Superbars denote parrial molar quantity-e.g.,
-
Gi
dG bni
= -
Superscripts co = critical phase composition 0 = pure substance ’ = first liquid phase ” = second liquid phase
literature Cited (1) Bachman, Irvin,
END.CHEM., ANAL.ED. 12, 38 (1940). SOC. (London) 1938, p: 70. University of Michigan, Ann Arbor, Mich., 1959. (4) Gibbs, J. W., “The Collected Works,” Vol. I, pp. 129-34, Longmans, Green, New York, 1928. (5) Haase, Rolf, “Thermodynamik der Mischphasen,” 1st ed., pp. 66-70, 86-91, 135-83, Springer-Verlag, Berlin, 1956. IN13.
(6) Marmles. M.. Sci. Bull. Akad. Wiss. Wien. Math. Naturw. Kl. ’ ’22, l O i , 1243 (1895). (7) McCants, J. F., Jones, J. H., Hopson, W. H., IND.END. CHEM.45,454 (1953). (8) Olsen, A. L., Washburn, E. R., J . Am. Chem. SOC.57, 303 (1935). (9)’ Odmer, D. F., Tobias, P. E., IND. ENC.CHEM.34, 696 (1942). 10) Redlich, O., Kister, A. T., Zbid., 40, 341 (1948). 11) Redlich, O., Kister, A. T., Turnquist, C. E., Chem. Eng. Progr., Symfosium SET.48,No. 2, 49 (1952). (12) Satterfield, C. N., Powell, J. H., Oster, E. A., Noyes, J. P., IND.ENC.CHEM.47, 1458-62 (1955). (13) Treybal, R. E., Weber, L. D., Daley, J. F., Zbid., 38, 817 (1946). (14) Van Laar, J. H., Z . phys. Chem. 185, 35 (1929). (15) Wegstein, J. H., “Accelerating Convergence of Iterative Processes,” Natl. Bureau of Standards, Washington, D. C. RECEIVED for review March 13, 1961 ACCEPTEDOCTOBER 3, 1961
THE CRITICAL TEMPERATURES OF TERNARY HYDROCARBON SYSTEMS R O B E R T B. G R I E V E S AND G E O R G E THODOS The Technological Institute, Northwestern University, Euanston, Ill.
experimental investigation concerned with the critical pressures of a ternary hydrocarbon system ( 3 ) , it was found that a simple pattern existed for the critical temperatures of the various mixtures comprising this system. This pattern consisted of straight lines when parameters of constant critical temperature were plotted on a triangular composition diagram of which the three sides were formed by the three binaries comprising the ternary system. These straight lines intersected the sides of N A RECENT
I critical temperatures and
the triangle a t the binary system compositions corresponding to the particular critical temperature parameter. Thus on such a diagram, each straight line connected all of the ternary compositions corresponding to a given critical temperature and the two compositions of the two binary systems having the same critical temperature. T h e detection of this behavior suggested a review of the available critical temperatures of other three component systems. Triangular composition diagrams were plotted for the
Methane Methane
A obtained from dato on ternary system
/
Propane
v
v
v
Y
v
v
v
v
v
\Ethane
flole Fraction
Mole Fraction
Figure 1. Critical temperatures of the methane-ethanepropane system (8)
Figure 2. Critical temperatures of the methane-ethanen-butane system (3) VOL. 1
NO. 1
FEBRUARY 1962
45
The critical temperature and critical pressure studies on system 13) revealed that the
the methane-ethane-n-butane
parameters of constant critical temperature on a triangular composition diagram were straight lines and represented the critical temperatures of the ternary system and the corresponding set of binary systems.
Thus, two different
binary compositions and all intermediate ternary compositions corresponding t o the same critical temperature ore connected by a straight line having a parametric value of that critical temperature.
This property has been tested by using the limited number of critical temperatures available in the literature for ternary systems, together with their corresponding binary systems.
By applying this method to 29 ternary composi-
tions critical temperatures were calculated that deviate b y
0.93%.
This behavior,
associated
with ternary systems,
appears to be a characteristic property and enables the prediction of their critical temperatures.
following six hydrocarbon systems for which experimental values were available in the literature: methane-ethane-propane ( 8 ) methane-ethane-n-butane ( 3 ) methane-ethane-n-pentane (7) methane-propane-n-butane ( 75) methane-propane-n-pentane ( 4 ) methane-n-butane-n-decane( 72, 73) These diagrams appear as Figures 1 through 6. In Figure 6, the two compositions corresponding to a critical temperature of 280" F. were obtained from reference (12). Each straight line plotted on these diagrams was drawn by connecting the pair of points corresponding to the two binary system compositions having the same critical temperature. Thus in Figure 5, the line with the indicated critical temperature of 225' F. was drawn by connecting the point with binary composition,
65.7 mole 70 methane, 34.3 mole % n-pentane, having t, = 225' F., and the point with binary composition, 93.6 mole 7, propane, 6.4 mole % n-pentane, also having t, = 225' F. Only two of the three possible binary systems for each ternary may have the same critical temperature, although the entire range of composition is included for each binary. The binary system containing the heaviest and the lightest components includes all of the critical temperatures of the ternary. Data for the eleven required binary systems were obtained from these sources (2, 5-7, 9-77, 74, 16-78). The reported literature values for the various ternary compositions are included in these figures on the composition coordinates and the critical temperature is designated for each point. The critical temperatures corresponding to the 29 ternary compositions presented in the six figures are reproduced quite well by the straight-line parameters connecting the binary systems. Some irregularities in the ternary data are to be expected. Except for the methane-ethane-n-butane system, the critical data have been reported as part of vapor-liquid equilibrium studies, and most of the values were obtained by indirect methods. The behavior of the hydrocarbon mixtures which have been investigated introduced the possibility of using this linear property to predict the critical temperatures of all ternary systems containing hydrocarbons. T o establish these values, only the data for the corresponding binary systems would be required. KO pseudocritical properties, average boiling points, average molecular weights, or equilibrium bubble points and dew points would be needed. Two approaches to the determination of such critical temperatures may be useful. The first is graphical and involves the establishment of the straight-line temperature parameters on ternary composition diagrams. For any mixture under consideration these linear parameters, obtained from binary data, establish the critical temperature for the given ternary composition. T h e second approach, although more exact, involves a trialand-error procedure. T h e triangular composition diagram may be translated to rectangular coordinates perpendicular to each other in the same manner as is done for liquid-liquid and solid-liquid extraction problems. The resulting x and y axes, both including the range of values of 0 to 1, represent two of
Methane
A
0
obtained from data on binary systems from data on ternary system
I obtained
/
v
n-Pentane
v
v
v
Mole
v Fraction
v
v
v
\
~ Ethone
Figure 3. Critical temperatures of the methane-ethane-npentane system ( I )
46
I&EC FUNDAMENTALS
/vvVVVVVVV\
n-Butane
Propane
Mole Fraction
Figure 4. Critical temperatures of the methane-propane-nbutane system ( I 5)
Methane
Methone
A
/
\
'
obtained from dato an binary syrtems obiained from data on ternary system\\
\\
/vvvvvvvv Propane
n-Pentane
Mole Fraction
Figure 5. Critical temperatures of the methane-propanen-pentane system (4)
the binary systems involved. T h e third binary is represented by the hypotenuse joining the two axes. O n such a diagram, the linear temperature parameters are described by the equation
where m and b are constants. The calculation procedure is then as follows: A temperature is assumed for the given ternary mixture, and the two binary compositions corresponding to this temperature are obtained from binary data; these two points then serve to establish the constants m and b in Equation 1 ; if the resulting equation is satisfied by the values of x and y corresponding to the composition of the given ternary mixture, the assumed value is the correct critical temperature; if this equation is not satisfied. a new temperature is assumed and the procedure is repeated. T o illustrate this method of calculation the following example is presented.
Example. Determine the critical temperature of a ternary mixture having the following composition : Mole Fraction 0.480 0.265 0.255 1.000
Methane Propane n-Pentane Total
-
A. Assume Critical Temperature of Mixture, t , = 225 F. Of the three binary systems to be considered, the methanepropane system may be eliminated since 225' F. is greater than the critical temperatures of pure methane and pure propane. T h e composition of the methane-n-pentane system with t, = 225' F. is 0.659 mole fraction methane and 0.341 n-pentane, while the composition of the propane-n-pentane system is 0.933 mole fraction propane and 0.067 n-pentane. Using Equation 1 in which y represents the methane content and x represents the propane content, for the two binary systems,
+b 0.000 = m(0.933) + b
0.659 = m(O.OOO)
Solving these equations, it is found that m = -0.706 and b = 0.659. Thus the linear temperature parameter corresponding to 225' F. is represented by Y ==
-0.706~
Table 1.
+ 0.659
Comparison of Reported and Calculated Critical Temperatures
Critical Temperature, F. Mole Fraction Reptd. Calcd. 7 0 Dev.O Methane-ethane-propane:( 8 )
(1)
y=mx+b
and
Figure 6. Critical temperatures of the methane-n-butanen-decane system ( I 3)
C1
CZ
CI
0.834 0,800 0.720
0.130 0.039 0.158
0.035 0.161 0.132
-48
-50 0 0
10
0.49 1.96 2.17
178 133 125 129
0.00 0.67 0.00 1.03
96 96
0.71 0.71
102 109 115 121
0.36 1.61 2.68 3.75
163 220
0.48 0.00
9
Methane-ethane-n-butane ( 3 ) C1
0.193 0,391 0.007 0.040
0.470 0.354 0.879 0.821
C1
cz
c,
0.461 0.196
0.443 0.758
0.095 0.045
C1
cs
c4
0.690 0,666 0,630 0,587
0.075 0.115 0.185 0.278
0.235 0.219 0.185 0.135
C1
CB
cs
0,531 0.480
0.348 0.265
0.121 0.255
0.337 0.255 0.114 0.139
178 137 125 123
Methane-ethane-n-jentant
7)
100 100
Methane-propane-n-butane
75)
100 100 100 100
Methane-propane-n-pentane ( 4 )
160 220
( 72, 73)
Methane-n-butane-n-decane
CI 0.802 0.700 0.535 0,808 0.674 0.342 0.680 0,501 0.711 0.522 0.559 0.379 0.509 0.428 a Based on
c 4
c 1 0
0 081 0 200 0 400 0 041 0 196 0 527 0.130 0.300 0.060 0.192 0 090 0 249 0 099 0 115
0.117 0 100 0 065 0 151 0 130 0 131 0.190 0.199 0,229 0.286 0.351 0 372 0 392 0.457
273
260
580
272 274 320 320 357 385 402 425 466 508 512 527 548
280 31 7 322 371 387 41 9 421 474 507 51 1 522 545
1.77 1.08 0.81 0.39 0.26 1.69 0 24 1.93 0.45 0.86 0.10 0.10 0.51 0.30
degrees absolute.
VOL. 1
NO. 1
FEBRUARY 1962
47
To check the estimated critical temperature, the ternary composition is substituted to obtain 0.480
? =
-0.706 (0.265)
+ 0.659
0.480 # 0.472
B. Assume Critical Temperature of Mixture, t , = 220' F. Following the same procedure, the compositions of the two binary systems for t , = 220 ' F. are found to be : Mole Fraction 0.666 0.334
Methane n-Pentane Total
1.ooo
Propane n-Pentane Total
Mole Fraction 0 950 0,050
I.000
These compositions produce values of m = -0.701 and b = 0.666 and the resulting linear temperature parameter corresponding to 220' F. is represented by y = -0.701~
+ 0.666
Again substituting the ternary composition, the following result is obtained 0.480
? =
-0.701 (0.265)
0.480
=
0.480
+ 0.666
Therefore, the assumed value oft, = 220' F. is the predicted value for this mixture. For this particular ternary composition Dourson, Sage, and Lacey ( 4 ) report a critical temperature of 220' F. T h e comparisons presented in Table I produce an average deviation of 0.93% for 29 ternary mixtures for which critical temperatures are reported. A maximum error of 3.75% is encountered for one of the compositions of the methanepropane-n-butane system. These results appear to be quite satisfactory particularly since several selected compositions from the widely boiling methane-n-butane-n-decane system are included. Most of the critical temperature correlations presented
in the literature are unable to predict accurately the critical temperatures of systems having widely boiling components. Also many of these correlations are based entirely on binary data and cannot predict critical temperatures for ternary systems with a comparable degree of accuracy. The possibility of the extension of this method to mixtures including olefins, naphthenes, aromatics, and nonhydrocarbons as components has a good deal of promise, once such ternary data become available.
literature Cited (1) Billman, G. TY., Sage, B. H., Lacey, LV, N., Trans. Am. Inst.
Mzning Met. Engrs. 174, 13 (1948).
iZl Bloomer. 0. T.. Gami. D. C.. Parent, J. D.. Institute of Gas Technology Research Bull. 22,' Technology Center, Chicago, Ill., July 1953. ( 3 ) Cota, H. M., M.S. thesis. Northwestern University, Evanston, Ill., 1960. ( 4 ) Dourson, R. H., Sage, B. H., Lacey, W. N.. Trans. Am. Inst. Mtnzng Met. Engrs. 151, 206 (1943). ( 5 ) Kay. W. B., IND.ENG.CHEM.32, 353 (1940). ( 6 ) Matschke, D. E., Ph.D. dissertation, Northwestern University, Evanston, Ill., 1962. (7) Nysewander, C. N., Sage, B. H., Lacey, TY. N., IND.ENC. CHEM.32, 118 (1940). (8) Price, A. R., Kobayashi, Riki, J . Chem. Eng. Data 4, 40 (1959). (9) Reamer, H. H., Olds, R. H., Sage, B. H., Lacey, TV. N., IND.ENC.CHEM.34, 1956 (1942). (10) Reamer, H. H., Sage, B. H., Lacey, TV. N.,Ibtd., 38, 986 (1946).
(iij-zdi.,42,534
(1950). (12) IEid., 43, 1437 ( 1 9 5 1 ) . (13) Zbid., 44, 1671 (1952). (14) Reamer, H. H., Sage, B. H., Lacey, M:. N., J . Chem. Eng. Data 5, 44 (1960). ( 1 5 ) Rigas, T. J., Mason, D. F., Thodos, George, Ibid., 4, 201 (1959). ( 1 6 ) Sage, B. H., Hicks, B. L.: Lacey, TV. N., IND.ENG.CHEM. 32, 1085 (1940). (17) Sage, B. H., Lacey, W. N., Zbid., 32,992 (1940). (18) Sage, B. H., Reamer, H. H., Olds, R. H., Lacey, 1%'.N., Zbid., 34, 1108 (1942).
RECEIVED for review May 8 , 1961 ACCEPTED December 6 , 1961
MIXING WITH A N ELECTROSTATIC FIELD W . P. CROPPER A N D H. S. S E E L l G Research and Development Department: American Oil Co., Whiting, Znd.
electrostatic fields can be used but more attention has been given to separation techniques. Precipitators are commonly used for air purification and smoke abatement. T h e separation of solid or liquid particles from a continuous liquid phase has also been accomplished by electrical methods. Polarization and movement of macroscopic particles in a nonuniform electrical field-called dielectrophoresis-has been used to separate poly(viny1 chloride) suspended in a mixture of carbon tetrachloride and benzene (7, 8). Water-in-oil emulsions formed during the water-wash step following such refinery operations as acid treating and desalting have been N A MACROSCOPIC SCALE,
0 either to separate or to mix substances,
48
l&EC FUNDAMENTALS
broken. Apparatus for electrical treatment of emulsions ( 3 ) and a process for desalting mineral oil (7) have been patented. O n the other hand, dispersions can be produced by applying a voltage across a boundary between electrolytes (2). I n the only commercial process, an emulsion of HzS04 in naphtha is subjected to a n electrical field to promote agitation of the acid particles in the oil, but for successful operation the phases must be mechanically premixed (6). O n an atomic scale, the dipole moment is a physical property that can be used to separate molecules. In nonhomogeneous fields, the electrical force moves polar molecules toward regions of maximum nonhornogeneity. Karagounis ( 5 ) showed
