ylene S VAPOR-LIQUID EQUILIBRIUM RELATIONSHIPS G. H. HANSON, R. J. HOGAK, w’. T. NELSON, AND 31. R . CINES Phillips Petroleum Co., Bartlesuille, Okla.
004
-
__
0.03
m
5
.-
0.02
0
u
RESULTS
\ 6
0.0031 -20
,
I 0
AUTHORS
,
I
20
40
GO
80
100
120
140
160
180
equilibrium phases was determined by volumetric absorption with a n aqueous nitrate solution (mercuric nitrate, potassium nitrate, silver nitrate, and nitric acid). The method is essentially the same as that described in ( 1 ) . The reproducibility of the analyses was 0.1 and 0.2 mole yo in the concentration ranges from 1 t,o 15 and from 15 t o 100 mole %, respcctively .
200
The vapor pressures obtained during this study are presented in Table I. The unpublished vapor pressures of Dean and Lang (3) determined in the Phillips Research Laboratory and the values reported by Reamer and Sage
March 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY 7EMEP F
IO 255
40
605
the conditions studied at this laboratory. In general, the agreement is good, the differences being within experimental error. The isothermal vapor-liquid equilibrium data are presented in Table 11, and the unpublished isobaric measurements of Dean and Lang are given in Table 111. Activity coefficients baaed on the Reamer-Stage data are given in Table IV. I n general, the p-x curves established by Phillips data are slightly more convex upward than those established by Reamer and Sage-i.e., the authors' data indicate that the propanepropylene system is less ideal than was indicated] by the data of Reamer and Sage. Similarly, the authors' experimental y-x values are smaller than the published data indicate.
8 2 7 100 1349 I60 190
CORRELATION OF DATA
All the data were correlated on the basis of an activity coefficient, y, which is defined by Equation 1. fVTl
(1)
y = -
fLX
MOLE FRACTION PROPYLENE IN EQUILIBRIUM LIQUID
Figure 3. Variation of y Correction Value with Concentration and Temperature
TABLE I. VAPORPRFSSURES Temperature,
F.
25 5 82 7 134 9
128 7 (128 8) 144 3 (144.2)
CaHs
CaH6 AUTHORS 76 4 76 3 76 4 (76 1)a 180.8 (181 0 ) 346.5 (345.9)
61.7 61 6 0) 9
8) 1 2)
322 5 S A Q E (6)
10 58 0 47 1 40 96.6 79 0 100 227.3 189 0 160 455 3 383.9 190 621 2 525 0 a All vapor pressures and bolling points given in parentheses are Interpolations of vapor pressure lnformatlon reported by Reamer and Sage (6).
TABLE 11. ISOTHERMAL EXPERIMENTAL DATA Equlllbrium Phase Compositions, pressure, Mole Fraction Lb./Sq. - Propylene InchAbs Vapor Liquid 63.6 70.0 70 0 75.2 76.1 76.2
0.122 0.516 0.515 0.865 0.969 0.966
0.098 0.472 0 466 0.857 0.966 0.963
Activity Coefficientsa CaHs C:Hs 25.5' F. 1.057 1,001 1.012 1.026 1.023 1.017 0.996 1.124 1.000 1.10. 1.001 1.11
154.2 168.2 176.5 179.1
0.124 0.546 0.818 0.907
0,107 0.514 0.799 0.900
82.7" F. 1.019 1.002 1.005 1.000
1,003 1.023 1.029 1.07
1.16 1.062 1.024 1.008
0.981 0.934 0.905 0.93
301.0 322.4 336.4 340.2 342.2
0.151 0.503 0.760 0.850
0.138 0.478 0.756 0.842 0.874
134.9'' F 0.992 1.002 0.986 0.997 0.999
1.010 1.022 1.085 1,054 1.061
1.09 1.052 1.005 1.010 1.007
0.985 0.952 0.98 0.95 0.96
0.880
The fugacity-pressure ratios for gaseous propylene and propane (Tables V and VI) were calculated in the conventional manner using the volumetric data reported by Farrington and Sage ( 4 ) and Reamer, Sage, and Lacey (7). The ratios for propylene at temperatures below 40" F. were obtained by extrapolation. For propane, the fugacity-pressure ratios at temperatures below 100 F. were calculated using an unpublished correlation of the compressibility factors of propane vapor. Values of fv for propane at pressures greater than its saturation pressure were obtained by extrapolating f / P vs. P curves. At the saturation pressure f L = fv. Because the effect of pressure on the liquid fugacity is small for the limited pressure range between the vapor pressures of propane and propylene at each temperature, f L at saturation pressure was used for all equilibrium pressures. The experimental activity coefficients calculated on the above basis are included in Tables 11,111,and IV. At 190 O F., which is only 6.5' F. below the critical temperature of propylene, all the activity Coefficientsfor Propylene are below unity. At conditions of temperature and pressure approaching the critical, the deviations of the equilibrium vapor from an ideal solution are significant. Since there appear to be insufficient thermodynamic data for propane-propylene mixtures to calculate 7's which inelude the departure of the equilibrium vapor from ideal solutions, O
(62 149 (149 290 (290
DEANA N D LANQ(5) 322 5
REAMER AND
where x and y = concentration of the component in the equilibrium liquid and vapor phases, respectively. fv = fugacity of the pure component as a vapor a t the equilibrium temperature and pressure of the mixture. f~ = fugacity of the pure component as a liquid a t the equilibrium temperature and pressure of the mixture.
K = y/z CsHs CaHs 1.24 1.093 1.105 1.009 1.003 1 003
0.974 0.917 0.908 0.94 0.91 0.92
As P-V-T data for propane-propylene mixtures were not available fugacities used in calculation of the activity aoe5cients were based od P-V-T d e t s for pure components.
TABLE 111.
ISOBARIC EXPERIMENTAL DATAAT PER SQUARE INCH ABSOLUTE
(See 9) Equilibrium Phase CompositionsQ, T ~ Mole ~ Fraction ~ ~ Activity ~ ~ ture, Propylene Coefficientsb ' F. Vapor Liquid CaHe CaHa 130.1 0.8516 0.8421 1.0003 1.049 132.1 0.7118 0.7001 0.9898 1.056 133.4 0.6080 0.5859 0.9997 1.029 0.5137 135.0 0.4882 1.0015 1,020 138.4 0.3159 0.2873 1.019 1,0040 140.8 0.1579 0.1443 0.996 1.0106 141.2 0.1515 0.1366 1,006 1.0061 141.4 0.1123 0.1255 1,012 1.0070
_-
322.5
-
POUNDS
K
= y/x ___..~_
CSH6 1.011 1.017 1.038 1.052 1.100 1.094 1.109 1.118
C~HS 0.940 0.961 0,947 0.950 0.960 0.984 0.983 0.985
Volumetric absorption analyses using 90% sulfuric acid as reagent. b As P-V-T data for propane-propylene mixtures were not available fugacities used in caloulation of activity coefficients were based on P-V-T data for pure components.
INDUSTRIAL AND ENGINEERING CHEMISTRY
$06
TABLEIv. ACTIVITYCOEFFICIENTS BASEDON DATA(6) Equilibrium Pressure Lb./Sq. Inch' Abs.
REAMER-SAGE
Activity Coefficients' CaHs CtHs
49.55 50.0 51.99 52.2 64.12 54.8 56.32 56.5
10' F. 1.038 1.066 1.044 1.023 1,0222 1.0181 0,9891 0.9966
1.0027 0.9961 0,9934 1.0015 1.010 0,996 1,105 1.046
82.82 83.3 87.16 87.8 90.29 91.7 94.8
40' F. 1.073 1.052 1,031 1.028 1.0115 1.0025 1.0109
0,9910 0,9941 1,0052 1.0063 1.019 1.033 0.996
100' F. 1.025 1.016 1.0148 1.0046
1,0005 1.0056 1.005 1.014
398.71 414.49 428.28 443.37
160' F. 1.015 1.001 1.0011 1.0005
1.0004 1.0084 1.014 1.020
543.89 665.49 682.76 603.65
190° F. 0.987 0.987 0.9895 0.9955
1.0045 1.0131 1,020 1.024
Vol. 44, No. 3
a correlation of all the vapor-liquid equilibrium data based on these activity coefficients and strictly obeying the Gibbs-Duhem relationship could not be expected at temperatures approaching the critical. p - x - t DATA
Phase relationships are exactly expressed thermodynamically by the Gibbs-Duhem equation. One expression of this relationship for binary mixtures is given in Equation 2 (2).
The Van Laar equations, Equations 3 and 4, are perhaps the most useful of the mathematical solutions of this differential equation, because they have been found to represent well the activity coefficient data for many binary systems ( 2 ) . log y1 =
(1
(3)
B
(4)
+ gy
log Y2 =
(1 f
a As P-V-T data for propane-propylene mixtures were not available, fugacities used in calculation of activity coefficients were based on P-V-T data for pure components.
A
gy
For each isotherm there is one set of Van Laar constants, A and B. Equations 3 and 4 are applicable for binary mixtures in which .. the vaiues of the Van Laar constants are about equal. When the and B values are considerably different, these equations are
RATIOS FOR PROPYLENE^ TABLE V. FUGACITY-PRESSURE Pressure Lb./Sa. Incd Abs.
l o o F.
Saturation 0.9158 Saturation pressure, lb./sq. inch abs. 58.0
25.5' F. 0.9746 0.9612 0.9477 0.9347 0.9211
0.8984 76.37
40' F. 0,9761 0.9640 0.9520 0.9399 0.9278 0.9032
0.8812 97.5
70' F. 0.9796 0. Q695 0.9593 0.9491 0.9391 0.9189 0.8986 0.8730 0.8472
0.8450 152.1
82.7O F.
0.8297 180.8
100OB. 0,9829 0.9744 0.9659 0.9574 0.9490 0.9321 0.9153 0.8943 0.8733 0.8309
0,8071 227.3
130'F.
134.9'F.
0.7659 327.1
160'F. 0.9877 0.9816 0.9755 0,9694 0.9633 0.9511 0.9390 0.9239 0.9088 0.8787 0.8184 0.7572
0.7582 346.5
0.7205 456.6
180'F. 0.9889 0.9834 0.9779 0.9724 0.9668 0.9559 0.9449 0.9313 0.9177 0.8906 0.8365 0.7820 0.7261 0.6891 562.0
190'F. 0.9895 0.9842 0.9790 0.9738 0.9685 0.9581 0.9477 0.9347 0.9217 0.8959 0.8444 0.7929 0.7405 0,6855 0.6719 622.1
Fugacity-pressure ratios a t 40' F. and abmove were calc ulated by K. H. Hachmuth (6) using volumetric data reported in (4). Ratio s a t temperatures below 40° F. were obtained by extrapolation. a
RATIOSFOR PRO PANE^ TABLE VI. FUGACITY-PRESSURE Pressure Lb./Sq. Inch' Abs. 20 30 40 60 60 80 100 125 150 200 300 400 500 Saturation Saturation pressure, lb./sq. inch abs. Propylene saturation pressureb, lb./sq. inch abs. Estimated, f / P
,.
10' F. 0.9710 0,9562 0.9414
0.9301
25.5' F. 0.9732 0.9595 0.9457 0.9318 0.9172
0.9147
40' F. 0.9751 0.9624 0.9498 0.9370 0,9240
0.8986
82.7' F. 0.9802 0.9703 0.9604 0.9504 0.9404 0.9200 0.8994 0.8730
0.8460
looo F. 0.9820 0.9730 0.9642 0.9547 0.9456 0.9271 0.9084 0.8848 0.8608
0.8228
47.1
61.65
79.0
149.9
188.7
58.0 0.9122
76.37 0.8908
96.6 0.8740
180.8 0.8113
227.3 0.7837
130" F. 0.9845 0.9767 0.9689 0.9611 0,9533 0.937.7 0.9219 0.9021 0.8822 0.8417
0.7806 273.5
134.9' F. 0.9848 0.9772 0.9696 0.9620 0.9644 0.9391 0.9236 0.9044 0.8850 0.8456
0.7730
160' F.
0.9865 0.9798 0.9730 0.9663 0.9595 0.9460 0.9324 0.9155 0.8985 0.8643 0.7946 0.7344
1900 F, 0.9882 0.9824 0.9765 0.9706 0.9648 0.9530 0.9413 0.9266 0.9118 0.8827 0,8239 0.7645 0.7027 0.6867
290.1
383.8
524.8
346.5 0.7266
455.3 0.6813
621.2 0.6162
Fugacity-pressure ratios at looo F. and above were calculated by K. H. Hachmuth (6)using volumetric data reported in (7). Ratios a t temperatures below 100' F. were calculated using a n unpublished correlation of com ressibility factors of propane. b Propylene saturation pressures at even temperatures were obtained Prom (6).
INDUSTRIAL AND ENGINEERING CHEMISTRY
March 1952
607 MOLE FRACTION PROPYLENE
MOLE FRACTION PROPYLENE ,]
*O+l
MOLE FRACTION PROPYLENE
,
, ,
0;s
,
I
I
I
t
..
0.:
I
I
, ,
]
]
'i" 1
fI
a
-
-
60
1
F""'"1 L
-I
1
1
25.5 F
1
I
I
I
I
I
" ' 7 t A
230
T VAPOR
190
I
600 LL
J
3
GI40
! i P 13E
550
m
s 0.0
MOLE FRACTION PROPYLENE
0.5 MOLE FRACTION PROPYLENE
1.0
I30
0.0
0.5 MOLE FRACTION PROPYLENE
Figure 4. Comparison of Phillips Correlation with Experimental Data
1.0
$06
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 ~
TEMP,F SYMBOL
IO 255 0 a
40 0
io0 134.9
a27
a
A
A
160
+
190
TABLE VII.
. I
ao6-
Vol. 44, No. 3
SMOOTHED VALUES-4T 190' F. BASEDON PHILLIPS CORRELATION
Smoothed Van Laar constants (Figures 1 and 2). Equilibrium Liquid Composition Mole Fraction Propylene 0.0
E uiiibrium calcd. *ctivitlf
0.1 0. 2
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .o
Figure 5. Comparison of Experimental and Smoothed y Miniis x Vttlites
also applicable for binary systeins in which the 8/13 ratio is approximately equal to Vl/V*,where V is the niolal volume ( 2 ) . When the molal volumes of both compounds are about the same, the Margules solution of Equation 2 is used (a). For other situations relationships developed by Scatchard and Hamer are recommended ( 2 ) . It was found that the p-z data for each of the eight isotherms could be correlated using Equations 3 and 4 and arbitrarily coneidering, for correlation purposes, that the equilibrium vapor at each temperature was an ideal solution. The Van Laar constants A and B which best express the p-x data for each individual isotherm are presented as the points in Figures 1 and 2. The best smoothed curves for A and B draivn through these points constitute the correlation of all of the p-x-t data. The ratio of the Van Laar constants for each isotherm is approximately unity, varying froin about 0.7 to 0.9.
TABLEVIII.
The smoothed curves of the Van Laar constants given in Figures 1 and 2 also correlate satisfactorily all of the p-y-t data at teniperatures up to 100" F. ITrwever, as was to be expected, particularly in connection a i t h the 190' F. isotherm, the calculated p - y curve gave g minus .2: values which were too large. The most serious situation was a t 190" F and 582.76 pounds per square mch absolute. The eiperimental compositions of the equilibrium liquid and vapor phases n ere 0.5520 and 0.5628 mole fraction propylene, respectively. Using the smoothed Van Lam constants a t 190" F. ( A = 0 00383 and R = 0.00430) the calcu! 255
0
0
40 0
827
m
.
100 134.9 A
b
160 I90 + v
i
Comparison of Experimental and Smoothed Residual Pressure Values
Calod.
Adjusted
0.0000 0,1088 0.2148 0.3182 0.4197 0.5190 0.6170 0.7137 0.8095 0.9049 1.0000
0.0000 0.1060 0.2099 0.3117 0.4123 0.5113 0 . 6096 0.7072 0.8046 0.9021 1,0000
S\ZOOTHED
VALUES
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
25.50 Y. 0.0000 0.1242 0.2403 0.3492 0.4523 0.5503 0.6443 0.7352 0.8240 0.9119 1 10000
61, 65 63.54 65.36 67.08 68.71 70.26 71.70 73.03 74.28 75.40 76.37
0.0 0.1 0.2 0.3 0.4 0 5 0.6 0.7 0.8 0.9 1.0
134.9' 0 0000 0.1134 0 2219 0.3261 0.4272 0.5256 0.6221 0.7171 0.8114 0.9055 1 0000
400 F. 0.0000 0.1220 0.2366 0.3448 0.4474 0.5455 0.6400 0.7318 0.8217 0.9106 1.0000
79.0 81.28 83.43 85.51 87.47 89.31 91.01 92.61 94.10 95.42 96.6
0.0
0.G 0.7 0.8 0.9 1.0
82.7' I;. 0.0000 0.1180 0. 296 0.8360 0 4378 015363 0.6316 0.7249 0.8169 0.9084 1.0000
ON
Phase Compositions, Equilibrium N o l e Fraction pressure, Lb./Sq. Liquid Vapor Inch Abs. 0.0000 0.1168 0.2271 0.3328 0.4345 0,5329 0.6286 0.7225 0.8152 0.9074 1.0000
0.0 0.1 0.2 0.3 0.4 0.5 0.6
BASED
PHILLIPS CORRELATION
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0 0.1 0.2 0.3 0.4 0.5
Figure 6.
525.0 536.1 546.7 557.1 567.4 577.4 587.2 596.4 605,3 613.6 621.2
Mole Fraction
Propylene _ _ _____
47.1 48.52 49.88 51.15 52.38 53.52 54. 60 55.58 56.49 57.30 58.0
0.7 0.8 0.9 1.0
MOLE FRACTION PROPYLENE I N EQUILIBRIUM LIQUID
Inoh ilbs.
10" F, 0.0000 0.1246 0.2409 0.3502 0.4532 0.5513 0,6452 0.7357 0.8244 0.9120 1.0000
0.1
10
ISOTIiERMAL
Phase Compositions, Equilibrium blolo Fraction Pressure, Propylene Lb./8q. Liquid Vapor Inch Ah.?.
p-y CURVES
TEMP,F SYMBOL
CaHa 1.0000 1.0001 1.0003 1.0008 1.0014 1,0022 1.0033 1.0045 1.0060 1.0079 1.0100
lated vapor composition in equilibrium with a 0.5520 liquid is 0.5701 mole fraction propylene. The experimental ?J minus 2 value was 0.0108 mole fraction, whereas the calculated y minus x was 68% larger, 0.0181. Consequently, an empirical correction was necessary. The correction curves for the calculated y values a t 190' F. and for the other temperatures are presented in Figure 3. The maximum y corrections at temperatures of 100' F. and below are less than 0.003 mole fraction. Since the y minus x quantities are relatively large a t these lower temperatures (maximum y minus x values a t 10" and 100 F. are 0.053 and 0.035 mole frac-
0.0
z4/-
3ressure
CoefficientE_-_ Lb./Yq.'
CsHe
A = 0,00383 B = 0.00430 Vapor Equilibrium Composition,
100" I'.
0.1
0.2 0.3 0.4 0.6 0.6
0.7 0.8 0.9 1.o
189.0 194.00 198.77 203.21 207.46 211.47 218.15 218.62 221.79 224.71 227 3 17.
160'F. 0.0000 0,1097 0.2161 0.3196 0.4207 0.5198 . 0.6174 0.7136 0.8091 0.9044 1.0000 1900 v,
290.1 297.36 304 41 311.08 317.20 323.10 328.60 333.68 338.37 342.61 346.6 383.9 392.61 400,87 408.83 416.48 423.93 430.93 437.63 443.96 449.92 455.3
March 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
tion, respectively), the 9 correction factors suggested are always less than 10% of the corresponding y minus 2. A tabulation of the calculated activity coefficients, smoothed equilibrium pressures, and the calculated and adjusted g values for 190”F. is presented in Table VI1 for illustrative purposes.
tween the experimental and the calculated equilibrium temperatures is 0.2’ F., the average net difference being slightly less than 0.2 F. The average absolute and the average net deviations between the experimental and calculated y minus x quantities are 12 and -275, respectively. O
ACKNOWLEDGMENT
COMPARISON WITH EXPERIMENTAL DATA
Smoothed p-x-y values for the eight isotherms are presented in Table VIII. The smoothed p-x-y curves for temperatures of 100 O F. and below can be considered to obey the Gibbs-Duhem relationship. A graphical demonstration of the good agreement b e tween all of the experimental data and the smoothed curves obtained from this correlation is given in Figure 4. Comparisons of the experimental and smoothed y minus x values and residualpressure values are presented in Figures 5 and 6, respectively. I n evaluating the correlation, the calculated equilibrium pressure (or temperature) for each experimental liquid composition and the calculated y minus x value were compared with the corresponding experimental quantities. The average absolute deviation.and the average net deviation (which considers the “deltas” algebraically) between the experimental and the calculated equilibrium pressures for all the isothermal data are 0.15 and -0.03%, respectively. The average absolute deviation between the experimental and the calculated y minus x quantities is 15.4%, whereas the average net deviation is only -0.02%. Since the isobaric data at 322.5pounds per square inch absolute were not used directly in the development of this correlation, the good agreement between those data and the smoothed curves is an independent check of the reliability of the correlation. The average absolute difference be-
609
The authors wish to acknowledge their indebtedness to the Phillips Petroleum Go. for permission to publish this paper, t o H. H. Reamer, B. H. Sage, M. R. Dean, and Mrs. 0. R. Lang for the use of their experimental data prior t o publication in the development of this correlation, to K. H. Hachmuth for the use of his fugacity-pressure ratios for propane and propylene, and to F. N. Ruehlen for his substantial assistance in the calculation of the smoothed p-x-y curves. LITERATURE CITED
Am. SOC.Testing Materials, Research Division IV, Section B, A.S.T.M. D-2, “Proposed Method of Test for Unsaturated’ Hydrocarbons in Gas Mixtures (Silver-Mercuric Nitrate Absorption Method).” ( 2 ) Carlson, H. C., and Colburn, A. P., IND.ENQ.CHEM.,34. 581;
(1)
(1942).
(3) Dean, M. R., and Lang, 0. R., private communication. (4) Farrington, P. S., and Sage, B. H., Im. ENG.CHEM.,41, 1734 (1949). ( 5 ) Haohmuth, I(.H., private communication.
(6) Reamer, H. H., and Sage, B. H., IND.ENG.CHEM.,43, 1628 (1951). (7) Reamer, H. H., Sage, B. H., and Lacey, W. N., Ibid., 41, 482 (1949).
RECEIVED for review April 2, 1951.
ACCEPTEDOotober 31, 1951.
Phase Equilibria in Hydrocarbon N
J
Systems n-BUTANE-WATER SYSTEM IN THE TWO-PHASE REGION H. H. REAMER, B. H. SAGE, AND W. N. LACEY California Institute of Technology, Pasadena 4, Calif.
ANY studies of hydrocarbon-water systems have been made. Water is an important component of the fluids encountered in petroleum production. At temperatures somewhat above the freezing point of water, such systems form hydrates (19, 88-84). At higher temperatures data concerning mixtures of methane, ethane, natural gas, and water (9, 14, 16) are available. These studies indicate a pronounced increase in the concentration of water in the gas phase above that predicted by the Poynting equation (16). The n-butane-water system has been investigated in the three-phase region at temperatures above 100”F., and a critical state was found between the less dense phases at 305.6” F. and 637.5 pounds per square inch (17). However, few data concerning the composition of the coexisting phases at higher pressures for the two-phase region appear to be available (18). The present work involved the measurement of the composition of the coexisting phases at pressures up to 10,000 pounds per square inch in the temperature interval between 100 and 460 O F. The results of the measurement of the volumetric behavior of a single mixture of water and n-butane are included.
THERMODYNAMIC CONSIDERATIONS
In part of the two-phase region investigated the n-butanewater system consists of one denser phase rich in water and containing but a small amount of n-butane and a less dense phase which is primarily n-butane with only a small proportion of water. This latter phase may vary continuously from gas t o liquid. For the purposes of this discussion the more dense waterrich phase will be called the aqueous liquid phase and the less dense n-butane-rich liquid phase will be identified as the hydrocarbon liquid phase. As a basis of correlation it is possible t o utilize the relations applicable to a dilute solution (11) for the water in the hydrocarbon phase and for the hydrocarbon in the aqueous liquid phase. The relations of an ideal solution (10) may be applied t o water in the aqueous phase and to n-butane with a somewhat larger uncertainty in the hydrocarbon phase. Under these circumstances there are obtained (14) the following quantities for the equilibrium distribution of water between the gas and aqueous liquid phases and the hydrocarbon liquid and aqueous liquid phases, respectively:
