Volume Changes in Mixing Hydrocarbons SYSTEM n-BUTANE-BENZENE-CY CLOHEXANE J. F. CONNOLLY Research Department, Standard Oil Co. (Indiana), Whiting. Ind.
I
N ORDER to produce gasoline with a specified vapor pressure, volatile hydrocarbons like butane are added to refined naphthas. Mixing these components gives a total volume of gasoline that is slightly less than the total volumes of the components. However, the quantities involved are so large that the shrinkages are economically significant. Most published data on the mixing of hydrocarbons are limited to those that are liquid under atmospheric conditions (3, 10-13). The few data available on more-volatile hydrocarbons have been obtained in equipment designed for work at high temperatures and pressures. The accuracy of such data is inadequate a t moderate pressures, where the volume changes are very small. Equipment designed for use a t moderate pressures should give greater accuracy. In the present work volume changes have been calculated from specific volumes determined in a glass pycnometer designed to allow measurements at pressures somewhat above atmospheric. Because of the data available on binary mixtures ( 1 2 ) , benzene and cyclohexane were chosen for mixing with n-butane. EXPERIMENTAL
Specific-volume measurements mere made on the three individual hydrocarbons, five mixtures of n-butane and benzene, five mixtures of n-butane and cyclohexane, and two mixtures of all three. The two binary systems contained about 12, 25, 50, 75, and 88% n-butane by volume. The two ternary mixtures contained, respectively, about 33 and 50% n-butane, 33 and 35% benzene, and 33 and 15% cyclohexane. The hydrocarbons were Phillips research grade; measured densities and stated purities are given in Table I. Within experimental error, the measured densities agree with those of the American Petroleum Institute ( 1 ) . Saturation with air may lower the API densities for benzene and cyclohexane by about 0.0001 gram per ml. ( I d , 14).
eter. The metal tubing has an inside diameter of about 0.S mm,; the vapor volume from the reference line to the lower valve is 0.3 ml. Measurements were made a t successively higher controlled temperatures within a few degrees of 60°, 80', looo, 120°, and 140' F. and a t pressures of 7.0 and 10.0 atm. Temperature was controlled to 0.02' F. in a water bath and measured with a platinum resistance thermometer calibrated by the National Bureau of Standards. Pressure, applied with nitrogen, was measured to 1 pound per square inch with a Bourdon gage. To introduce benzene or cyclohexane, the pycnometer was disconnected at the Teflon seal and the liquid was added through a hypodermic needle. The pycnometer was reassembled, cooled with liquid nitrogen, evacuated, warmed, and weighed. A roughly measured volume of n-butane vapor was then condensed into the bulb. The pycnometer was warmed and shaken to mix the contents before the liquid rose into the capillary. The pycnometer was placed in a bath and the temperature was adjusted to bring the liquid level into the capillary. Cold watei was passed through the cooling jacket, and the lower valve was opened in turn to pressures of 7.0, 10.0, and 7.0 atm. of nitrogen. After each pressure adjustment, the distance from the meniscus to the reference line was measured with a cathetometer. With the upper valve closed, the temperature was raised to about 10' F. higher than desired for the next run. Then the lower valve was closed. The cooling jacket was disconnected from the water tap and dried, and the pycnometer was weighed. The upper valve was then opened. Heating the upper portion of the pycnometer with an infrared lamp and simultaneously freeding the contents of the bulb uith liquid nitrogen permitted complete evacuation of the expansion chamber while all of the liquid from the capillary and seal distilled into the bulb. The pycnometer was then ready for a run a t a higher temperature. The pycnometer volume was corrected for the effect of temDerature by calibration with water a t different temperatures.
(g)
This yielded: ;
Table I.
Densities of Hydrocarbons
%-Butane Purity, mole % 99.85 Density a t 68' F. (20.00° C.) 0,57895 Observed, g./ml. 0.5788O API, g./ml. Density a t 77' F. (25.00' C . ) Observed, g./ml. 0.573Zn 0.6730" API, g./ml. At vapor pressure. b At 1 atm.: free of air. 0 At 1 atm.; saturated with air.
Beneene 99.89
Cyclohexane 99.83
0.8791b 0 , 8 7 9 0 1C
0.7787h 0.77855
0.87396 0.87370C
0.7741h 0.77389C
=8X
per
C. The effect of pressure
was found by measuring the apparent compressibility of water in the range 1 to 7 atm. and subtracting the literature value (8) to 1 bv obtain the stretch of the pycnometer. This yielded ;(G) = 11 X 10-8 atm.-'.
The liquid volume was corrected for the
Shrinkage of volume of gasoline in manufacture, when n-butane is mixed with refined naphthas, though small percentagewise, i s economically significant. Data presented here show how to predict and limit these shrinkages.
One pycnometer was used for all measurements; its volume was known within O.Olgo from calibration with water. As shown in Figure 1, it consists of a 35-ml. borosilicate glass bulb, having walls 3 mm. thick, and a calibrated 1-mm. capillary surrounded by a cooling jacket and attached through a Teflon seal to a 3-ml. metal expansion chamber. This chamber is attached to equipment for filling, evacuating, and pressurizing the pycnom-
813
INDUSTRIAL AND ENGINEERING CHEMISTRY
814
temperature of that portion surrounded by the cooling jacket. The weight of the filled pycnometer v a s corrected for nitrogen in the expansion chamber. For each mixture specific volumes and compositions were calculated from the measured volumes and weights. From these specific volumes and the corresponding temperatuies, the constants A , B, and (3 for the equation u
=
A
+ B ( t - + C ( t - ti)* ti)
(1 1
m-ere determined by the method of least squares. In the equntion, v is the specific volume in milliliters per gram and t is the temperature in degrees Fahrenheit, Values of the constants A , B , C, and tl for each mixture are given in Table 11. Equation 1 was then used to calcu!ate specific volumes at 60.00", 80.00', 100.00", 120.00°, and 140.00" F. and 7.0 atm. These specific volumes gave volume changes on mixing fioni the definition
yo volume change
Vol. 48. No. 4
sevcral test runs only 0.00570 of noncondensable gas was found after the liquid level had been raised just above the lower valve, the valve closed, the contents of the bulb frozen, t'he expansion chamber evacuated, the valve opened, and the pressure measured with a Pirani gage. This experimental method gives specific volume with an estimated average error of 2 parts in 1O;OOO. The uncertainty results in an average error of 0.03 in the percentage volume change. on mixing. Such accuracy is lower than that attainable with nonvolatile systems at atmospheric pressure (12, I S ) . BINARY S I STEnlS
The percentage volume changes for the n-butane-benzene and n-butane-cyclohexane systems were htted a t 7 atm. and 60.0", SO.O", 100.0", 120.0", and 140.0" F., by the method of least quares, to equations like
% volume change = Z,Z,(a,, = 100
em - Do (2) vo
+
~ 1 . 2=
bj.2
+
- 1 . 4 3 - 3.81 X 10-*(t - 60.0) 0.59 X
= -0.62
+ 2.22 X
C I ~3 =
-1.75
- 2.44 X
(t
- 60.0)'
10-'(t - 60.0) -
5.70
SOURCES OF ERROR
The weight of the mist,ure plus pycnomet'er (about 1400 grams) can be determined to 1 mg., but the meight of the evacuated pycnometer cannot be reproduced so xell because of adsorption of hydrocarbons in the metal portions of the pycnometer. Therefore, the average error in the weight of a mixture is 5 mg. Composition would be expected t o change because of selective evaporation a t several points in the procedure, but t,his error is believed t o be n e g l i g i b l e . Evaporation from the liquid surface in the capillary is not detectable, inasmuch as the nitrogen pressure is several atmospheres higher than the n-butane vapor pressure. The lower valve is allTays closed when the mixture is not under nitrogen pressure, and the volume from the reference line t o the lower valve is small. bforeover, the removal of portions of the mixture is carried out under a pressure of nitrogen 5 to 10 atm. above the vapor pressure of n-butane, and mixing between the liquid in the expansion chamber and that in the pycnometer is prevented by the small diameter of t'he connecting tubing. Little nitrogen dissolves in the mixture, because the area of liquid exposed is only 0.6 ,sq. mm. I n
(3)
where Zi and Zj are volume fractions a t 60' F. and 7 atm. and nij and bij are constants at each temperature and at 7 atm. Hoviever, the volume change varies only slightly with pressure below 10 atm., so that aii and b j j may be considered independent of pressure in this range. By the method of least squares these constants tTere fitted t o temperature functions
where 0, is the specific volume of the mixture in milliliters per gram and 00 is the ideal specific volume of the mixture-Le., eo = U'IL'I w202 , , , where u1, US, etc., are specific volumes of the pure components and the wJs are TT-eight fractions. The calculated per cent volume changes are listpd in Table 111.
+
+ bijZi)
x
10-4(t - 6 0 . 0 ) ~
(4)
10-'(t - 60.0) -
0.82 X 10-4(t - 60.0)' b1.a
= -1.44
+ 0.13 X
lo-'(!
- 60.0) 2.79 X 10-'(2
- 60.0)'
wheie 1 is butane, 2 is benzene, 3 is cyclohexane, and t is tempei ature in ' F. Substituting constants from thefie equations ir Equation 3 yielded the plots for both systems shown in F'iguie 2 . The circles are experimental points, sized to represent the extent of eiror. The equation represents the n-butane-benzene data TI ith an average deviation of 0.013 and a maximum deviation of 0.04. The n-butane-cyclohexane system shows an average devibtion of 0.014 and a maximum deviation of 0.04. TERNARY '3YSTEM
The representation of the data for ternary systems is necessarily more complicated than for ternary systems. Scatchard (8)has suggested an equation to repiesent the excess free encrgLof a ternary system in XThich one component behaves differently than the other t u o
TThere X is a mole fraction and A&, etc., are functions of temperature and pressure, in which the superscripts are marks of identification rather than exponents. The number 1 must be assigned to the "different" component, n-butane in this case. Such a form might apply to volume changes on mixing because: Figure 1. Diagram of pycnometer
Volume change on mixing per mole =
(=) ap
T
(6)
April 1956
Constants for Equation 1
Table 11. Weight Fraction
n-
Butane
Benzene 0 1.0 0 0.90976 0.81976 0.60884 0.35192 0.18849 0 0
1.0
0
0 0.09024 0.18024 0.391 16 0.64808 0.81151 0.09635 0.19639 0.42512 0.67261 0.83447 0.26168 0.41255 P
d
=
Cyclohexane 0 0
1.0
0 0
0 0
0 0.90365 0.80361 0.57488 0.32739 0.16553 0.34208 0.39333
0 0
0 0.39623 0.19412
Constants5 B X 10s C X 106 5.819 0.815C 0,989 0.928 1.850 1.5384 2.814 4.055 1.237 1.471 1,990 3.094 4.298 1.788
A 1.71201 1.131460 1.27495 1.18035 1.23122 1.35228d 1.50409 1.59282 1.31592 1.35728 1.46047 1.54981 1.62613 1.33338
...
Difference % b ti,
F.
Max.
Av.
...
7.0 atm. unless otherwise noted.
P = 1.0 atm. P = 3.0 atm.
VOLUME FRACTION OF BUTANE
If Equation 5 is differentiated, we obtain the same form for the volume change on mixing per mole. Arbitrarily writing this expression for the molar volume change in terms of volume fractions [Expressions in terms of volume fraction usually fit experimental data better than those in terms of mole fractions for nonpolar systems ( 7 ) . ] we , have
.2
.4
.6
.8
I .o
BUTANE-BENZENE
- 0.4
Y
- 0.8
”
Y
where V” is the volume change per mole of solution. VOis the ideal molar volume of the XZVz XIV,, solution and equals XIVI in which VI is the molar volume of pure component 1. 21,ZZ,and 2 3 are volume fractions XIVI etc. Discarding terms after and equal -,
+
+
vo
Y
815
INDUSTRIAL AND ENGINEERING CHEMISTRY
=
0 and
P
= 1 and rearranging gives
W
g -1.2
/
r,,
-
a
I V
W
2
3 -1.6 0
> w
9 +3
[a*,,-I-
(2,
: I- Z,)]
o
z (8)
W
0 E
W
p.
where UI,Z,b l , ~ , etc., are functions of BY,*, B ~ J BP,3, , etc. If 1 is assigned t o butane, 2 t o benzene, and 3 t o cyclohexane, the terms a1.2, etc., can be identified with the analogous terms of Equation 3 for binary systems by letting 21, ZZ,and Z3 successively cqnal zero. The terms a , ~bl.2, , a1,3, and bl,3 are given by Equations 4; a2,8 and bz,s are given by Wood and Austin ( I d ) . Values of the percentage volume change calculated from Equation 8 are compared with experimental values in Table IV. The compositions of mixtures 1 and 2 are given in the last two lines of Table 11. The average deviation (0.027) is within experimental error and is better than that obtained (0.084) by using ( X I - X Z )rather than ( 2 X 1 1) in
-
-0.4
-0.8
- 1.2
- 1.6 Figure 2. Volume changes of butane-penzene and butane-cyclohexane on mixing
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
816
Table 111. V o l u m e C h a n g e s on lliixing T\ eight Fraction BenCyclozene hexane
nButane 0.090 0.180 0.391 0.648 0.812 0.096 0.196 0.425 0.673 0 834 0.262 0.413
0.910 0,820 0,608
0.352 0.188 0 0 0 0 0 0.396 0.194
Table IV.
O
F.
60 80 100 120 140
0 0 0 0 0 0.904 0.804 0.575 0.327 0.166 0.342 0.393
BO 0’ F. -0.18 -0.29 -0.44 -0.38 -0.22 -0.21 - 0 40 -0.61 -0.56 -0.32 - 0 10 -0.39
Volume Changes Wr a t 80 0’ 100 0’ 120 0’ r. F. F. -0.23 -0.30 -0.39 -0.45 -0.60 -0.74 -0.58 -1.04 -0.78 -0.48 - 0 65 - 0 . 8 7 -0.29 -0.54 -0.40 -0.27 - 0 35 - 0 . 4 4 -0.50 -0.82 -0.77 -0.74 -0.92 -1.14 -0.68 -0.84 -1.04 -0.40 -0.50 -0.64 -0.25 -0.42 -0.61 -0.57
110 0’ F. - 0.90 -0.86 -1.36 -1.14 -0.71 -0.53 -0.94 -1.40 -1.29 -0.80 -0.81
P e r c e n t a g e \‘olume C h a n g e s €or T e r n a r y Mixtures
the same form as Equation 3 for a binary system. Ioffe (3) and others, working with nonvolatile systems, have also observed that mixing individual hydrocarbons into mixtures gives the same form of curve as binary systems. Thus, n-butane-naphtha systems might be expected to show the same pattern of behavior as simple binary systems. The effect of the molecular xeight of the second component on volume changes in light hydrocarbon-hydrocar bon systems 1s marked (6). However, the similarity between the volume changes in the n-butane-benzene and n-butane-cyclohexane systems suggests that the structure of the second component is not important. To confirm this view, further work on mixing n-butane with other types of hydrocarbons of about the same molecular weight as benzene and cyclohexane would be needed.
Mixture 2
Mixture 1 Predicted -0.10 -0 14 -0.25 -0.28 -0.44 -0.42 -0.61 -0.63 -0.81 -0.86
Obsd.
Predicsed -0.41 -0.56
Obsd. -0.39 -0,57
Diff. -1-0.04 +0.03 +0.02 t0.02 +0.05
Diff. -0.02 -0.01
T a b l e Y.
COMPRESSIBILITIES
Av
10.0
‘E
(9)
- 7.0
n here Ti, is the volume of liquid in the pycnometer a t 7 atm , and AT’ is the change in volume when the pressure is raised from 7.0 to 10.0 atm. a t constant temperature. The experimental error depends on the magnitude of the compressibility and ranged from about 4 to 9 X low6atm.-’. For each mixture the compressibilities were fitted by t h e method of least squares to equations of the form
+ b ( t - t l ) Jr c ( t -
?iY
2:
Compressibility, p, in atm. -I, 7%-ascalculated from
p = -- 1x V?
C o n s t a n t s for E q u a t i o n 10
Weight Fraction Constants Difference“ nBenx 104 Eiatane zene al$ o‘+. XTTZL 1.0 1.75 1 . 9 2 6 0 . 6 =tl 0 0 267 +2 0 0 90 60.0 0 0 0.46 -0.03 1.0 0 1.0 101 0 0.52 0.08 57.9 0 +1 0,090 0 99 -1 0.52 0.02 5 8 . 5 +1 0.910 0.180 0 111 0 . 4 8 +1 0.26 58.7 & 1 0.820 0 142 0 0 0,391 0.77 0.30 5 9 . 7 0.609 0 193 0,648 1.06 0.82 6 2 . 2 &1 0.352 0 216 1.37 1.23 56.4 0 0.812 0.188 0.904 111 -1 0 0.53 0.20 60.2 & l 0.096 0.804 126 +2 0.51 0.40 60.8 k 1 0 0.196 0.575 160 0.425 -1 0 0.84 0.44 67.0 J 1 0.327 180 0 1.07 0 . 9 3 52.5 & 1 0.673 0 834 0 166 216 1.26 1 . 3 0 55.0 i l 0 +2 0,262 0.342 128 0.65 0 . 2 4 62.3 i l 0.396 a Obser T,ed c o m p r a;sibility minus c,ompressibility from Equation 10.
,“,Y,“,‘zi
Equation 5 , as is often done to represent the excess free energy of more symmetrical systems (4,8, 9 ) .
p = a
Vol. 48, No. 4
11’12
(10)
There t is temperatuie in O F and a, b, c, and tl are constant$ given in Table V. Equation 10 xvas used to calculate the deviations of the compressibilities from ideality-i.e., p - Po, n-heie the ideal compressibility is PO = Z,pi Z&. These deviations n’ere directly proportional to the per cent volume changc.9 within the accuracy of the measurements
+
p - PO = k ( % volume change)
(11)
where k is a constant independent of tempeiature, pressure, and composition in the range studied, and per cent volume change is given b y Equations 3 and 4. The k for the ?e-butane-benzene system, 77 X 10-6 atin.-’. gives an average deviation from experiment of 3 X atm.-’ and a maximum deviation of 9 X 10-6 atm.-’. The k for the n-butane-cyclohexane system 61 X 10-6 atm.-’ gives an average deviation from experiment of 4 X 10-6 atm.-l and a maximum deviation of 12 x 10-6 atm.-’
ACKNOWLEDG3IENT
The author thanks Herman S. Seelig for valuable suggestions made during the course of this work. REFERENCES
Am. Petroleum Inst., “Selected Values of Physical and Thermodynamic Properties of Hydrocarbons,” BPI Project 44, Car-
negie Press, Pittsburgh, Pa., 1953. Dorsey, N. E., “Properties of Ordinary Water Sub.tance,” p. 243, Reinhold, New York, 1940. Ioffe, B. V.,Zhur. Priklad. Khim. 22, 1263 (1949). Redlich, O., Kister, A. T., IND.ENG.CHEM. 40, 345 (1948). Reeves, E. J., Petroleum Refiner 31, 154 (1952). Sage, B. J., Lacey, TI’. X., Trans. Am. Inst. Mining M e t . Engrs. 136 (1940). Scatchard, G., Chem. Revs. 44, 17 (1949). Scatchard, G., Ticknor, L. B., J . Am. Chem. SOC.74, 3724 (1952).
Scatchard, G., TT-ood, S. E., Mochel, J. hf., Ibid., 62, 712 (1940) Scatchard, G., Wood, S. E., XIochel, J. XI.,J . Phgs. Chem. 43, 119 (1939).
Thiele, E. W., Kay, W. B , ISD. EXG.CHEM.25, 894 (1933). Wood, S. E., Austin, A. E., J . Am Chem. SOC.67, 480 (1945). IT’ood, S. E., Brueie, J. P., Ibid., 65, 1891 (1943). Wood, S. E., Gray, J. A., 111,I b z d . , 74, 3730 (1952). RECEIVED for review Beptember 6, 1955. ACCEPTEDNovember 30, 1955. Division of Industrial a n d Engineering Chemistry, 126th Meeting, A C S , S e w York, S. Y . , September 1954.
COiYCLUSIONS
For mixing n-butane into constant-composition mixtures of benzene and cyclohexane, Equation 8 can be reduced to
% volume change
= 21(1
- &)(a + bZi)
(12)
where 21 is the volume fraction of n-butane, and a and b are func, a2.3, b2.3 and 2 2 / 2 8 . Equation 12 has tions of al+ bl.2, a ~ b1,3,
Correction I n the article “Volumetric and Phase Behavior in the Nitric Acid-Water System” [C. H. Duffy, W H. Corcoran, B. H. Sage, IKD, EKG.CHEII. 48, 431 (1956)] the legends for Figures 3 and 5 m r e interchanged. Figure 5 now appears on page 432 and Figure 3 on page 433.
