Saturated liquid Phase Enthalpies at High Pressures Ethane-n-He ptane System JAMES H. WEBER Department of Chemical Engineering, University of Nebraska, Lincoln 8, Neb.
As part of a continuing study of thermal data of binary systems, saturated liquid phase enthalpies are presented for the system ethane-n-heptane at 100, 200, 300. 400, 500, and 600 p.s.i.a. Saturated liquid phase enthalpy data have been presented for other hydrocarbon systems (5; 7). T h e method used for calculating the saturated liquid enthalpy data is outlined by Dodge ( 4 ) and has been discussed in detail (5, 7 ) ; the procedure is thermodynamically rigorous. The differential heat of condensation is calculated and, in turn. the saturated liquid enthalpy. The differential heat of condensation is the heat given up when one mole of liquid is condensed from a very large quantity of vapor, the process taking. place under conditions of constant pressure and temperature. T h e basic expressions used in the calculations are
0.95. T h e smoothing technique, described by Hobson and Weber ( 5 ) , in which the quantities ( y - x ) ( d V C ; ~ dTy ,) P , and ( y - x ) (dH,/dy) 7 , P are plotted against y was used to detect erroneous values. With the calculated data and the equilibrium data determined by K a y ( 6 ) , the saturated liquid enthalpy values could be calculated by using Equations 1, 2, and 3. T h e enthalpy values of pure ethane presented by Barkelew. Valentine, and H u r d (2) were used. These data had to be changed to the datum plane used in this work--namely, the enthalpies of the pure components in the ideal gas state at 0" R. and unit fugacity were set equal to zero. Equation 5 was used to calculate enthalpy values for pure n-heptane in the saturated vapor state. These calculated data and the latent heat of vaporization data for n-heptane ( 8 ) were used to determine the enthalpy values of n-heptane in the saturated liquid state. The final results presented in Figure 1 and in Table I are believed to be accurate within *37c. The enthalpy data are reported to four or five figures for consistency. ACKNOWLEDGMENT
and
This work was done under a retainer agreement with the Phillips Petroleum Co. The author thanks Phillips for permission to publish these data.
From Equations 1, 2, and 3 it is evident that volumetric data for the saturated and superheated vapor states and saturated liquid state are required. Vapor-liquid equilibrium data are also necessary. including pressure and temperature information. K a y (6) obtained P-V-T-x data for the ethane-n-heptane system, including volumetric data for the saturated liquid and vapor states only. Additional saturated vapor and superheated vapor volumetric data were required; so the Benedict-WebbRubin equation state ( 3 ) P
=
RTd
+
(RoRT
~
'4,
-
C,-,/'T')d'
am&
+
+
(bR7
c d 3 ' T 2 (1
+
-
a)di
+
y d ' ) exp ( - y d 2 ) (4)
was utilized. T h e validity of this relationship was established by comparing results calculated from the equation with the experimental results of Kay. With the exceptions of the critical regions, the calculated results and the experimental data for various mixtures were in good agreement, usually within i1 Vc. The differences at the critical points were 15.7. -14.4, and -12.1", at pressures of 400, 500. and 600 p.s.i., respectively. T h e positive percentage figure indicates the experimental value was greater than the calculated; the negative percentage figures indicate the opposite. Once the validity of the Benedict-Webb-Rubin equation ( 3 ) was established. the necessary volumetric data for the solution of Equation 1 could be calculated. Also, by using the equation ( 3 ) and enthalpy data ( 7 ) for the pure components in the ideal gas state (7), the required vapor phase enthalpy data could be calculated. The relationship used was H
=
Zx,H;' +
(Bar -
2A0
-
4CoIT')d
25
? 0 -
20
x
W
0
f
.2 m
15
5
I
;I O -I
4
r
I-z W
5
+ (2bR'T - 3 a ) d 2 / 2 + 0
Because ethane and n-heptane differ greatly in volatility, the determination of partial volumes. (a Vc/ay) T , P , and partial enthalpies (aH,!ay) T , P , was difficult. The difficulties were greatest when the concentration of ethane in the vapor phase was high-e.g., when the mole fraction was between 0.995 and VOL. 4, No. 4, OCTOBER 1959
-4
0
0 10
0.20
0.30 0.40 0.50 0.60 0.70 MOLE F R A C T I O N ETHANE
0.80
0.90
Figure 1 . Enthalpy vs. composition diagram
301
Table 1. Enthalpy-composition Data for Ethane-n-Heptane System Mole Fraction Ethane,
zq
0
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.96 0.99 0.995 1.00 0
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.96 0.99 0.995 1.oo 0
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.96 0.99 0.995 1.oo
“H
=
Bubble Point Temp., l b , ‘F.
358 165 83 41 14 -5 -18.5 -29 -37
... ... ...
... -46 430.5 292 176 115 78.5 53 34.5 20 9.5 1.5
... ... .., -6.2 478.2 375.6 254.2 176.3 126.7 93.6 71.2 54.7 41.8 31.2
... ... ... 21.6
Dew Point Temp., ld. ‘F.
Enthalpy at a Bubble Point, Hb,
Mole Fraction Ethane,
Enthalpy at‘ Dew Point, Hd’
B.t.u./Lb. Mole B.t.u./Lb. Mole
Pressure, 358 347 334 320 305.5 290 272.5 251 223 179 132 78 55.5 -46
100 P.S.I.A. 14,743 +3,802 -425 -1,463 -1,852 (-2,060)’ (-2,170) (-2,220) (-2,290) (-2,240) ...
... ... -2,061
Pressure, 200 P.S.I.A. 430.5 20,165 415 8,650 399 2,716 382 + 205 364.5 -902 345 -1,375 324 (-1,440)’ 298 (- 1,510) 264 (- 1,510) 214.5 (-1,480) 162 ... 102 ... +78 ... -6.2 -1,230 Pressure, 300 P.S.I.A. 478.2 24,268 459.1 13,808 439.1 5,392 418.7 1,798 397.8 + 562 376.8 -20 354.3 -366 326.4 ( -504)’ 290 ( -600) 235.3 ( -600) 178 ... 113 ... 90.5 ... 21.6 -650
25,256 23,148 21,032 18,947 16,951 15,014 13,104 11,245 9,360 7,397 6,057 5,028 4,687 3,299 28,396 25,818 23,429 20,997 18,755 16,487 14,364 12,231 10,051 7,852 6,349 5,178 4,780 3,467 30,195 27,410 24,760 22,122 19,631 17,271 15,019 12,792 10,467 8,072 6,436 5,135 4,751 3,515
29
(2)
(2)
enthalpy, B.t.u./lb. mole. H = 0 for a pure component in the ideal gas state a t unit fugacity and 0” R. H a = enthalpy of a component in the ideal gas state and unit fugacity, B.t.u./lb. mole A H , = differential heat of condensation, B.t.u./lb. mole P = pressure, p.s.i.a. R = gaslaw constant, l.9870B,t.u./lb.mole - OR. 7 = absolute temperature, R. V = molal volume, cu. ft./lb. mole d = density, Ib. mole/cu. ft. x = mole fraction in liquid phase y = mole fraction in vapor phase 2 = mole fraction in either liquid or vapor phase Ao, Bo, Co, a, b, c, a and y = empirical constants of BenedictWebb-Rubin equation of state
Subscripts G = vaporphase b = bubblepoint
302
512 435.5 322 232.5 171 131.5 103 82 67 54
0.113 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.96 0.99 0.995 1.oo
497.5 382.3 285.7 220.8 168.2 130.6 106.6 89.3 74.2
0.20 0.177 0.193 0.236 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.96 0.99 0.995 1.oo
484 475 450 400 337 256 198 158 130 110 92.5 ... ...
... ... ... 42.8
... ...
... 61.0
...
75.8
Dew Point Temp., I d , ‘F.
Enthalpy at a Bubble Point,
Enthalpy at Dew Point, Hd’
Hb,
B.t.u.!Lb. Mole B.t.u./Lb. Mole
Pressure, 400 P.S.I.A. 512 (28,058)’ 490 17,796 468 8,883 445 3,502 423 1,512 400 807 377.5 405 348 195 307.5 ( +5) 249 ( -70) 187 ... 120 ... 99 ... 42.8 -68
(28,058) (26,950 25,050 22,658 20,241 17,855 15,489 13,085 10,683 8,156 6,406 5,039 4,640 3,497
(2)
Pressure, 500 P.S.I.A. 497:5 (26,130)’ 483.5 13,633 462.8 6,378 440.5 2,992 417.0 1,803 390.5 1,212 359.3 883 320 604 259 407 192.5 ... 126 ... 104.5 ... 61.0 369
(26,130)’ (24,905) 22,854 20,495 18,047 15,603 13,195 10,798 8,192 6,326 4,901 4,469 3,398
(2)
Pressure, 600 P.S.I.A. 484 (23,622)’ ... 22,720 ... 19,895 15,832 471 10,906 450 6,397 426 4,302 400 3,098 370 2,303 328 1,711 264 1,261 198 ,.. 131 ... 109 ... 75.8 870
(23,622)’
. I .
... ...
... 22,504 20,317 17,941 15,597 13,242 10,790 8,114 6,236 4,747 4,251 3,194
(2)
’All values in parentheses are extrapolated data.
0 for pure components in ideal gas state at unit fugacity and 0’ R.
=
0.003 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 0.96 0.99 0.995 1.oo
(2)
NOMENCLATURE
H
Bubble Point Temp.. l b , ‘F.
d
=
dew point
z = acomponent j = total number of components
LITERATURE CITED (1) Am. Petroleum Inst. Research Project 44, Table 2u-E, Carne@e Institute of Technology, Pittsburgh, Pa., 1953. (2) Barkelew, C. H., Valentine, J . L., Hurd, C. O., Tram. Am. h s f . Chem.Engrs. 43,25 (1947). (3) Benedict, M., Webb, G. B., Rubin, L. C., J . Chem. Phys. 8, 334 (1940); 10,747 (1942). (4) Dodge, B. F., “Chemical Engineering Thermodynamics,” p. 130, McGraw-Hill, New York, 1944. CHEM.ENG.DATA (5) Hobson, M., Weber, J. H., IND.ENG.CHEM., SER.2,7 (1957). (6) Kay, W. B., Znd. Eng. Chem.30. 459 (1938). (7) Stiehl, J , G., Hobson, M., Weber, J. H., A.I.Ch.E.Journal 2, 389-92 (1956). (8) Stuart, E. B., Yu, K. T., Coull, J , , Chem. Eng. Progr. 46, 311 (1950). RECEIVED for review November 14, 1958. Accepted March 20, 1959.
JOURNAL OF CHEMICAL AND ENGINEERING DATA
