VOLUMETRIC BEHAVIOR OF METHANE R . H. OLDS, H. H. REAMER, B. H. SAGE, AND W. N. LACEY California Institute of Technology, Pasadena, Calif.
The volumetric behavior of methane was investigated at pressures up to 10,000 pounds per square inch in the temperature interval between 100' and 460' F. The results of the experimental work are presented in tabular form, and are compared with values obtained in earlier investigations. ~
HE volumetric behavior of methane was investigated in some detail by Kvalnes and Gaddy (2) a t pressures up to 15,000 pounds per square inch 'between -13" and 392" F. Somewhat earlier Keyes and Burks (1) studied the volumetric behavior of this gas with some accuracy. The measurements of Michels and Nederbragt (3) represent one of the most recent and accurate studies of the behavior of methane. Owing to the importance of this substance in natural hydrocarbon gases and to its frequent use as a component of binary and ternary hydrocarbon systems studied in the laboratory, it appeared desirable to compare measurements obtained with apparatus a t the authors' laboratory with those obtained by other investigators. For this reason the volumetric behavior of methane was determined a t pressures from above atmospheric to 10,000 pounds per square inch at seven temperatures from 100' to 460' F. The equipment and methods have already been described (4), and no particular modifications were necessary. The equipment for the establishment of the primary variables (weight, temperature, and pressure) was calibrated before the study by comparison with accurate secondary standards. These comparisons permitted corrections to be made for the deviation of the platinum resistance thermometer from the thermodynamic scale of temperature. The volume of the working chamber was large enough so that adsorption did not play a significant part in the uncertainty of measurement. The gas from a field in the San Joaquin Valley, Calif., was used as the source of methane. This gas consists essentially of methane with water vapor and a small amount of carbon dioxide. The gas as received a t the laboratory was passed over granular calcium chloride, sodium hydroxide, activated charcoal, magnesium perchlorate, an ascarite at pressures in excess of 1000 pounds per square inch before introduction into the apparatus, Gas, purified as described above, was subjected to a partial condensation analysis carried out under such conditions that the hydrocarbons heavier than methane were separated quantitatively. The results of these measurements showed that the quantity of ethane and heavier hydrocarbons was less than 0.0002 mole fraction. The specific weight of the purified gas, as determined gravimetrically a t atmospheric pressure, agreed with that for pure methane, 922
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INDUSTRIAL AND ENGINEERING CHEMISTRY
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after correction for the deviation from the perfect gas laws, within 0.1 per cent. Combustion analyses showed that the quantity of nitrogen and other inert gases was less than 0.001 mole fraction. These analytical procedures indicated that the purified material could be expected to contain not more than 0.001 mole fraction of material other than methane. The smoothed experimental results presented in Table I show the compressibility factor as a function of pressure and temperature. The average deviation of experimental values from the smoothed data was less than 0.1 per cent. The compressibility factor is defined by the following equation:
0.04(
0.03l
Z
=
PV/bT
(1)
I n carrying out the calculations necessary to arrive at the values recorded in Table I, the molecular weight of methane, M , wtts taken as 16.042,and the value of the universal gas constant, R, was taken to be 10.732 (lb./sq. .in.) (cu.ft./lb. mole)/' Rankine.
0.0 3I
0.0 2
0.021
Figure 1. Effect of Pressure and Temperature on Residual Specific Volume of Methane
m
J
'=.
0.01
LL
5
u w
i:
a
0.0I
J
0
> J
U
3
e
0.00
v)
w
a
- 0.oc - 0.0
- 0.0 - 0.0; - 0.0; 1000
2000
3000
4000
PRESSURE
5000
L&/SO.
6000
IN.
7000
a000
9000
Vol. 35, No. 8
INDUSTRIAL AND ENGINEERING CHEMISTRY
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TABLE
Pressure, Lb./Sq. In. Abs. 0 200 400 600 800 1000 1250 1500 1750 2000 2500 3000 3500 4000 4500 5000 6000 7000 8000 9000 10000
70OF. 1 .oooo 0.9749 0.9503 0.9264 0.9037 0.8823 0.8582 0.8378 0.8222 0.8122 0.8059 0.8163 0.8410 0.8764 0.9191 0.9650 1.0610 1.1624 1.2664 1.3673 1.4713
100" F. 1 .oooo 0.9795 0.9598 0.9410 0.9235 0.9072 0.8892 0.8739 0.8615 0.8526 0.8 1 0.8%4 0.8758 0.9054 0.9415 0.9813 1.0681 1.1612 1.2555 1.3508 1.4470
130'F. 1.0000 0.9833 0.9673 0.9522 0.9383 0.9257 0.9119 0.9004 0.8913 0.8849 0.8809 0.8886 0.9060 0.9312 0.9622 0.9968 1.0761 1.1613 1.2480 1.3365 1.4259
160°F.
1 .oooo
0.9865 0.9736 0.9617 0.9508 0.9410 0.9303 0.9216 0.9152 0.9109 0.9095 0.9165 0.9316 0.9535 0.9807 1.0119 1.0840 1.1615 1.2425 1.3250 1.4080
I.
FACTOR FOR
COMPRESSIBILITY
190'F. 1.oooo 0.9891 0.9789 0.9695 0.9610 0.9535 0.9456 0.9394 0.9349 0.9321 0.9321 0.9393 0.9535 0.9735 0.9979 1.0266 1.0925 1.1628 1.2384 1.3158 1.3937
220'F. 1.0000 0.9913 0.9833 0.9760 0.9695 0.9639 0.9582 0.9539 0.9510 0.9497 0.9512 0.9587 0.9721 0.9912 1.0138 1.0395 1.1000 1.1650 1.2355 1.3084 1.3822
250'F. 1 .oooo 0.9932 0.9869 0.9814 0.9766 0.9725 0.9685 0.9657 0.9641 0,9639 0.9671 0.9752 0.9884 1.0062 1.0271 1.0511 1.1069 1.1682 1.2341 1.3029 1.3722
280'F. 1.0000 0.9947 0,9900 0.9859 0.9825 0.979,8 0.9772 0.9758 0.9754 0.9760 0.9807 0.9894 1.0025 1.0192 1.0391 1.0612 1.1134 1.1708 1.2327 1.2975 1.3635
METHANE
310'F. 1.0000 0.9960 0.9926 0.9897 0.9875 0.9858 0.9845 0.9842 0.9848 0.9864 0.9923 1.0018 1.0148 1.0308 1.0496 1.0707 1.1197 1.1739 1.2320 1.2937 1.3554
340'F. 1 .0000 0.9972 0.9948 0.9929 0.9916 0.9908 0 I9905 0.9911 0.9927 0.9950 1.0020 1.0120 1.0250 1.0406 1.0587 1.0787 1.1253 1.1765 1.2315 1.2898 1.3490
370'F. 1 .oooo 0.9981 0.9966 0.6956 0,9951 0,9950 0.9957 0.9970 0,9991 1.0019 1,0098 1.0204 1,0334 1,0489 1.0664 1.0857 1.1297 1.1786 1.2312 1.2870 1.3425
4OOOF. 1.0000 0.9989 0,9982 0.9979 0.9981 0.9986 1.0000 1.0020 1.0047 1.0079 1.0164 1.0273 1.0404 1,0558 1.0728 1.0916 1.1335 1.1803 1.2307 1.2837 1.3375
430'F. 1.0000 0.9996 0.9995 0,9999 1.0006 1.0018 1.0037 1.0063 1,0094 1.0131 1.0222 1.0333 1.0465 1.0617 1.0784 1.0967 1.1371 1.1822 1,2303 1.2813 1,3330
46O0F. 1,0000 1.0002 1,0007 1.0016 1.0028 1.0044 1 ,0069 1.0100 1.0135 1.0177 1,0272 1.0385 1.0515 1.0663 1.0829 1.1008 1.1402 1.1830 1.2296 1.2791 1.3290
utilized in the several investigations varied widely, and it is probable that values critically chosen from these data may form a satisfactory basis for the volumetric and thermodynamic properties of this hydrocarbon for engineering purposes.
The residual specific volume may be defined by the following expression: V = -bT --V P
This variable is of special utility in describing the behavior of a gas a t relatively low pressure. The influence of pressure upon the residual volume of methane as established from the present experimental results is shown in Figure 1. I n general, the results obtained are similar t o those found for other hydrccarbons a t comparable reduced temperatures and pressures. The values recorded in Table I probably do not involve uncertainties greater than 0.2 per cent. The smoothing operations were carried out so that inconsistencies in the data of greater magnitude than0.05 per cent are unlikely. Smoothed values for a number of temperatures, in addition to those of the experimental measurements, are included in the interest of utility. The earlier experimental work cited above is compared with the present data in Table 11. This comparison was made on the basis of centigrade temperature and pressure expressed as international atmospheres in order to avoid the uncertainties associated with the interpolation of the earlier measurements to the units employed in this study. I n general, the four sets of data are in good agreement except a t pressures above 300 atmospheres where deviations of as much as 0.25 per cent occur between the measurements of Kvalnes and Gaddy and those of the authors. It is believed that the agreement of the several sets of data recorded in Table I1 is an indication of the relatively small uncertainty associated with modern volumetric measurements. The sources of methane
ACKNOWLEDGMENT
This work was a part of the activities of Research Project 37 of the American Petroleum Institute. H. A. Taylor assisted in the experimental work and Virginia Jones in the calculations. NOMENCLATURE
b = specific gas constant, R/iM M = molecular weight P = pressure, Ib./sq. in. abs.
R = universal gas constant, (lb./sq, in.) (cu. ft./lb. mole)/"R. T = thermodynamic tem erature, R. (" F. 459.69) V = specific volume, cu. &./lb. = residual specific volume, cu. ft./lb. Z = compressibility factor
+
LITERATURE CITED
(1) Keyes and Burks, J . Am. Chem. Soo., 49,1403(1927). (2) Kvalnes and Gaddy, Ibid., 53,394(1931). (3) Miohels and Nederbragt, Physica, 3, 569 (1936). (4) Sage and Lacey, Trans. Am. Inst. Mining Met. Engrs., 136, 136 (1940). PAPER 39 in the series "Phase Equilibria in Hydrocarbon Berim". Previous articles appeared during 1934-1940, inclusive, 1942, and in July, 1943.
--
OF COMPRESSIBILITY FACTORS FOR METHANE TABLE 11. COMPARISON 7
Pressure, Atm.
so
100 120 140 160 180 200 300 400 600 600
Kvalnes and Gaddy 0.9112 0.8969 0.8852 0.8776 0.8742 0.8747 0.8801 0.9517 1.0632 1.1895 1.3199
50' C. Keyes Michels and and Burke Nederbragt 0.9110 0.9107 0.8952 0.8948 0.8834 0.8835 0.8761 0.8760 0.8728 . . . . 0.8739 0.8791 ....
.... .... .... ....
....
....
.. .. .. ..
-
Authors 0.9106 0.8952 0.8835 0.8758 0.8725 0.8735 0.8786 0.9500 1.0635 1.1918 1.3218
7
Kvalnes and Gaddy 0.9564 0.9506 0.9467 0.9448
....
0.9499 0.9548 1.0066 1,0901 1.1885 1.2946
c.
1000 Keyes Michels and and Burks Nederbragt 0.9567 0.9565 0.9506 0.9506 0.9466 0.9468 0.9449 0.9449 0.9454 0.9482 0.9493 . . . . 0.9530
.... .... ....
.... ....
.... .... .. .. .. ..
Authors 0.9567 0.9507 0.9467 0.9450 0.9452 0.9479 0.9526 1.0054 1.0900 1.1890 1.2962
Kvalnes and Gaddy 0.9818 0.9811 0.9814 0.9834
....
0.9914 0.9983 1,0453 1.1119 1.1939 1,2836
150° C.Xeyes Michels and and Burks Nederbragt 0.9827 0.9819 0.9816 0.9812 0.9819 0.9815 0.9836 0.9834 . . . . 0.9867 0.9912 0.9916 0.9970 0.9979
....
....
.. .. .. ..
.... .... ....
.,..
~200oc.-. Kvalnes and Authors Gaddy Authors 0.9986 0.9975 0.9830 1.0005 0.9995 0.9820 1.0035 1.0028 0.9824 1 ,0073 1.0069 0.9842 .... 1.0120 0.9873 1.0176 1.0174 0.9916 1.0242 1.0228 0.9973 1.0673 1.0680 1.0432 1.1279 1.1272 1.1118 1.1971 1.1930 1.1980 1,2745 1.2830 1.2745 1
