July, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
Acknowledgment The writer wishes to thank C. L. Lovell, professor of Chemical Engineering, Purdue University, for advice and criticism, and C. S. Robinson and E. R. Gilliland for permission to use their problem.
Nomenclature = mole fraction of a component in liquid = mole fraction of a component in vapor = number of a plate above feed counting down from top
x g
n
(contrary t o usual practice but used here because that is the direction of the computation)
6.
=
reflux ratio, 0
D
=
a43
0,
~
Vm
- On
Vm
b, =
O m - Vm P = vapor pressure of a component T
= absolute pressure in still, same unit as P
XD, xw =
K
=
mole fraction of a component in distillate and bottoms, respectively
(in equilibrium); ?Tr! (when Raoult’s law is obeyed)
B, T,X = benzene, toluene, xylene, respectively
m = number of a plate below feed, counting up from first
plate above still D = moles of distillate withdrawn as overhead product, per unit time W = moles of bottoms withdrawn per unit time Vn,V,,, = total moles of vapor passing from one plate to the next, per unit time, above and below feed plate, respectively O,,, Om = total moles of overflow from one plate t o the next, per unit time, above and below feed plate, respectively
Literature Cited (1) Hibshman, IND.EN*. CREM.,32,988 (1940). (2) Lewis and Cope, Ibid., 24, 498 (1932). (3) Lewis and Matheson, Ibid., 24, 494 (1932). (4) Robinson, C. S.. and Gilliland, E. R., “Elements of Fractional Distillation”, New York, McGraw-Hill Book Co., 1939. (6) Sorel, “La rectification de l’alcool”, 1893. (6) Walker, Lewis, McAdams, and Gilliland, “Principles of Chemical Engineering”, New York, McGraw-Hill Book Co., 1939.
Critical States of Two-Component Paraffin Svstems J
Empirical correlations of literature data are presented by means of which critical temperatures, pressures, and compositions of two-component normal paraffin hydrocarbon systems can be predicted. Values calculated by means of these correlations are compared with existing published data on ten systems. Disregarding positive and negative signs for the errors, and excluding two systems, the average error for the calculated pressures is 13 pounds per square inch or 1.3 per cent, and the average error for the calculated temperatures is 6.4’ F.
HE past decade has seen considerable compilation of data on the phase behavior of multicomponent hydrocarbon systems. From the standpoint of the engineering profession, probably the most needed of these data have been volumetric and vaporization equilibrium data on the compounds found in the mixtures encountered in oil and gas production and in petroleum refining. Knowledge of the critical states is of prime importance in such studies, particularly in work on vaporization equilibria. The purpose of this paper is to present empirical correlations by means of which the critical states of two-component normal paraffin hydrocarbon systems can be predicted. The critical state has been defined by Gibbs (W) as that state of a system at which all distinction between the two coexistent phases vanishes. A one-component system has only one critical state, whereas a multicomponent system has
T
1
Present address, The Dow Chemical Company, Midland, Mich.
F. DREW MAYFIELDl Phillips Petroleum Company, Bartlesville, Okla. an infinite number of critical states. Confining our attention to binary normal paraffin hydrocarbon systems, it is to be noted that all critical temperatures of such mixtures lie between the critical temperatures of the two pure components; the critical pressures of the mixtures may be far in excess of, or even many t i e s the critical pressure of either of the two pure components. This is readily apparent from Figure 1. For a more detailed discussion of phase behavior of multicomponent hydrocarbon systems, work such as that of Sage and Lacey (I?‘) and of Katz and Kurata (6)should be consulted. Previous means of predicting critical states of multicomponent systems have been reported by Roess (IS) and by Smith and Watson (10). These two correlations were developed for complex petroleum hydrocarbon fractions, and no attempt has been made here to compare the accuracy of these previous methods with that of this paper.
Data Selected The following systems are considered in this study: methane-propane ( I 8 ) , methane-n-butane ( I @ , methane-npentane ( $ I ) , methane-n-hexane ( I @ , ethane-n-butane (8), ethane-n-heptane (T), propane-n-butane ( I I ) , propane-npentane (167, n-butane-n-heptane (Q), n-pentane-n-heptane ( I ) . Direct experimentally determined critical states were reported for all of these systems except methane-+pentane and methane-n-hexane. Critical states for these two systems have been estimated from the published data by extrapolation of the reported bubble-point pressure-composition isotherms, the maximum pressure on such an isotherm being the critical pressure. This method of estimating critical pressures does not permit accurate estimations of critical state compositions. Furthermore, such estimated critical pressures should be accepted with some reservation until more data become available.
INDUSTRIAL AND ENGINEERING CHEMISTRY
a44 2000
1750
IW
3 1500
0 VI m
a
f 1250
d
rm v)
1 I
W
1000
a
3
v)
W
E
750
500
250 -eo0
-100
0
100
200 TEMPERATURE
-
300 OF.
400
500
600
Vol. 34, No.
I
the experimental critical temperatures with the calculated ones. No values for critical temperatures for the methane-pentane or the methane-hexane system were calculated, as the compositions could not be accurately estimated from the literature data. The poorest agreement between the experimental and calculated temperatures is found for the methane-butane and the ethane-heptane systems. The greatest error in the calculated value is for the mixture of 50 weight per cent butane in methane-namely, 35.6"F. Disregarding positive and negative signs for the errors, the average error for the calculated critical temperatures is 6.4" F. as reported in Table I. The calculated temperatures for all systems are found t o be generally higher than the experimental values. I n order t o demonstrate more clearly the extent of these greatest errors, Figures 2 and 3 present the calculated and experimental values of critical temperature for the methane-butane and the ethaneheptane systems as a function of weight
FIGURE 1. TEMPERATURE-PRESSURE PLOTOF CRITICALSTATESOF TwoCOMPONENT n-PARAFFIN HYDROCARBON SYSTEMS
Ruhemann and co-workers reported data on the methane-ethane (4, 1 4 ,methane-ethylene (4, and ethane-propylene (10) systems. Kone of these data were employed in this study. The critical data on the first two of these systems seem to be of questionable accuracy. The data on the ethane-propylene system appear t o be good but are not reported here because the correlations of maximum critical pressure deviation of Figures 6 and 7 fail for this system. Critical Temperatures The prediction of critical temperatures of hydrocarbon mixtures presents no serious problem and has generally been made by assuming the additive lam in some form. For the systems studied here, the additive law is found to be more accurate on a weight composition basis as expressed by Equation 1:
(1) This relation was employed by Pawlewski ( l a ) as early as 1882. Equation 1, on a weight per cent basis, is used in this study to compute the critical temperatures of the mixtures. Table I compares
TEMPERATURE- 'F OF POOREST AGREEMENTBETWEEN EXPERIMENTAL AUD CALCUFIGURE 2. EXAMPLES LATED VALUES
Abobe, ciiticrtl states of methane-n-butane system; below, critical states of ethane-n-heptane system.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Jdy, 1942
-
a45
TABLE I. COMPARISON OF EXPERIMIONTAL AND CALCULATED CRITICAL STATES wt. % of
System
CHrC4Hio (16)
CHrCsH19 ( $ 1 )
Heavy Component
Exptl. -116.5 50.7 88.0 115.3 138.7 159.6 178.2 195.8 206.3
-
in P' _ Calod. Error
...
+7.4 f4.4 +4.9 +4.6 1-3.2 +1.2 -2.0
...
....
...
-116.5 59.2 110.1 163.9 217.7 266.0 306.0
94.8 137.0 179.3 221.5 263.8
0
-116.5 100 160 220 387.0
... ... ... ... ...
-116.5 100.3 160 220 454.6
... ... ... ... ...
....
100
0
....
....
....
100
0 9.74 29.54 50.15 70.18 90.12 100
90.1 108.4 147.6 191.2 237.4 283.1 306.0
0 9.78 29.78 49.76 70.09 90.22 100
90.1 120.3 189.8 276.8 373.9 468 2 513.3
0 18.3 36.7 55.3 72.0 83.8 100
206.25 224.4 243.5 264.4 280.2 290.4 306.0 206.25 250.4 285.8 300.9 339.0 387.0
0 9.89 29.98 50.19 70.00 90.12 100
306.0 325.51 366.17 407.64 448.93 492.13 513.3
0 31.99 52.38 80.23 100
387.0 428.0 452.8 489.5 513.3
...
iii:i
153.9 198.4 241.6 284.7
...
i8i :5
216.1 300.7 386 7 471.9
...
22416 242.9 261.5 278.1 289.9
...
254:3 260.6 308.7 342.3
..
326:5 368.1 410.0 451.1 492.8
...
427:4 453.2 488.3
...
Average errorb
Exptl. P c Lb./Sq. ,;I
....
58.1 92.4 120.2 143.3 162.8 179.4 193.8
0 50 60 70 80 90 100
.... ....
CaHs-CIHie ( ff )
-------Tc
673 1468.1 1406.4 1291.8 1158.0 1018.4 890.6 765.7 617.4
....
673 1924 1901 1799 1537 1093 550.1
-35.6 -26.9 -15.4 3.8 2.2
--
...,
....
.... .. .. .. ..
673 2550" 2435" 21790 485.3
....
673 2880'1 2920" 2780a 435.3
.... .. .. .. .. I...
....
712 759.2 827.2 841.6 780.8 646.1 550.1
+2:7 +6.3 +7.2 +4.2 4-1.6
...,
....
+11.2 +26.3 +23.9 4-12.8 3.7
+. . . .
-0.6 -2.9 -2.1 -0.5
....
....
....
....
+1.0 fl.9 +2.4 +2.2 f0.7
....
.... -0.6
-t 0 . 4 -1.2
....
.... ....
1959 1903 1744 1446 1056
....
550.1 575.8 596.1 584.4 538.0 451.6 396.0 485.3 492.0 479.5 445.0 396,O
lb./sq. in.
....
-12.1 -11.4 7.8 -13.0 8.4 -15.6 -21.7
-
.... ....
+35
5-i - 91 - 37
.... .... .... .... .... ....
....
.... .... .... .... .... ....
.... ....
....
760:O 829.4 844.8 781.6 643.8
....
....
631 7 638.1 630.2 610.4 588.6
6Bi ' 664 662 602
804
....
6.36
-0.8 -1.7 -2.8
.... ....
4-1.8 f0.1 -3.1 -5.9 -3.4
....
.... .... .... , . . .
....
....
....
4-0.8 +2.2 +3.2 4-0.8 -2.3
....
+30.
5;; - 23
- 7
.... ...,
4-0.7 4-0.1 +0.2 4-1.4 +0.6
....
-3 -7 4-4 -6
-10.2 6.7 5.7 2.3
-
--
.... ....
+12.0 - 41 . 05
+
.... 12.6
7-Pc
Lb,/ aq. in.
Calod., Temp. Basis--
.... 1444
1382 1273 1149 1011 868 715
*. ....
1916 1932 1779 1441 1005
,...
....
....
481 44 1
-1.1
....
.... - 9.0
....
-0.8 -0.8 -0.6
....
....
...
....
....
....
.... 566.8
585.9 577.7 532.3 449.3
%
.... ....
.,..
....
617.4 664 671 648 608 485.3
+3.9 +4.8 1-7.8 +3.3
1458' 1395 1284 1145 1010 875 744
1151 1243 1083 675
617.4 631 638 630 609 588 550.1
f0.2
s q . In.
sso.
712 850 1132 1263 1106 682 396
....
--Lb,/P c Crtlcd., Wt. BaaisError, Error,
....
+0.1
+0.3
+0.4
+0.1 -0.4
....
....
....
2463 244 1 22.77
.... ....
2923 3037 2937
.... ....
761.1 833.6 848.4 785.8 645.7
.... .... 866.4
+3.5 +1.7 -1.6 -2.1 -1.0
1134 1265 1120 689.5
.... 4-0.1
.... 633.2
....
4-0.02 +0.03 +0.2 +0.1
640.9 628.7 606.9 587.4
....
.... 664.6
-0 5 -1 0 +0.6 -1 0
.... .... -1.6 -1.7 -1.1 -1.1 -0.5
.... .... +2.4
4-0.3 -0 9
*... 1.2
678.4 657.6 604.8
....
Error
Ib./sq.
-24 4 -18 8 9.0 7.4 -22.6 -50 7
-
..... ..... -
?-;A
9.0
96
-88 ...
...
I .
- 87
+ 6 +..... 58
.....
+ 43 4-117 +I57
..... .....
+1.!9
+6.4 f6.8 +5.0 -0.4
...
.....
4-16 4 + 2 + 2 14 7 5
++ ..... ..... f4.2 f2.9 -1.3 -2.1 -0.6
.....
4-0.6
f7.4 4-9 6 -3.2
.....
.... 569.6
..... -6.2
.... 493.4
..... fl.4
....
.....
591 .o 578.8 533.0 448.8
481.0 438.2
Error.
%
{I],
.- .2.4.. .1
-5.1 -5.6 -5.0 -2.8
... -1.6
-1.7 -1.6 -0.8 -0.7 -2.5 -6.6
...
I
.
.
-0.5 4-1.6 -1.1 -6.2 -8.1
... ...
-3.4 +0.2 12.7
...
+1:5 +4.0 +5.7
...
+0:3 +0.8 4-0.8 +0.6 -0.1
...
+1:9 +0.2 +0.2 + I .3 +1.1
...
46:7 +0.5 -0.2 -0.3 -0.1
...
+o: 1 +1.1 +1.5 -0.5
...
...
-1.1 -0.9 -1.0 -0.9 -0.6
...
+l.5 -6.8
+0:3 4-0.3 -1.5
13.G
1.3
...
L
a Extrapolated
b Exclusive of
CHrCsHii and CHrCaHir aystems
per cent. The critical pressures plotted in these figures will be discussed later. This correlation of critical temperatures on a weight basis is in agreement with the reports of Kay (6) and of Smith and Vatson (20)on multicomponent mixtures for which it was reported that critical temperatures could be predicted from some property of the constituents on a weight basis while the pseudocritical temperature (6) could be predicted from some property of the constituents on a mole basis.
Critical Pressures The prediction of critical pressures of hydrocarbon mixtures is a much more difficult problem than that of predicting
critical temperatures. The critical pressures of mixtures, instead of falling between the critical pressures of the two pure components, tend to be considerably higher than would be indicated by the additive law; the deviations are generally greater, the greater the ratios of the molecular weights of the pure components. The nature and order of these deviations from the additive law are evident from Figure 1and Table 11. Figure 3 shows two characteristic pressure diagrams of the subject of this paper. One might attempt to calculate the critical pressure of mixtures of A and B by assuming the pressure to be proportional to weight fraction or temperature, in which case the values indicated by the lines labeled "additive lawJJ in Figure 3 would be obtained. However, the actual critical pressures are always greater than these addi-
INDUSTRIAL AND ENGINEERING CHEMISTRY
846
Vol. 34. No. 7
t K
1 E a.
0
WEIGHT PERCENT
100
TEMPERATURE
-
FIGURE 3. TYPICALCRITICALPRESSURE-COMPOSITION AND CRITICALPRESSURE-TEMPERATWRE PLOTS FOR SYSTEMS OF THISSTUDY
value, are plotted against weight fraction, a reasonably accuTABLE 11. MAXIMUM DEVIATIONS OF CRITICAL PRESSURES rate common curve results for all the systems studied. This FROM ADDITIVE LAWVALUES plot is presented in Figure 4. Similarly, when values of PCD, M a x . P C D ,Lb./Sq. In. calculated from Equation 3 and divided by the corresponding System Wt. basis Temp. basis maximum such value, are plotted against (TCM- TcL)/ CHcCaHs 827 826 ( T c H - TcL),a common curve results similar to that shown CHI-~~IHID 1318 1308 .... 1959 in Figure 5. CHrn-CaHu CH
