INDUSTRIAL AND ENGINEERING
July, 1933
CHEMISTRY
ACKNOWLEDGMEKT
125
LITERATURE CITED
This work was carried out in the Research Laboratory of Applied Chemistry with the cooperation of the Humble Oil and Refining Company, for which the authors express their appreciation.
(1) Calingaert and Hitchcock, J. Am. Chem. Soc., 49, 750 (1927). (2) Filson and Wylde, IXD. ENG.CHEX.,15, 801 (1923).
RECEIVED April 10, 1933. G. L. Matheson’s present address is Standard Oil Development Company, Bayway, N. J.
Vapor-Liquid Equilibria of Hydrocarbons a t High Pressures W. K. LEWISAND C. D. LUKE D e p a r t m e n t of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass.
T
HIS laboratory (3, 7) has recommended the use of a single reduced graphical equation of state for hydroc a r b o n s having m o r e than 3 carbon a t o m s per m o l e c u l e , e x p r e s s e d as a p l o t of the c o r r e c t i o n f a c t o r to the gas laws, p , against the r e d u c e d pressure, PR,a t constant values of r e d u c e d temperature, TR. It was r e c o g n i z e d t h a t the h y d r o c a r b o n s of low molecular weight deviate f r o m t h i s c h a r t . The c h a r t was constructed a t the critical temperature, and below, from data on h i g h e r h y d r o c a r b o n s , but, a b o v e TR = 1, t h e d a t a of Amagat (1) on ethylene were used, i n a s m u c h as they were the only data over wide ranges of t e m p e r a t u r e and pressure available to the authors a t that time. Later the authors’ attention was called (2) to the data of Young on N-pentane . ( I O ) and particularly isopentane
originally presented to correspond to these data of Young. The chart t h u s c o r r e c t e d is s h o w n in Figure 1. There is no change on the TR = 1 isotherm except beyond PR = 1. The isotherms f o r TR = 1.05 and 1.10 have b e e n l o w e r e d somewhat, but the diagram is o t h e r w i s e unchanged. It is b e l i e v e d that this d i a g r a m represents closely the data a t present available for hydrocarbons with m o r e than 3 carbon atoms per molecule. Along with the p chart (7) was presented a fugacity chart, on which was plotted the ratio of the fugacity to the pressure, f/P, as a f u n c t i o n of the reduced pressure, PR. This chart has been corrected f o r t h e changes in the p chart just described and is given in Figure 2. Fundamentally, of course, this chart applies only to the vapors of Pure hydrocarbons.
Curaes f o r the correction factor, p, to the gas laws, applicable to hydrocarbons with more than 3 carbon atoms per molecule, are corrected in minor details. The corresponding corrections hate also been made to the generalized fugacity plot. Preliminary experimental data on the colatility of benzene in nitrogen at high pressures are presented, and the results indicated tentatively on the fugacity plot as a means of estimating the volatility of high-boiling hydrocarbons at high pressures. The correction factor f o r the internal energy qf hydrocarbon mpors at low capor volumes has been determined by graphical integration f r o m the isometrics of those hydrocarbons .for which adequate data are available. The resulling corrections appear to be relaticely independent of the temperature, at least over considerable ranges, and differences in the correction f o r hydrocarbons having more than 3 carbon atoms per molecule are probably small at corresponding reduced conditions. (11).
VAPOR-LIQUID EQUILIBRIA13 HYDROCARBON SYSTEMS REDUCED P-V-T RELATIOSSHIPS FOR VAPORS
PURE
EIYDROCARBON
A study of these data shows that they check the original curves a t TR = 1 and below, closely up to the critical pressure, but that a t higher pressures they indicate lower values of p than those obtained from Amagat’s data on ethylene. However, a t high values of TR the differences between the data on ethylene and the pentanes are apparently within the experimental error through the limited range of overlap. It has therefore been deemed desirable to correct the p chart
Despite the importance of the subject, there are almost no data available on the volatility of hydrocarbons a t temperatures below their critical in the presence of noncondensable gases a t high pressure. This laboratory is conducting an intensive investigation of this field, and, while the work has just started, the preliminary results are so interesting and of such obvious importance to the oil industry that it seems desirable to give a preliminary presentation. The work to date has been limited to the binary mixture of benzene and nitrogen. Two sets of measurements have been
TABLEI. DATAON VOLATILITYOF BENZENE 13NITROGEN AT HIGHPRESSURES (4) TEMP. C. 100 100 125 125 150 150 175 175 200 200 O
a
Atn. 75 98 75 98 75 9s 75 98 75 98
“R 1.565 2 090
1.565 2,090 1.565
2,090 1,565 2.090 1,565 2.090
Z(CeH5) 0.9550 0.9405 0.9550 0.9405 0.9550 0.9405 0,9550 0.9406 0.9550 0.9405
Y(C5H6) 0.0360 0.0320 0.0664 0.0588 0.1060 0.0956 0.1665
0.1470 0.26 0.224.:
P 1.80 1.80
3.35 3.35 5.70 5.70 9.18 9.18 14.0 14.0
/. PIP
PR
TR
0.955 0.955 0,927 0.927 0,895 0.895 0.851 0.851 0.808 0.808
0.0376 0.0376 0.0699 0.0699 0.1190 0.1190 0.1916 0.1916 0.2922 0.2922
0.665 0,665 0.709 0.709 0.754 0.754 0.798 0,798 0.843 0.843
fP
1.72 1.72 3.11 3.11 5.10 5.10 7.82 7.82 11.31 11.31
=
fPZ u
45.6 50.6 44.7 49.8 45.9 50.2 44.9 50.0 41.6 47.4
/J. 0.608 0.516 0.596 0.508 0.612 0.512
0,598 0.510 0.555 0.484
I ND U S T R I A L AN D E
726
TABLE
11.
D A T A ON
K G I N E E R I N G C H E R.I I S T R Y
Vol. 25, No. 7
REFLUXAND RESIDUEGAS COMPOSITIONSa
(* = 268.4
pounds abs.
-
18.3 atm.) 2i/z
COM-
PONENT
Gas
(v)
LIQUID
P 16
(2)
Pc
Te
..
,.. ...
Lb./sq. in. ( K g . / s q . em.)Atm.
CI Ct CI Cc
0.393 0.257 0.261 0.088
0.027 0.125 0.460 0.374
4100 650 140 40.5 13.0
(288.2) ( 46.7) ( 9.8) ( 2.8) ( 0.9)
'R
R.
..
42 38 32
670 765 846
TR
"E
fp/P
...
..
...
..
0:226 0.073 0.028
0:SO 0.70 0.63
01435 0.48 0.57
0:82 0.91
fp
... ...
115 36.9 12.8
f,/r
u/z fp/fr (OBSVD.) (CALCD.)
..
...
..
0182 0.77 0.75
0:567 0.235 0.07
0:5Z
0.18 0.014 0.98 0.06 1.000 1.000 0 The first three columns represent the data of Raigorodsky and Rector (9). The third column-i. e . , the vapor pressure of the pure hydrocarbon at the temperature of the vapor-liquid equilibrium-is estimated by them, using values somewhat higher than those corresponding to the saturated normal paraffin because of the presence of momers and of some of the corresponding olefins. These pressures are accepted as satisfactory estimates in the circumstances. The remaining columns have been added by the present writers. The critical temperatures and pressures are estimated much au the pressures of column 3. The computation of the rest of the table is obvious.
Cr
0.001
made. I n the first experiments nitrogen was saturated with benzene under pressure a t controlled temperatures by bubbling the gas through two bodies of benzene in series, the first a t a temperature slightly higher than the second. The vapor mixture leaving the container was analyzed by freezing out and weighing the benzene in a trap cooled by carbon dioxide snow and acetone. This gave an experimental determination of the relation between the mole fraction, y,
(1) Whenever operating at temperatures below the critical but at a point on the fu acity curves above these dotted lines, use the full lines of the fugacity plots. (2) Whenever operating at temperatures below the critical for the com onent in question but at pressures such that the use of the &l lines would throw one below the dotted lines, use the dotted curves instead of the full line..
3 20
I
2
3 4 PI-REDUCED PRESSURE
FIGURE1.
CORRECTED
5
b
/.lC H 4 R T
of benzene in the vapor, the total pressure, 7, and the temperature, T , of the two-phase system. The second group of experiments involved the introduction of a measured amount of nitrogen under pressure into a bomb, followed by the injection of a measured quantity of liquid benzene. The mixture was then compressed by the introduction of liquid mercury to the point of complete liquefaction. Homogeneity was assured by agitation under pressure. The initial boiling point of the mixture-i. e., the point of incipient vapor evolution, was determined by pressure reduction a t constant temperature. These second experiments have been conducted a t only 100' C., but a t that temperature the compositions of the liquid phase were determined a t pressures to 500 atmospheres. The results of the two sets of experiments are summarized in Table I. I n the calculation of Table I change of liquid composition with the temperature a t constant pressure has been neglected, but these data will be furnished a t a later date. However, the mole fraction of benzene in the liquid will not vary greatly in this range of temperature, so that the error introduced in calculating f./a is not large. For benzene T , = 288.5' C. and P , = 47.9 atmospheres. The engineer is vitally interested in the equilibrium between liquid and vapor phase, This is given by the equation: fPX
=fry
in Table I. The results are shown in the dotted curves of the fugacity plot of Figure 2. It will be noted that the fugacity, f r , thus calculated, is much higher a t low temperatures and high pressures than one would anticipate from any extrapolation of the full lines of the fugacity chart. Furthermore, the data indicate that a t temperatures below approximately TR= 0.8, this fugacity, I., is relatively independent of the temperature and determined only by the total pressure. At higher reduced temperatures the curve seems to start to move, somewhat a t least, in the direction which one would anticipate from extrapolation. The present data a t hand are sufficient only to estimate this movement for a value of T R = 0.85. These curves are tentative only, but it is the present practice of this laboratory to use them as follows:
(1)
The fugacity of both liquid and vapor is influenced by the pressure and by the presence of foreign substances, but it has seemed desirable, rather than to attempt to correct the fugacities of both phases, t o neglect change in the fugacity of the pure liquid component (in this case the benzene) and throw all the correction to &, the fugacity of the vapor itself. This quantity has therefore been computed on this basis
There have recently appeared (9) data on the performance of a natural gasoline compression plant a t high pressure showing high-pressure vapor-liquid equilibria which are of interest in this connection. Table I1 is constructed from the data on the reflux and residue gas compositions of that article. The ratios y/x = fp/fir, calculated in the last column of Table 11, using the fugacity chart in the way just recom-
PR=Reduced
Pres~ure
FIGURE2. CORRECTED FUGACITY CHART mended, check the experimental results of this plant test remarkably closely. It is believed that this method of computation is the most dependable a t present available.
INTERXAL ENERGY AND ENTHALPY OF HYDROCARBON VAPORS Previous articles (3, 7 ) gave methods for determining the internal energy and enthalpy of hydrocarbon vapors at high pressures, but, in the effort to solve this important problem involved in so many thermal calculations, every legitimate avenue of approach should be employed. Therefore, the isometrics of methane, ethylene, isopentane, and N-pentane hare been constructed from the data on those
July, 1933
I
ix D u S T
K I A I> A N D E N G I N E E 1% I N (4
gases obtained by 1,arirJusinvcaiigatora ( I , 6 , 6, 10, 11). The isomebrics were found to have remarkably little curvature over wide ranges of temperat.ure. Consequently, the folio~v. ing equation may l i e rrrittcn for each gas: Pa = Tn%(Vd - M V R ) (2 1 where *,(F'r) = slopes of isometrics :LS furiet.ioii oF reduced
volume *%(Vp)= iritercepts of isometrics on Pa axis :it, Ta = 0
c H E M 1s
KY
727
doan to I'n = 2.5, tlie equation %( VB) = a/ V'n held iatisfactorily. At smaller volumes, wlrere the intercepts ceased to vary linearly wit:h l j V z n , it v a s convenient to integrate Equation 6 grapliically. Fignre 3 gives the value of the integral so obtained plotted vs. I'x. Calling this integral F, one obtains A E = &RTeF as the volnme correction t.o the internal energy of the vapor. Hence, the general expression for internal energ!: reduces to:
and for critiialpy (total lieat or lieat content) to
Granting that liydrocarhons with inore tiiari 3 carbon atonis per molecule conform substnntially to the curres of Figiirc 1 , the isojmitane curves of Figure 3 can be used for them, so that tlie above equations for E a.nd If are general in applicability. For values oS V n greater than 2.5, the integrd, F = -a/Vn, vhere (I = 5.20 for methane, 7.0 for ethylene, and 9.4 for pentane and other higlier hydrocarbons.
Following the method of Pliilligs (8), use was made of the eqnation:
= v q m prcssurc OS pure oomponent at T = t
