INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1945
TABLE 111. MOLES OF EQUILIBRIUM VAPOR PER MOLEOB MIXTURE CALCULATED BY A MATERIAL BALANCE ON INDICATED COMPONENT AT 100' F.
Mirt.
A
Mixt. B
-Pressure, 1046 CHd 0.753 CiHn 1.043 CaHa 0.782 n-CeH~r 0.781 ~-CSHII0.656
Trim
Lb./Sq. In-. 1822 0.507 0.645 0.629 0.434 0.607
-Pressure. 1431 517 CHI 0.674 0.806 CiHn 0.885 1.027 0.830 CsHs 0.677 TL-C~HIO0.845 0.808 0.813 ~-CIRI: 0.676
1419 0.731 1.624 0.760 0.676 0.682
1639 0.633 0.752 0.596 0.605
0.650
1235 0.690 0.811 0.701 0.677 0.674
Lb./Sq. In. 946 0.738
oms
0.744 0.701 0.763
1297 0.682 0.617 0.682 0.679 0.685
823
In connection with the binary and ternary mixtures the authorlr (5,9) report that no uncertainties in the compositions of the equilibrium phases greater than 0.005 mole fraction are to be expected except in the immediate vicinity of the critical state. This uncertainty is of the same order of magnitude as the uncertainty in the compositions of the equilibrium phases from mixtures A and B. Within the limits of experimental error, it a p pears that the curves of log K against log P for a paraffin in paraffin mixtures having the same convergence pressure a t a given temperature can be considered coincident.
1736 0.698
ACKNOWLEDGMENT
0.607
The authors wish to express their appreciation to the Ethyl Corporation for fellowship grants and to B. B. Kuist and C. F. Weinaug for assistance in the experimental determinations.
0.402 0.696 0.692
patane, having a critical temperdture of 100' F, and a critical (convergence) pressure of about 2000 pounds per square inch absolute (5). Figures 3 and 4 present equilibrium constants from published correlations by Robinson and Gilliland (8), by Brown (f, a), and as modified by White and Brown (fl). The equilibrium constant curves from Brown are repreaented as reliable only for conditions unaffected by the critical, which should always be moditied a t high pressures. Figures 3 and 4 give an equilibrium constant curve for methane for a convergence pressure of 2ooo pounds per square inch absolute at 100' F. from an unpublished correlation by the authors. This correlation of methane equilibrium constanta from binary paraffin systems was made on the basis of convergence pressure.
LITERATURE CITED
Brown, P&roleum Ewr., 11, No. 8, 25 (1940). Zbid., 11, No. 9, 56 (1940). Carter, Sage, and Lacey, Trans. Am. Znst. Minino Mct. Enqra. 142, 170 (1941). Gilliland and Scheeline, Im. ENO.C E ~ M 32,48 ., (1940). Hanson, Kuist, and Brown, Ibid., 36, 1161 (1644). Kat94 and Brown, Ibid., 25, 1373 (1933). Kurata and Kats, Tram. Am. Imt. Cham. Engr8., 38,996 (1942). Robinson and Gillidand. "Elements of F~actionalDistillation", 2rd ed., g. 46,New York,MeGraw-Hill Book Co., 1939. Sage, Hicks.and Lacey, INB.ENO.CEBM., 32, 1086 (1940). Souders, Selheimer, and Brown, Ibid., 24,617 (1932). White and Brown, Zbid., 34,1162 (1942). ABSTBACTI~D from a theals submitted by 0. H. Hanson to the Horaoe E. Rackham School of Graduate Studies, Univenity of Miohigan, in partial ful6llment of the requirementsfor the P1.D. degree.
Thermodynamic Properties of Methane at Low Temperature W. H. CORCORAN, R. R. BOWLESI, B. H. SAGE, AND W. N. LACEY California Zmtitute of Tedhnology, Pasadena, Calif.
I
N THE solution of many engineering problems the use of de-
tailed thermodynamic data is very convenient. Frequently wch data are not readily available and must be obtained from measured physical and thermal properties by lengthy calculations. Thermodynamic properties of methane above 70' F. have been tabulated by several authors. Corresponding information for temperatures below 70' F. is not so easily available. Keeaom and Houthoff (4) presented a temperature-entropy diagram for methane covering the temperature range from 100' to 270' K. and the pressure range from 1 to 40 atmospherea. The thermodynamic quantities were determined by utilizing information from a single source (6). The results are given in metric units and no tabulated data are shown. Subsequent experimental work has afforded increased information on the physical and thermal properties of methane. It has, therefore, seemed desirable to utilize the more recent methane data in preparing a temperature-entropy diagram for the low temperature region, in terms of English units. The thermodynamic properties of methane from 70' to -230' F. and from 1
Preaent addreas, Standard Oil Company of California, El Segundo, Calif.
atmospheric pressure to 1400 pounds per square inch absolute have been derived from data existing in the literature and are p r s sented in tabular and graphical form. METHODS
Molal heat capacities at zero pressure were determined from fundamental vibrational frequencies given by Vold (9). At aero pressure the isobaric heat capacity is given by the equation:
The first two terms within the bracket are concerned witb tramlational and rotational energy, respectively; the third term is related to the difference between the isobaric and isochoric heat capacities. The characteristic temperature c% is obtained by multiplying the vibrational frequency by hc/k in consistent units. Since the methane molecule has five atoms, it posaeases nine degrees of vibrational freedom and hence thelimits for the last tern
826
INDUSTRIAL AND ENGINEERING CHEMISTRY
ENTROPY
B.T.U/LB.
'R.
Figure 1. Temperature-Entropy Diagram of M e t h a n e in Low-Teuiperat lire Kegion
Vol. 37, No. 9
September, 1945
INDUSTRIAL AND ENGINEERING CHEMISTRY
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82?
in Equation 1 are from i 1 to i 9. The values for the vibrational heat capacity 89 a function of Oc/T are given by Werner (10).
Enthalpies of methane at zero pressure were calculated by i n t e grating graphically the differential relation between CP, and T, and arbitrarily setting the enthalpy equal to zero at a datum state corresponding to zero pressure and 60' F. To obtain enthalpy values at various pressures and temperatures, isothermal enthalpy changes for pressure intervals of 10 kg./sq. cm. given by Eucken and Berger (8)were utilized. Enthalpies of saturated gas and saturated liquid methane were taken from Wiebe and Brevoort (11)and converted to the basis of the given reference point. Vapor presuures were obtained from data presented by Eucken and Berger (3). The critical constants were determined with €he assistance of the law of rectilinear diameters as applied to plots of H us. T and H us. P . These plots were smoothed simultaneously by reference to the vapor pressure curve. It is believed that the uncertainty in the enthalpy values should not be greater than 0.5 B.t.u./lb. From a plot of enthalpy u8. pressure a t constant temperature, values of - ( d H / b p ) ~were read, and (bZ/bT)p was calculated using the following expression, which may be obtained by combining the definition of compressibility factor with a suitable thermodynamic equation of state (6) :
A plot of ( b Z / b T ) pagainst temperature was utilized for integration t o give isobaric changes in the compressibility factor, 2. Compresaibility faotdrs at 70" F. in the pressure range from 0 to 1500 pounds per square inch were obtained from the values of Sage, Budenholzer, and Lacey (7). Using calculated values of AZ, the Compressibility factors for temperatures from 70" to -SO0 F. and pressures from 0 to 1400 pounds per square inch were determined. It was not believed desirable to extend compressibility factor calculations below a temperature of -80" F. because of the uncertainty in (bH/bP)T resulting from the rapid variation of H with respect to P at the higher pressures. Specific volumes of methane for temperatures down to -80" F. were calculated from the compressibility factors. Specific volumes of the gas at saturation were obtained by combining saturated liquid densities (6),vapor pressures (3), and smoothed values of the latent heat of vaporization (If) in the Clapeyron equation. To bridge the gap in specific volume values from -80" F. to saturation, a plot of P against T at constant even values of V was prepared from an isothermal plot of log P us. log V. By nearly linear interpolation of the even-volume P os. T plot between -80" F. and saturation, the remainder of the specific volumes for the given pressure range were obtained. Sufficient care was taken in graphical integration and interpolation that uncertainty in specific volume at any point should not be greater than 0.5% of the value. Entropies in the temperature region from 70" to -80' F. were determined from a relationship involving the isobaric residual volume-temperature derivative and the specific heat. The isobaric residual volume-temperature derivative was obtained from the equation:
H
P
The equation for change in entropy can be written in the following form:
ds-- CpdT + a ( g ) p d P - - abdP P
(4)
Vol. 37, No. 9
INDUSTRIAL AND ENGINEERING CHEMISTRY
828
In the superheated region, comparison with enthalpy values obTABLE11. THERMODYNAMIC PROPERTIES OF SATURATED-GAS tained by Sage, Lacey, and os-workers (1,7,8) from Joule-ThornAND SATURATED-LIQUID METHANE son studies and P-V-T measurements, and values calculated by -Saturated GasA a t u r a t e d LiquidT$y., Edmister (2) from P-V-T data indicate a maximum uncertainty P H V S H V S of 1 B.t.u./lb. in the enthalpy values. -230 43.42 -162.9 3.076 0.4378 -220 62.58 -150.0 2.168 0.4095 Comparison of the superheated vapor volumetric data with -210 86.94 -147.3 1.613 0.3831 those of Edmister (9)showed good agreement, but no volumetric 117.33 -145.1 1.243 0.3691 -200 164.21 -143.4 0.979 0.3372 190 data near the critical point were available for comparison. En180 198.61 -142.4 0.784 0.3149 249.23 -142.2 0.634 0.2923 -- 160 170 tropies in the superheated gas region agree with those calculated 308.18 -142.9 0.613 0.2683 by Edmister ( 2 ) to within 0.01 B.t.u./(lb.)("R.). -- 140 I60 376.84 -146.1 0.413 0.2420 453.11 -149.2 0.327 0.2130 Using temperature and volume as independent variables, a 130 641.38 -156.3 0.262 0.1765 - 120 638.70 -173.6 0.176 0.1140 comparison of data was made with the diagram presented by -116.6 678.00 - 206.4, 0.116 0.0186 (critical values) Keeaom and Houthoff ( 4 ) . The comparison between the two sets of data was inconvenienced by the absence of tabulated thermodynamic properties in the publication by Keesom and Houthoff (4). It was found that the pressures differ by about 3%, Since values of CP at zero pressure had been calculated, the change Average deviations in enthalpies of about 4 B.t.u./lb. and in in entropy was obtained by integration from 60" F. and 1 atmosentropies of 0.01 B.t.u./(lb.)( O R.) were observed. Threetypical phere to the desired state a t T and P: points of comparison in the superheated region are given in Table 111.
--
IF
-
14.696
01
[ T = 519.691 x'
