Phase Equilibria in Hydrocarbon Systems J
J
The Methane-n-Butane System in the Two-Phase Region' B. H. SAGE, B. L. HICKS, 4ND W. N. LACEX California Institute of Technolog), Pasadena. Calif.
L
Compositions and specific volumes of the dioxide at the freezing point of E T H A K E and n-butane water. It is believed that these are important coexisting phases of the methane-n-butane calibratiolls were made with nents of naturally occursystem were determined throughout the cient accuracy to determine the r i n g h y d r o c a r b o n mixtures. pressure in the equilibrium vessel two-Phase region at above within 0.05 per cent, except at However, the measurements of pressures below 300 pounds per 70' F. From these data equilibrium conSederbragt (12) appear to fursquare inch where a somewhat nish the only information availstants for methane and n-butane were larger uncertainty involved. to t h e phase computed and have been reported as funcThe volume of the sample wab behavior of mixtures of these t& ascertained from the elevation tions of state. From other unpublished of the mercury sur.ace hydrocarbons. These d a t a corer data the fugacities of the components in the the equilibrium vessel. Experionly a part of the conditions ence with this equipment indiencountered in Droduction riraccoexisting cates that the total volume of the - -phases were established. tice, and therefore i t was desirasample may be measured within 0.1 per cent throughout the ble to study in detail the phase range of conditions encountered in t,his investigation. The behavior of this binary system as a part of a more general weights of n-butane and methane employed probably did not study of its thermodynamic properties. T h e volumetric and involve uncertainties larger than 0.1 per cent. It is believed, phase behavior of each of the components has already been therefore, that the composition of the bubble-point liquid was known with an uncertainty of not more than 0.002 weight fracinvestigated. Kvalnes and C a d d y (8)determined the volution, while the specific volume of the bubble-point liquid metric behavior of methane at pressures u p t o 15,000 pounds does not involve uncertainties greater than 0.3 per cent except per square inch a t temperatures between 32" and 403" F. in the neighborhood of the critical state where the uncertainty i* Beattie and eo-workers (1) measured the vapor pressure of somewhat larger. n-butane at a number of temperatures, determined the critiFigure 1 present's a n illustrative set of experimental resilti cal constants, and established t h e volumetric behavior above for a mixture containing 0.07395 weight fraction methane. the critical temperature. Vapor pressure and volumetric Only the experimental information pertinent t o the location d a t a for the gas and liquid phases of n-butane at temperaof the bubble point is included in the diagram. The agreetures between 70" and 250O F. for pressures u p to 3000 pounds ment of the points shown is typical of t h a t obtained througliper square inch are also available (20). These d a t a taken out this investigation. These data, which were ohtainetl together serve t o establish the volumetric and pha-e behavior upon both increase and decrease in t h e total volume of t h e of the two components of t h e system with sufficient accuracy system, are a n added indication of the attainment' of phaCe and detail for present purposes. (All pressures used in this equilibrium. paper are expressed in pounds per square inch absolute.) Experience has indicated t h a t it is experimentally difficult to establish dew-point stat'es a t elevated pressures from voluMethods metric data. This results from the relatively small change i n The composition and specific volume of the bubble-point the isothermal compressibility which occurs a t these states, liquid was ascertained from studies of the volumetric behavior and from apparent hysteresis effect's owing t o nonequilibriuni o f mixtures of methane and n-butane in the two-phase and conadsorptions on t h e walls of t h e confining vessel. For the densed liquid regions. The equipment employed for these measurements has been described (1.9). In essence, the method reasons i t was considered desirable to ascertain the composiinvolved the addition of known weights of methane and n-butane tion of the dew-point gas as a function of pressure and temto a chamber whose effective volume was varied by the addition perature in a n independent fashion. The method used ino r withdrawal of mercury. Equilibrium between the phases volved t h e withdrawal of a portion of the gas phase under was established by means of a mechanical agitator while the temperature of the chamber was maintained constant by immerisothermal, isobaric conditions when a t eqiiilibrium with a sion in an agitated oil bath whose temperature was controlled liquid phase. T h e composition of the gas was determined nutomaticall\-. The temperature of the material under investib y the accurabe measurement of its specific volume a t atgation was ascertained by means of a strain-free platinuni resistmospheric pressure and 140" F. ance thermometer which was frequently compared with a similar instrument recently calibrated by the National Bureau of Actual gaseous mixtures d o not, appear t,o follow the l a w Standards. It is believed that the temperature was determined of ideal solution with great accuracy even a t pressures in the within 0.08" F. relative to the International Platinum Scale. vicinity of one atmosphere. For this reason it was considered The pressure was measured by means of a pressure balance similar i n principle t o that recently described (23). This instrument desirable to employ factual information concerning t h e volu\$-ascalibrated by reference t o the vapor pressure of carbon metric behavior of gaseous mixtures of methane a n d n-butane to permit t h e estimation of t h e composition of the dew-point i This is the thirty-first paper i n this series. Prerious articles h a v e 3ppenred during 1934-1940, inrlusi\-e. gas from it,s measured atmospheric specific volume. Figure 2
1086
INDUSTRIAL AND ENGINEERING CHEMISTRY
VOL. 32, NO. 8
of 10-5 inch of mercury. The relative elevations of the mercury surfaces in this manometer were established by a vertical-component cathetometer with mJ an uncertainty of not more than 0.005 inch in a difference in elevation of not less than 25 inches. 0.06 The temperature of the manometer was mainw tained constant. The outlet of the bulb was closed a after the attainment of equilibrium, and it was F removed from the air thermostat and conditioned LL in a closed vessel of controlled humidity in order j 0.05 0LE P O I N T L O C U S to reproduce the quantity of moisture adsorbed U in its exterior surface. It was then weighed, using a nearly identical tare, and the change in W weight was determined by the substitution procI 3 ess. The substituted neights were corrected for 0.04 air buoyancy, but the two bulbs were near enough > to being identical to render unnecessary any corrections for the change in buoyancy result2 ing from changes in the barometric pressure. It LL -u is believed that by this process the specific volume W 0.03 of the gas was established within 0.1 per cent a t a the state corresponding to the temperature of the VI air thermostat and the pressure indicated by the mercury-in-glass manometer, and the composition of the gas phase was determined with an uncertainty of not more than 0.001 in the weight frac500 750 1000 1250 I500 tions of the components. I n the first measurements some difficulty was PRESSURE LE. P E R SQ. IN. experienced in obtaining satisfactory agreement between samples withdrawn at the same state. It FIGURE 1. REPRESENTATIVE ILLUSTRATIVE EXPERIMENTAL RESULTSIN was found that this resulted from the nonattainTHE VICINITY O F BUBBLE P O I N T FOR A MIXTURECONTAINING 0.07396 ment of equilibrium within the gas phase, which WEIGHT FR.4CTION METHANE caused significant discrepancies bstween the compositions of samples withdrawn near the top of t h e e q u i l i b r i u m v e s s e l and those withdrawn near the liquid-gas interface. Extended agitation over a shows the residual specific volume of the methane-n-butane period of hours was usually sufficient to reduce the discrepancy system at atmospheric pressure as a function of composition between the samples withdrawn at different points in the gas for several temperatures. These data are not highly acphase to less than 0.002 mole fraction. It is believed that the curate, but they do indicate a much larger deviation from the values obtained for the composition of the dew-point gas as a function of state do not involve uncertainties larger than 0.003 laws of ideal solution than the probable Uncertainty of the mole fraction except in the critical region where the compositions measurements used t o establish this behavior. The residual become extremely sensitive to environment. specific volume is related to the specific volume and the composition by the following equation:
I n the pressure range covered b y the atmospheric density measurements it is within the experimental uncertainty of measurement to assume that the residual specific volume is independent of pressure. This is equivalent to the assumption that ( 3 Z l b P ) is ~ independent of pressure in this range. On the basis of this assumption, experimental information concerning the specific volume of the gas at the state in question together with the data presented in Figure 2 permits the trial solution of Equation 1for the composition of the gas. The equipment employed to obtain this information concerning the heterogeneous equilibrium at elevated pressures was the same as that used for obtaining the volumetric data. The pressure and temperature a t equilibrium were established within the same uncertainties as were discussed earlier in connection with the data for the bubble-point liquid. In addition, the apparatus w-as equipped with a movable liquid-level indicator of the electrical resistance wire type (14). This device served to preclude the possibility of removing any of the liquid phase from the apparatus and permitted the withdrawal of samples of the gas phase a t different points relative to the liquid-gas interface. Comparison of the Composition of the gas phase a t different points afforded a useful criterion of the attainment of composition equilibrium xithin this phase. After equilibrium was reached, an adequate sample of the gas phase was withdrawn into a highly evacuat,ed gas bulb having an accurately known volume of approximately 0.0176 cubic foot (500 ml.). This vessel was located in an air thermostat whose temperature was controlled within 0.03' F. of the desired value (140" F.), The pressure existing within the glass bulb after temperature equilibrium had been attained was measured by a mercury-in-glass manometer with tubing approximately 0.5 inch in diameter. The arm of the manometer not connected to the bulb was evacuated by a mercury diffusion pump to a pressure
m
0.15
-1
LI W
a
+.
0.10
LL
5 U
" 0.05
L
I
I
I
I
0.2
0.4
0.6
0.8
WEIGHT
FRACTION
I
METHANE
FIGCRE 2. EFFECTOF COMPOSITION UPON RESIDC-LL SPECIFIC VOLUME FOR METHANE+-BUTANE SYSTEM IN THE GAS P H A S E AT ATMOSPHERIC PRES~CRE
The specific volume of the dew-point gas was ascertained from volumetric data obtained in the gaseous and two-phase regions for a series of mixtures of fixed composition. The pressure corresponding to dew point was ascertained by interpolation of the dew-point composition data for a series of pressures described above. At the higher pressures the specific volume a t dew point was estimated by interpolation of the isobaric variation in the residual specific volume with respect to composition. This procedure was especially advantageous since the residual specific
INDUSTRIAL AND ENGINEERING CHEMISTRY
AUGUST, 1940
1087
1500
same pressure and temperature are sufficient to establish the specific volume of the dew-point gas in a binary system. These quantities are related in the following way:
1250
Vd = (V"- V b h d - V"n*b n1 - n 1 b
z
+ Van1
(2)
I n general, the agreement between these three essentially independent methods used t o ir 1000 w establish the specific volume of the dewn m' point gas was better than one per cent. This large a n uncertainty probably results from w 750 selective adsorption of the components on the walls of the vessel. Uncertainties of this c1 Y nature are especially important for states in a r 500 the gaseous region adjacent t o dew point. I n the course of the calculations associated with the preparation of these experimental data it 250 was necessary t o employ constants whose numerical values directly affect the recorded data. The universal gas constant was taken , as 10.732 when the pressure was expressed 0025 0.05 0075 0.10 0.125 0.15 a175 in pounds per square inch, the volume in WEIGHT FRACTION METHANE cubic feet per pound mole and the temperature in O R. A temperature of 491.69' R. FIGURE 3. PRESSURE-COMPOSITION DIAGRAM FOR BUBBLE-POINT LIQUID ( " F. absolute) was used for the ice point. Molecular weights of 16.043 and 58.121 were employed for methane and n-butane, respectively.
2
[I
Lo
1
1
I
1
1
I
I
1
Materials The methane employed in this investigation was obtained from the Buttonwillow gas field in California. This material as produced is saturated with water and contains approximately 0.003 mole fraction of carbon dioxide and less than 0.0003 mole fraction of heavier hydrocarbon material. This material was passed through granular calcium chloride, sodium hydroxide, activated charcoal, Ascarite, and magnesium perchlorate a t a pressure in excess of 400 pounds per square inch in order t o remove the water, carbon dioxide, and heavier hydrocarbons from the methane. It is believed t h a t the methane employed contained less than 0.001 mole fraction of material other than methane. The n-butane used was obtained from the Philgas Department of the Phillips Petroleum Company whose special analysis indicated t h a t this sample of n-butane contained less than
230:
0 ,
02
0.3
WEIGHT
a4 FRACTION
0.5
1
I
0.6
0.7
METHAYE
FIGURE 4. PRESSURE-COMPOSITIOX DIAGRAM FOR DEW-POINT GAS
i u Lo
1503
CL W
a m
IO00
-!
w LL
volume in the one- and two-phase regions did not change rapidly with respect to composition under isobaric, isothermal conditions.
3 Lo LO
500
W
LI:
As a further check upon the interpolated values of the specific volume a t dew point, the volumetric d a t a in t h e twophase region were employed in a n independent fashion t o establish this state. These d a t a together with information concerning the composition and specific volume of bubblepoint liquid and t h e composition of the dew-point gas at the
n
IO0
I50
200 TEMPERATURC
250
r.
FIGURE 5. PRESSERE-TEMPERATURE DIAGRAM
300
INDUSTRIAL AND ENGINEERISG CHEMISTRY
1088
.).0004 mole fraction of material other than nbutane. This hydrocarbon was subjected to a series of careful fractionations a t a large reflux ratio in a column packed with glass helices. The middle portion from the first fractionation was used in the second distillation. After each fractionation the material was collected by means of a partial condensation a t a pressure only slightly greater than the sublimation pressure of solid n-butane a t liquid air temperatures. The purified material exhibited a change in vapor pressure of 0.3 pound per square inch during the course of a condensation from dew point to bubble point a t 160" F.
TABLE
m
PROPERTIES O F COEXISTING LIQUID AND
METHANE*-BUTANESYSTEM Pressure Ternn.. Lb./ F-. ' R q . In.
70
Experimental Results The experimental results obtained for the bubble-point pressures are presented in Figure 3 as a function of composition for each of the temperatures investigated. The agreement of the extrapolated bubble-point pressures with the vapor pressure of n-butane (2'0) indicates a Satisfactory degree of consistelicy between the$e two independent sets of results. Figure 1 presents the experimental data obtained for the composition of the dew-point gas. The curves for the bubble-point liquid are included also. The agreement of the experimental pointh is comparable with the uncertainty of the experimental measurements. In the critical region indirect methods were employed to establish the location of these curves. For the most part the change in slope of the isochors a t the boundary between the one- and two-phase regions was employed to delineate this region. The loci of the critical states and the cricontlentherm (4)states are included in Figure 4. These data indicate a maximum pressure for the existence of two phases in the neighborhood of 1920 pounds per square inch. The vapor pressures and the critical constants of n-butane depicted in this diagram were taken from published data (1, 20). Figure 5 presents a pressure-temperature diagram for this system. The bubble-point :inti dew-point curves for the mixtures of
I.
1011
l.iU
Compn.. 13-t. Fraction Methane Liquid
Gas
80 76"
100 150 200 300 400 .500
600 800 1000 1200 1250 1400 1500 1600 1700 1750 1800 1850 18i6b
0 0 0018 0 0066 0 0115 0 0214 0 0317 0 0424 0 0534 0 0769 0 1028 0 1322 0 1403 0 1662 0 1855 0 2088 0 2362 0 2560 0 2756 0 3131 0 3610
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 05675 1724 2546 3672 4387 4867 .5194 5559 5688 5711 5697 5600 5481 5,313 5040 4858 4617 4266 3610
0.08
a 0.06
5 w
0.04
0 >
0.02
0.I
0.2
0.3 WEIGHT
YICL-RE 6.
0.4
FRACTION
0.5
0.6
METHANE
SPECIFIC. ~ ~ ~ . ~ ~ ~ E - C ' O ~ ~ P ODSII~TG IO RSI FOR J I KUBBLE-POIXT IXKID
SP. Volunle
C u . Ft.;Lb.
Liquid
31 30Q 0 0 40 0.0010 0.0ti84.j 60 0.0031 0.1899 80 0.0052 0.2795 100 0.0074 0 3489 150 0 0129 0.4651 200 0 0185 0,5387 800 0 0301 0.6265 400 0 . 0 4 2 3 0.6758 500 0 . 0 5 5 1 0.7081 600 0 0686 0.7300 son 0 . 0 9 7 1 0 7540 1000 0.1289 0.7610 1'00 0 . 1 6 4 4 0.7550 1250 0.1726 0.7510 1100 0.2014 0 7331 1500 0.2232 0 . 7 1 9 0 1600 0.24485 0.7000 1700 0.2812 0.6750 1730 0 . 3 0 9 0 0 6590 1800 0 3 2 m 0.6392 1850 0 3591 0.6120 1'400 0 4094 0.5659 191.10 0 482 0 482 n n 5162' 60 0 0008 0 040s xn 0.0029 0.1230 iOii 0 0049 0.1901 130 0.0100 0 3128 200 0 01,52 0.3948 300 0 02.57 0.4983 400 0 0868 0 , ,5636 500 0.0484 0.6060 600 0.0604 0.6333 SO0 0,0869 0 , 6 6 4 0 1000 0 . 1 1 3 6 0.6712 1200 0.1452 0.6690 1250 0.1540 0.8664 1400 0 1821 0.6550 1300 0.2030 0.6418 o 2270 n em:! 1600 1700 0 2ikG 0 . 5 6 6 0 1750 0 2790 0 5823 IF90 0 3024 0 X l t i 1860 0 . 3 3 2 5 0.5330 0.3954 0.4813 1!400 1912h 0.4195 0.4195
w (L
5
YOL. 32, NO. 8
Gas
Fugacity, Lb.iSq. In. Methane n-Butane
0 02734 2 . 9 0 7 0 027,513 2 680 0 02763 2 . 2 6 3 0.02769 1.959 0.02773 1 727 0 02791 1 . 3 2 7 0.02807 1 . 0 7 6 0 02841 0 7750 0 02877 0.6030 0.02917 0 . 4 9 1 1 0.02961 0 . 4 1 2 0 0 03062 0 3073 0.03184 0,2401 0 08338 0 1925 0 . 0 3 3 7 8 0.1825 0.03523 0 . 1 5 5 1 0 03647 0 1390 0.03795 0 . 1 2 4 2 0 04005 0 1099 0 04148 0 1029 0 04330 0.09536 0 01G00 0.08717 0 0314 0 0704 0 . 0 6 2 1 0 0021
0 8 61 27.65 46.66 65 80 113.3 160 2 252.3 341.6 428. 2 513.5 674 9 823 3 9% 6 990.6 1084 1143 1198 1250 1274 1299 1322 134.5 1355
0.0285G 1 800 0.01858 1 . 7 1 4 0 02S(iS 1 . 533 0.028il 1 88i 0 02888 1 118 0 02900 0 9334 0.02942 0 6985 0.02980 0 . 5 5 6 5 0 03022 0 4595 0.03067 0 3891 0.03168 0 2928 0 03285 0 2292 0.03437 0 . 1 8 4 8 0 03485 0 1755 0 03652 0 . 1 3 0 5 0 03798 0 1353 0.03984 0 1209 0 n u ? 0 ioio 0 04418 0.09989 0 0462s 0 09209 0 04935 0 08318 0.05765 0.07083 0.06113 0 06113
0 8 00 26.94 45.94 93 11 140.0 2.32. 7 32-1 0 413 4 498.1 661 2 814 0 956.9 990 6 1089 1149 1207 1261 1286 1311 1336 1339 1365 0 17.91 64 42 110 7 202.4 292 5 380 2
0 02963 0 02969 0 02986 0 03004 0.03043 0.03085 0.03132 0 03181 0 03288 0.03418 0.0338.3 0 03633 0.03809 0.03960 0 04157 0 04409 0.04610 a 04852 0 05312 0 06062
1.162 1.076 0 9036 0 7757 0 6037 0 4919 0.4127 0.3547 0.2688 0 2122 0.1720 0.1633 0.1389 0 1266 0.1131 0.09888 0.09203 0 08421 0.07438 0.06062
GAS P H A S E S
20 6 20.7 21.5 22 3 23.4 24.7 25.4 26.2 27.1 28 1 28.7
IN
Equilihriurn Constant \Tnthn_._l".. ane Butane
2 216 0 1403 2.127 0.1464 1.902 0.1748 1.768 0 . 1 9 8 7 1 . 6 4 1 0.2318 1 , 3 0 5 0.2797 1 . 4 3 8 0.3160 1 361 0 3670 1 . 2 7 1 0.4503 1 . 1 5 5 0.6119 1.000 1 . 0 0 0
46.5.7 630.4
785 5 931 3 966 0 1067 1131 1186 1241 1265 1289 1314 1325
fixed total composition were interpolated from large-scale diagrams corresponding to Figures 3 and 4. The loci of the critical ctate and the cricondentherm are also included. The relatively large temperature interval between the critical state and the cricondentherm within which the phenomenon of isothermal retrograde condensation ( 7 ) may take place is clearly indicated, and the presbure interval between the critical state and the point of maximum preswre within which isobaric retrograde vaporization ( 5 ) may take place is also noticeable in Figure 5. The intersections of dew-point and hubblepoint curves on this diagram for a biliary svsteni correivond to the states a t which iew-point andLbubble-point material of their respeetire compositions coexist.
IUDUSTRIAL AXD ENGIhEERING CHEMISTRY
AUGUST, 1940
1089
bubble-point liquid are also included. Experimental points are not shown in this diagram Equilibriuiii since these data result from interpolation of Compn., W t . Sp. Volume, Fugacity. Constant the direct,ly measured quantities. The locus Pressure, Fraction Alethane Cu. F t . / L b . Lb./Sq. In. ______ AlethTemp., Lb./ F, ,qq, In, Liquid Gas Liquid Gas Alethane ,?-Butane ane Butane Of the factor corresponding 102,3 23,05 0000 to the critical state is shown, and this curve 120.99a 0 0 0.03090 0 . 7 7 4 3 1(io 150 0.0025 0 . 0 5 4 3 0.03101 0.7123 2.7.91 100.5 19.27 0.8353 is cofisistent with the compressibility factor for 200 0.0068 0,1303 0 . 0 3 1 2 3 0 6254 7 0 . 5 1 97.13 14.48 0.6648 9.333 0 4957 n-butane at the critical state which was calcu160.3 92 2 :300 0.0165 0 . 2 3 8 7 0.03168 0 5021 4 0.4187 249.1 87.1 7 . 0 1 8 0.4142 lated from the measurements of Beattie (1). 337.1 8 2 . 5 5 . 6 2 4 0.3681 4 0.3575 4 . 8 9 2 0.3418 The specific volumes of the coexisting liquid 600 0.0469 0.4030 0.0:3318 0.3097 422.3 78 8 8.516 0.3236 800 0.0691 0 . 4 4 6 5 0 . 0 3 4 4 3 0.2400 58.5 73 lj 1000 0.0943 0 . 4 6 2 8 0.03588 0,1908 742 70 4 2 . 7 8 9 0.3332 and gas phases are recorded as a function Of 1200 0.1210 0 . 4 6 5 5 0.03772 0.1545 890 68.5 2 . 2 8 8 0.3605 state in Table I. It is believed that the tabu1250 0.1285 0.4K48 0,03828 0.1470 927 68.2 2 . 1 7 8 0 3696 1400 0 . 1 5 0.4567 ~ 0.04038 0 . 1 2 4 8 1027 67 4 1.894 0 4103 lated specific volumes of the liquid do not in0.1740 0 . 4 4 5 0 0 , 0 4 2 2 0 0 1134 1089 66 9 1.721 0.4500 1500 1 . 5 5 ~0 . j l 1 8 rolve uncertainties larger than 0.3 per cent, 66.ij 0 . 0 4 4 4 8 0.1001 1147 0 . 1 9 8 4 0 4255 1600 0.04747 0,08601 1202 W.4 1700 0 . 2 2 3 4 0.3959 1 . 3 7 9 0.6138 whereas the specific volumes of the dew-point, 1750 0.2466 0,3730 0 , 0 5 0 3 5 0,07807 1227 Cifj. 2 1 , 2 6 2 0,6926 1 103 0.8647 gas may exhibit uncertainties as large as 0.8 0 , 0 5 3 2 2 0 06663 1252 66.2 1800 0 . 2 6 6 5 0.3330 l8lOb 0 . 3 0 7 3 0.3073 0.06068 0.06068 1256 dti 2 1.000 1.0000 per cent, ~1~~~~ limits of uncertaintydo not 174.4" 0 0 0 . 0 3 2 6 3 0 5275 190 ::h: apply in the immediate vicinity of the critical 200 0,0022 0,0333 0:3274 0 , 4 9 g 6 800 0.0110 0 1357 0 . 0 3 3 2 2 0.4130 110.3 1 H 1 . 2 9 . 3 3 3 0.6640 st,ate since the specific yolumc is exceedingly 400 0.0202 0.2062 0 03371 0 . 3 4 9 6 1 9 7 . ~1 2 4 . 8 G.97.5 0 5534 .a..3.59 0.4910 sensitive to its environment under these circum300 0.0299 0 . 2 5 8 4 0 03425 0 . 3 0 2 4 284.0 119.8 0,0399 0 . 2 9 6 0 0 03454 0 . 2 6 4 8 3 6 7 . 5 11.5 8 4 . 607 0 4567 600 3 40.j 0 . 4 3 0 ~ stances. The pressure, t e m p e r a t u r e , and 0 0614 o.:341i 0.03622 0 20x2 52s 109.4 800 1000 0.0851 0 3610 0 03800 0 1668 677 104.3 2 66.5 0 439s specific \-olume at the critical state, the point 1200 0.1128 0 3638 0.04030 0 1345 822 101 8 2 13s 0 . 4 7 6 3 2 02.j 0 4904 of maximum pressure, antl the cricondentherm 8.57 100,.j 1250 0.1206 0 3627 0 04103 0 1278 0,1479 0.3534 0 0 4 3 7 5 0 1086 957 99 2 1 . 7 1 8 0 5490 1400 1702 :3406 (141i30 09636 1019 98 1 ti082 are presented as functions of compositioii i n 1.500 1ti00 0 19.57 0 : 3 1 i i j O.O4!)78 0 0830.5 1078 98.1 1 0 7072 Figure 8. Again 110 experimental points are 1650 0 210s 0 2 9 i . i 0 . 0 5 2 2 0 0 07498 1106 98 1 1.2:31 0 h061 I C ~ O R ~ 0.2.52.5 0 . 2 3 2 5 0 .oiioti,i 0 . 06065 1132 HS.0 1 , 0 0 0 1 ,0000 shown since these values result from graphical interpolation of the directly measured quanti2x13 j a 1S7.0 1 1 . 4 7 1.0000 0 0.03476 0.3604 0 0 320 49.13 180.2 9 ? H i 0 8,548 0 03306 0 3300 0.0049 0.0499 :No ties. The information presented in Figure 8 is 135.3 1 7 1 . 3 6 . 8 2 2 0 7095 0.03566 0.2861 0 0136 0 1169 500 S .:3ii0 0 (i291j 2 2 2 . 1 lii4.3 0.03133:3 0 2499 0 0229 0 . 1 6 8 6 recorded in Table 11. .IO0 4 . 8 8 8 0 583s 3 0 7 . 9 160 3 0 03708 0 . 2 2 1 0 0 . 0 3 2 8 0 2030 000 The gas-liquid equilibrium constants ( K = 4 6 9 . 4 1.56,3 3 1.74 0 5519 0 08885 0 17.51 0.0543 0 2468 300 1.54.5 616 2 . 3 9 1 0 5716 0 04118 0.1393 0.0784 0 2623 1000 !/, x) for methane and n-butane mere computet1 153.8 1.8ti4 0 6304 756 0,04438 0.1099 0.1063 0.2610 1200 789 153 8 1.7413 0 6520 0.04.730 0.1033 12.50 0 1145 0 2586 from the composit.ions of the coexisting phases, 153.8 1 . 6 4 4 0 6779 S22 0 . 2 5 4 5 0 04(i32 0 09682 0 1227 1300 885 154.1 1 . 4 0 0 0 7433 0,04960 0.08371 and are recorded as a function of state in 1400 0.1457 0 2425 91: 154.2 1 . 2 9 5 0.7990 0.05159 0 07661 0 1575 0 . 2 3 2 2 14.50 Table I. The equilibrium constantsfor methane 134.4 1 . 1 4 0 0 8852 0.05.-,33 0.06789 944 0 1768 0 . 2 1 8 4 1500 955 l54..5 1.000 1.0000 0.06160 0.06160 0 1980 0.1950 I.520b are presented as a function of pressure in Fig239.1 0 03797 0 2417 0 8 099 1 0000 330 4" 0 0 250 ure 9. In this instance the product of the 6 520 0 8776 0 03860 0 . 2 2 2 5 Js 96 2 2 8 . 3 400 0.0061 '0 0436 141:9 2 1 7 . 5 equilibrium constant and the pressure was ern.5 018 0 . 2 7 6 2 0 039tiO 0 . 2 1 4 3 0.0162 0 0905 io0 4.008 0 . ,204 0 04068 0 1756 224.6 210.5 ti00 0.02.50 0 1250 pluyed to allom the representation of this vari2 . 7 8 1 0 6906 0.04345 0 1388 3 9 5 . 3 203 2 800 0.0471 0 1636 547 202.7 1.975 0.7270 0 04712 0 . 1 0 7 6 1000 0,0719 0 . 1 7 3 9 able on a somewhat larger scale than mould 203.5 617 1 . 6 2 8 0 7669 0 . 0,5049 0 ,09344 0.0900 0.1720 1100 205.2 be possible otherwise. At the critical state 684 1.3.58 0 84.53 0.0.5425 0,07836 1200 0.1067 0.1610 716 205.9 1 , 1 4 7 0.9256 0,05868 0.06886 1250 0.1243 0 1 4 7 4 the equilibrium constants for all components 206.3 725 1.000 1.0000 0.06297 0.06297 1264b 0.1345 0.134.5 are unity. Therefore, the locus of the critical Vapor pressure of n-butane. b Critical pressure of system at t h e temperature in ouestion. states in Figure 9 is a straight line characterized by $le numerical equality of the ordinate and ahscissa. Values of the equilibriuin constant for methane interpolated from the The compositions of the coexisting phases are recorded in measurements of Nederbragt (12) antl Bowman ( 3 ) are included on this diagram. I n general, the agreement is fairly Table I as a function of pressure and temperature. It is satisfactory. believed that the experimental results were obtained with sufficient accuracy and the graphical interpolation made with The equilibrium constant for n-butane is also shown as afunction of pressure for the several temperatures in Figure 9. This such precision that no uncertainties in the mole fraction equilibrium constant at each temperature has a value of unity greater than 0.005 are to be expected except in the immediate vicinity of the critical state where detailed experimental at the vapor pressure of n-butane, and decreases to a minimuin investigations by the methods employed are difficult. and again becomes unity at the critical pressure of the system The specific volume of the bubble-point liquid is presented at the temperature in question. Sederbragt's (12) and in Figure 6 as a function of composition for the temperatures Bowman's (;7) valuez for n-butane are included on this diagram. investigated experimentally. The agreement of the individual experimental points with the smooth curve was well within the u n c e r t a i n t y of measurement. These TABLE 11. PROPERTIES O F h ~ E T H I X E - ? L - B U T \ X E SYSTEM IN THE C R I T I C 4 L REGIOS bubble-point states were determined from TABLE I.
(Concluded)
IL-
0
,:,,,:$A:
"
0
'
factory agreement between the specific volume of the bubble-point liquid and the specific volume of liquid n-butane (20). The compressibilit,y factor for the clewpoint gas is presented as a fuiiction of p r e s s u r e in F i g u r e 7 . Data for t h e
0 10 20 30
3 60 70
305 ti2 266.0 217.7 163.9 110 1 .59.2
,550.7 1093 15.37 i m 1901 1924
...
..
...
...
0 07113 0.0613 0.0615 0.0603 0.0609 0.0628
...
...
62 273 5 240.4 209.5 150.0 151.1 122.3 91.9
55:) 7 S57 104s 1129 1158 1153 1141 1044
0.07113 0.09093 0.1107 0.1298 0.1487 O.lti87 6.lY.E 0.222.3
305.63 244.;7 186.8 1.37 5 97.9 tjl.2
.. ,
,
550 7 1181 1622 1835 1906 1924 ,
.,
. ,
0.07113 0 0304 0.0496
o.o.izti 0.0577 006:32
.. .
..
,
1090
INDUSTRIAL AND ENGINEERING CHEMISTRY
VOL. 32, NO. 8
coexists may be evaluated in the present case by rewriting Equation 3 in the following form: 0.0
The solutioii of Equation 4 for each component requires information concerning the partial volumetric behavior of methane and n-butane in the 0.7 gas phase of the methane-n-butane system throughout the pressure interval from infinite attenuaItion t o dew point. This information, which is 0.0 available but not yet published, has been employed li t o evaluate the fugacities of the components in the N bubble-point liquid and dew-point gas which are recorded for a number of states in Table I. 0.5 The pressure-composition diagram of Figure 4 shows t h a t the fugacity of the dew-point gas cannot be obtained by the direct solution of Equation 0.4 4 except a t pressures below the cricondentherm pressure. The fugacity fdrk of the components of the dew-point gas along the boundary curve from 0.3 the cricondentherm t o the critical state was established by the extrapolation of the quantity f h / E k P under isobaric, isothermal conditions from states 250 500 750 1000 1250 I500 1750 in the gaseous region t o the phase boundary. I n PRESSURE LB. P E R sa. IN. most cases this extrapolation could be made with only little uncertainty, since the change in the COMPRESSIBILITY FACTOR FOR DEW-POINT GAS FIGURE 7. quantity f k / E k P with composition under isobaric, isothermal conditions was small in the easeous region. It is believed t h a t this procedure e s t a k s h e d the Attempts were made (14) t o correlate the phase behavior of fugacity of the components in this part of t h e two-phase methane by the use of equilibrium constants. The d a t a region with greater accuracy than could be obtained b y available indicated t h a t there was a regular Drogression in t h e equilibrium constant of methane with rei spect t o the molecular weight of the less volatile 9 0.20 component from a homologous series. Figure a 10 presents the equilibrium constants for D methane in a number of binary paraffin hy+. 0.15 drocarbon systems at 160' F. The experi5 mental points correspond t o the behavior of W methane i n t h e m e t h a n e - p r o p a n e ( I 7 ) , I methane+-butane, methane-n-pentane @ I ) , 2 0.10 0 methane-hexane (8, 15), methane-decane (18) systems. It appears possible, therefore, t o u predict roughly the phase behavior of methane :k: 0.05 VI a in paraffin hydrocarbon systems of relatively low molecular weight, so long as pressures approaching the critical pressure of the system 300 . 1750 involved are not encountered. 0.8
>
I
------t
2
/
Fugacity The fugacity of a component in a phase is a measure of its escaping tendency (9),and therefore the fugacities of each. component in each coexisting phase are equal (IO). I n the present instance i t is convenient t o determine t h e fugacities of the components in the coexisting phases from a consideration of the volumetric behavior of the system. It has been shown (18) t h a t the fugacity is related t o the residual partial specific volume in the following way:
I
250
I
I
2 I500
F K w
2
200
I250
w cc
I-
w a
2 w
r;
a I 000
I50
w
3 VI
IO0
0.I
0.2
WEIGHT
The fugacity of a component in the dew-point gas or in the bubble-point liquid with which i t
I
0.3
0.4
FRACTION
0.5
0.6
METHANE
FIGURE 8. EFFECTOF COMPOSITION UPON PRESSURE, TEMPERATURE, AND SPECIFIC VOLUMEFOR THE CRITICAL STATE,THE CRICONDENTHERM, AND THE POINTOF MAXIMUM PRESSURE
AUGUST, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
1091
tion yields the following relation for each component of a binary system under isothermal conditions :
(6)
A combination of Equations 5 and 6 when applied t o a binary system results in the equation:
For the purposes of calculation it is convenient to rewrite Equation 7 as:
1 2.3026 P
PRESSURE
FIGCRE 9.
LB. P E R 59. IN.
E Q U I L I B R I r M CONSTANTS FOR
?*fETHANE AND n-BUTANE
appropriate integration through the two-phase region. However, values obtained from a consideration of the behavior of the system in the two-phase region yielded results which were in substantial agreement with those obtained by extrapolation of the single-phase values. The fugacities of methane and n-butane in the coexisting liquid and gas phases are recorded in Table I. It is believed t h a t t h e values at pressures below the cricondentherm pressures do not involve uncertainties greater than 1 per cent. However, in the immediate vicinity of the critical state somewhat larger uncertainties are involved. The ratio of the fugacity of methane t o the pressure is shown as a function of pressure for several temperatures in Figure 11. This ratio does not vary greatly with pressure in the regions where there is a small isothermal change in the composition of the dew-point gas with pressure. Figure 12 shows the variation in the fugacity of n-butane in the two-phase region of the methane-n-butane system as a function of pressure for several temperatures. The escaping tendency of n-butane does not change greatly with pressure. Thermodynamics affords a means of ascertaining the consistency of values of the fugacity or of the chemical potential of the components of a binary or multicomponent system (6). I n the case of isobaric, isothermal changes in state for a binary system the following equation (11) is applicable: (5)
(8)
Equation 8 affords a direct means of ascertaining the consistency of the fugacity data presented in this paper. This equation was applied to the data a t 130" F. and indicated consistency within approximately 1 per cent in the rate ,of chanBe of the logarithni of the fugacity of the codponent with pressuke for states a t pressures below t h a t of the criconl
bSLE?ULAR
W'E I G H T
FIGURE 10. EQUILIBRIUM CONSTANTS FOR METHANEAS A FUNCTION OF MOLECULAR WEIGHT& &E LESSVOLATILE COMPONEXT I N BINARY , PAR.4FFIN HYDROCARBON SYSTEMS AT 160" F. i
dentherm. At higher pressures inconsigtenciks ak large as 5 per cent were encountered, b u t these were not unexpected since the uncertainty in estabI#@g ,the fuga,cities in this region was much larger. The evaluation of the fugacity of the ,Components as a function of state for a variety of systems may afford a useful approach to the prediction of the phase bebflvjor I$ simple PI
The fugacities recorded in Table I involve both changes in pressure and composition a t a constant temperature. Under these circumstances the general equation of partial differentia-
2.3028 biT
,'1
1092
INDUSTRIAL A h D EUGINEEAING CHEMJSTRY VOL. 32, NO. 8 = residual partial specific volume, cu. ft./lb.
mole fraction of component in bubblepoint liquid = mdle fraction of component in dew-point
-x
=
y 111
log
= =
gas
natural logarithm common logarithm
Subscripts 1 = methane
2 = n-butane b = bubble point
d = dew point d, = retrograde dew point k = either component
Literature Cited (1) Beattie, Simard, and Gouq-Jen Su, J . A m . Chem. Soc., 61, 24, 26 (1939). (2, Boomer and Johnson, Can. J . Research, B16, 328 (1938). (3) Bowman, Calif. Oil W o r l d , May, 1938. (4) Cummings. Stones, and Volante, IsD.. Ex-o. CHEX, 25, 728 (1933). ( 5 ) Duhem. J . Phys. Chem., 5, 91 (1901). (6) Gibhs, Collected Works o f , Xew York, Longmans, Green and Company; 1931. PRESSURE La PER 59. IN. (7) Kuenen, “Verdampfung und Verflussigung von Gemischen”, Leipaig, Barth, 1906. (8) Kvalnes‘ and Gaddy, J . Am. Chem. Soc., 53, OF PRESSURE UPON THE FUGACITY OF METHANE IN THE FIGURE 11. EFFECT TWO-PHASE REGION 394 (1931). (9) Lewis, PTOC.Am. A c a d . A r t s Sci., 37, 49 (1901). (10) Lewis and Randall. “Thermodynamics and Free Energy of and complex hydrocarbon mixtures. It must be realized Chemical Substances”, p. 206, New York, McGraw-Hill that the fugacity of each component is a function of the state Book Co., 1923. of the phase in which i t is found, but we believe that it may cll) I h i d , , p , 209. (121 Nederhragt, ISD. ESG. C m x , 30, 587 (1938). offer a simder means of correlating behavior than is likely t o result from the use of equilibrium constants which depend upon the states of all of the phases involved. Additional experimental information must be accumulated before i t will be possible to ascertain how great may be the usefulness of fugacity in the prediction of the behavior of hydrocarbon mixtures.
Acknowledgment This work has been carried out as a part of the activities of Research Project No. 37 of the American Petroleum Institute, and we wish to express our appreciation for financial assistance. J. V. Reynolds assisted with the experimental program, and R. A. Budenholser, Louise M. Reaney, and L. F a y Prescott assisted with the extensive numerical calculations associated with the preparation of the experimental data.
loo’ 7 0’
250
b
f
K 7~
2 P
T I’ 5’”
-
J7
+’
specific gas constant (universal gps constant/mol. weight) = fugacity, lb./sq. in. = equilibrium constant = weight fraction = mole fraction = pressure, lb./sq. in. abs. = thermodynamic temperature, O F. abs. = specific volume, cu. ft./lb. = specific volume in two-phase region, cu. ft./lb. = residual specific volume, cu. ft./lb. = partial specific volume, cu. ft./lh.
750
PRESSURE
FIGURE
Nomenclature
500
12.
IO00
LB. PER
I250
1500
1750
SP. IN.
EFFECT O F PRESSURE UPON THE FUGACITY O F n-BUT.4NE TWO-PHASE REGION
IN THE
=
(13) Sage and Lacey, Am. Inst. Mining Met. Engrs., Tech. Pirb. 1127 (1939). (14) Sage and Lacey, ISD.EXG.CHEM..26, 103 (1934). (15) Ibid., 30, 1296 (1938). (16) Ibid., 31, 1497 (1939). (17) Sage, Lacey, and Schaafsma, Ibid., 26, 214 (1934). (18) Sage, Lavender, and Lacey, Ibid., 32, 743 (1940). (19) Sane. Webster. and Lacey. Ibid., 29, 658 (1937). (20) Ibid., 29, 1188 (1937). (21) Taylor, U’ald. Sage. and Lacey, Oil Gas J . . 38, S o . 13, 16 (1939).
