure 1. Glass Piezometer and carried out a t 50°, Platinum Contact Circuit
11
March 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
PIEZOMETER STEEL HOOD
GAS I N L E T
Figure 2.
Lower Section of High Pressure Bomb
loo", and 150' C. in order to determine the change of bulb volumes with temp e r a t u r e . During operation, t h e p i e zometer circuit was connected as shown in Figure 1 using a resistance meter having a sensitivity of 20,000 ohms per volt. Contact of the rising mercury with any one of the platinum wires was indicated by a 5ohm change in the resistance of the circuit. Thepressurebomb
was machined from a chrome-van a d i u m , SAE 6150, steel forging and then oil quenched a t 1550' F. and tempered a t 1000' F. It was designed to withstand a pressure of 1000 atmospheres a t 900' F. according to the maximum principal stress formula. The main section of the bomb is 24 inches long and has a diameter of 5 inches, A 16/s-inch hole was drilled in the center to a depth of 21 inches from one end. The closure a t the top is made by a cap which fits over the head and engages threads around the outside of the bomb. The final pressure seal was effected by tightening eight 3/d-inch cap screws which seat an annealed copper gasket between the head and main body of the bomb. It was necessary to bring an insulated elec-
Figure 3. High Pressure Bomb and Glass Piezometer Which Fits inside Bomb
601
trical lead out through the head of the bomb in order to determine the level of the mercury inside the piezometer. The sample gas was admitted through a special inlet tube a t the bottom of the bomb. A view of the lower section of the bomb is given in Figure 2. The steel hood prevented mercury from entering the inlet tube. A photograph of the bomb and piezometer is shown in Figure 3. TO ATMOSPHERE
TO VACUUM PUMP
SAMPLE CYLINDER
Figure 4.
Apparatus for Filling Piezometer at Low Pressure
The constant temperature bath is a modification of a design described by Beattie (8). The bath temperature was controlled by a mercury-in-glass thermoregulator within ~t0.03"C. The temperatures were measured by mercury thermometers calibrated by the National Bureau of Standards. EXPERlMEh'TAL PROCEDURE
Approximately 120 cc. of mercury was placed in the bomb, and the piezometer was installed in its support. No oil was added to the bomb a t this time. The bomb was sealed and connected t o the low pressure filling system shown in Figure 4. The space inside and outside of the piezometer was evacuated, and sample gas was slowly bled into the piezometer a t B. Simultaneously, air was bled into the annular space a t A to maintain equal pressure on both sides of the glass piezometer. After several purginga, the piezometer was filled with sample gas to approximately atmospheric pressure. The head of the bomb was removed and the annular space above the mercury was filled with oil. The bomb was resealed, placed in the temperature bath, and connected to the measuring apparatus shown in Figure 5. Since the first pressure reading was only slightly above 1 atmosphere, it could not be taken with the dead-weight gage. Instead, the mercury manometer a t D was used with its left side open to the atmosphere through valve 4. Temperature equilibrium was established, and the mercury level inside the piezometer was brought just below the lowest contact by forcing oil into the system from one of the oil injectors. Oil was then slowly forced into the system until the resistance meter indicated that the mercury was just touching the contact. The manometer, the barometer, and the bath temperature were read. The manometer was then isolated from the system by closing valve 3, and more oil was injected into the system until the mercury filled the lowest bulb in the piezometer and rested just below the next contact. Approximately 1 hour was allowed for the heat of compression to be dissipated and for temperature equilibrium to be re-established. The dead-weight gage was connected t o the system through valve 7 after its pan had been loaded to approximately balance the pressure indicated by the Bourdon gage. Then the weights were adjusted so that the mercury level rested just below the contact. Additional weights were then added in 1-gram increments until the resistance meter showed a deflection. The load on the dead-weight gage pan, the tem-
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
608
Vol. 45, No. 3
measured were the pressure, volume, and temperature of an unknown mass of gas. Because the mass of gas varied with each filling, it was necessary to reduce the PV products calculated from the measurements on each filling t o a comnioii basis. The PTT product for each experimental point was calculated, and the values for each of the first three fillings were fitted t o three separate equations of the form
il 1
V P R E S S U R E GLASS MANOMETER
4%-
Figure 5.
@2,000 Lb. GAUGE
111
USAMPLE
CYLINDER
Apparatus for Filling Piezometer at High Pressure
perature of the bath, and the barometer ieadingwerelecorded. The readings for the upper contacts were taken in a similar manner. I n order to cover the complete pressure range, it was necessary to fill the piezometer a t successively higher pressures. This was accomplished by bringing the mercury below the level of the steel hood and adding additional gas from the sample cylinder. Four fillings were necessary. All measurements were made a t 50.07' C. Corrections were made for the differences in the meicury levels inside the bomb and the oil levels between the bomb and the dead-weight gage. The gases used were nitrogen and four nitrogen-ethylene mixtures of 19.8, 40.1, 59.7, and 79.6 mole nitrogen. They were made up approximately to the desired composition and analyzed in a Fischer gas analyzer by absorbing the ethylene in fuming sulfuric acid. The precision of analysis was better than 1 part in 200. Figure 6 shows the control panel and the temperature bath. The nitrogen and ethylene wele claimed by the suppliers to have a purity of 99.99 and 99.96yc, respectively. No attempt was made to purify these gases further, Pressure readings were taken successively a t each contact as the mercury rose in the piezometer until the top contact was reached. The pressure was then lowered and check readings were taken a t three or more contacts on the way down. These check readings agreed to better than 1 part in 2000 in most cases and depended on the sensitivity of the platinum contacts. The contacts decreased in sensitivity during the investigation because of the formation of a black nonconducting film on the platinum. It was necessary to dismantle the equipment several times in order to clean the contacts.
by the method of averages ( I d ) . The first pressure of the fourth filling was then chosen as a normal pressure, P,v. S e x t the volumes corresponding to P N for each of the first three fillings were determined using Equation 1. This volume was measured directly for the fourth filling, and was designated as the normal PV V'V volume, V N ,for each filling. The values -and -~~ P.yV'y v were calculated for each experimental point and fitted to the equation
The data were now reduced to a common basis, and C was calculated as follows:
that the perfect gas law is exact at this limit. PV
PnRT
Then
P r-
(3:
where a is the constant term in Equation 2 . The evperimental data were well represented by Equation 2 up to 100 atmospherea. and this equation was used to obtain smoothed values of C within this range. Beyond 100 atmospheres no attempt J Y a j made to smooth the data.
RESULTS
The data were expressed in terms of the compressibility factor, C = P V / nRT by the following method. Since the moles of gas confined in the piezometer were not measured, it was not possible to calculate C directly from this relation. The only variables
Figure 6.
Control Panel and Thermostatic Bath for Piezometer
March 1953 TABLEI. Pressure, Atm. 11.898 12.633 13.718 19.923 22.408 23.085 24.425 25.284 26.104 45.543 49.910 52.560 56.154 57.617 61.728 67.698 76.693
INDUSTRIAL AND ENGINEERING CHEMISTRY COMPRESSIBILITY FACTORS FOR 100% NITROGEN PV PV c = a c =_.
nRT Miohels, 50° 50.07' C. C. (18.13) 1.0001 1,0001 1.0001 1,0001 1.0001 1.0002 1.0003 1.0005 1.0005 1.0006 1.0005 1.0007 1.0006 1.0008 1.0006 1,0009 1.0007 1,0009 1.0024 1.0032 1.0030 1.0039 1.0034 1.0044 1.0040 1.0051 1.0042 1.0056 1.0050 1.0063 1.0062 1.0078 1.0083 1.0101
TABLE11. COMPRESSIBILITY FACTORS FOR N I T R O G E N - E T ~ Y L E N ~ MIXTURESAT 50.07' C.
nRT
Pressure, Atm. 84.191 86.483 94.502 95.0110 103.893 112.459 118.376 130.696 155.173 197.07 226.04 250.89 253.16 303.49 378.42 531.12 659.39
50.07' C 1.0104 1.0111 1.0137 1.0138 1.0171 1.0210 1.0247 1,0291 1.0419 1.0685 1.0897 1.1097 1.1129 1.1571 1.2303 1.3843 1.5391
Pressure Atm:
Miohels 50° C. (f!2.'18) 1.0117 1.0130 1.0157 1.0159 1.0191 1.0225 1.0251 1.0307 1.0436 1.0703 1,0911 1.1110 1.1135 1.1574 1.2304 1.3939 1.5376
Pressure, Atm.
C 19.8%
Nz
C 40.i%
Ns
1.50
1.30
.....
:/F
,
...
. .. ..
....
Pressure, Atm. 1,213 3.990 5.346 9.736 10.463 12.041 14.086 17.379 17.389 19.498 21,202 22.408 33,626 38.568 41.600 44.936 55.115 61.631 66.885 79.312 90.811 93.294 105.77 130.19 146.44 160.11 184.16 217.13 267.10 374.15 470.70 572.64
C. 59 7% Na 0.9985 0.9951 0.9s34 0.9882 0.9873 0.9854 0.9830 0.9792 0,9792 0.9768 0.9749 0.9736 0.9615 0.9564 0.9534 0.9502 0.9410 0.9356 0.9315 0.9230 0.9165 0.9153 0.9103 0.9047 0.9060 0.9075 0.9174 0.9381 0.9840 1.1130 1.2449 1.3894
Pressuxe,
4%.
e ET;
79.6%
1 245
3 10 10 12 14 17 18 20 22 23 33 39 44 45 56 63 69 87 140 103
948 249 799 441 575 365 022 249 053 725 962 089 749 744 494 456 106 537 97 61 118 63' 148 12 167 87 184 64 213 62 254 20 814 48 439 40 546 96 655 74
.....
....
1.10
TABLE111. COMPARISON OF COMPRESSIBILITY FACTORS FOR
II
NITROGEN AT 50" C.
V
PV
c - -nRT 1.70
1.50
0
I
1
100
200
I 300
I
I
I
I
400
500
600
7CQ
I
PRESSURE-ATMOSPHERES
Figure 7.
Pressure, Atm. 50 100 150 200 300 400 600
Bartiett (1)
1.0044 1.0178
....
1.0766 1.1584 1,2564 1.4763
Holborn and Otto (6) 1.0042 1.0176 1.0402 1.0722
Michels (1% 18) 1.0041 1.0177 1.0405 1.0723 1.1545 1.2526 1.4708
... ... ... ...
Smith and Taylqr (16) 1,0018 1.0127 1.0263 1.0630
.... .... ....
This Work 1.003Q 1.015f3 1.0388, I . 0705 1.1539 1.2522 1.472
Compressibility Factors for Nitrogen-Ethylene System
T The resulting compressibility factors for nitrogen are recorded in Table I and compared with those of Michels et al. ( l a , I S ) . The maximum deviation is 0.2%. The compressibility factors €or the mixtures are given in Table 11. Table I11 is a summary of the work of the various investigators who have measured the compressibilities of nitrogen a t 50' C. Figure 7 presents in graphical form the values of C as a function of pressure for the five gases. Michels' data (9) for ethylene are included to complete the nitrogen-ethylene system. The comparison of these measurements with the values predicted by several rules for mixtures and the fugacity calculated from the measured values is contained in a paper by Bennett ( 4 ) . 4
ACKNOWLEDGMENT
The Engineering Experiment Station, University of Illinois, furnished a research assistantship for 2 years and the Graduate College a university fellowship for one semester. This assistance is gratefully acknowledged. NOMENCLATURE
a, ai, b, bl, c, cl, and d = constants
PV C = compressibility factor, nRT
= number of moles P = pressure, international atm. PN = normal Dressure, international atm. (dc.) (atm.) R = gas constant, (mole) ("K.)
n
609
= absolute temperature, = volume, cc. V N = normal volume, cc.
V
O
K.
LITERATURE CITED (1) Bartlett, E. P., et al., J . Am. Chem. Soc., 49, 687, 1955 (1927)i
50,1275 (1928); 52,1363 (1930). (2) Beattie, J. A., Rev. Sci. Instr., 2, 458 (1931). (3) Beattie, J. A., and Bridgeman, 0. C., Ann. Physik, 12, 82iC (1932). (4)Bennett, C. O., Chem. Eng. Progr., in press. (5) Gilliland, E. R., IND.ENQ.CHEM., 28,219 (1936). (6) Holborn, L., and Otto, J., 2.Physik, 33,l (1925). (7) Kay, W. B., IND. ENQ.CHEM.,28,1014 (1936). (8) Keyes, F. G., Ibid.,23,1375 (1931). (9) Michels, A., and Geldermana, M., Phygica, 9, 967 (1942). (10) Michels, A., and Gibson, R. O., Ann. Physik, 87, 850 (1928). (11) Miohels, A., Michels, C., and Wouters, H., Proc. Roy. Soc. (A),. 153,214 (1935). (12) Michels, A., Wouters, H., and de Boer, J., Phusica, 1, 687(1934); 3,585 (1936). (13) Otto, J., Miohels, A., and Wquters, H., Physik. Z., 35, 97(1934). (14) Scarborough, J. B., "Numerical Mathematical Analysis," p. 7, Baltimore, Md., The Johns Hopkins Press, 1930. (15) Smith, L. S., and Taylor, J. Am. Chpp SOC., 45, 2113 (1923); 48,3122 (1926). RECEIVEDfor review August 23, 1852. ACCEPTEDNovember 12, 1952,Based on a Ph.D. Thesis in Chemical Engineering by ai. P. Hagenbaoh,. University of Illinois, 1951.
