PREDICTION OF INFINITE DILUTION ACTIVITY COEFFICIENTS FOR POLAR-POLAR BINARY SYSTEMS JAMES G. H E L P I N S T I L L I A N D M A T T H E W VAN W I N K L E T h e UniversiQ of T e x a s , Austin, T e x .
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A correlation is given for predicting infinite dilution binary activity coefficients for saturated, unsaturated, and aromatic hydrocarbons from which the selectivity of solvents can b e calculated for solvent-hydrocarbon systems. This correlation represents an extension of the Scatchard and Hildebrand activity coefficient equations as applied to polar-nonpolar and polar-polar binary hydrocarbon systems. The energy density of the Scatchard-Hildebrand equations for polar substances is divided into a polar and nonpolar part composed of polar and nonpolar solubility parameters. A method for calculating nonpolar and polar solubility parameters has been developed to include polar-polar binary systems. Data from over 80 binary hydrocarbon-solvent systems were used in developing the correlation.. Results are compared with those predicted by the original, more limited method developed by Weimer and Prausnitz.
XTRACTION
and extractive distillation is one of the most
E important methods available to the chemical engineer for the separation of close boiling compounds or azeotropic mixtures. However, determining the best possible separating agent experimentally is usually a very costly and time-consuming process. Because of the lack of accurate theoretical or empirical relationships, preliminary selection of a separation agent is often based upon intuition or previous experience. T h e correlation presented provides a relatively simple method of systematically screening promising solvents for a given separation. T h e efficient separation of hydrocarbon mixtures by extraction or extractive distillation requires that the polar solvent have a much higher selectivity for one hydrocarbon molecule than another. One definition of selectivity is the ratio of the infinite dilution activity coefficients of the binary components when individually dissolved in excess solvent; S" = - y ~ " / - y n " , where S" is the selectivity and y mis the infinite dilution activity coefficient. Better selectivity and hence easier separation between the two components are obtained when the ratio of the activity coefficients is greatly different from 1.0. Investigators interested in solution characteristics have devised various methods of calculating terminal activity coefficients for binary solutions. Van Laar (1 906) developed one of the first mathematical treatments of the change in enthalpy \vhen t\vo liquids are mixed. H e based his work upon the van der Waals equation of state for gases. Carlson and Colburn (1942) modified Van Laar's equations to make them temperature-independent. T h e terminal or infinite dilution activity coefficients can be determined from experimental activity coefficient data by least-squares curve fit, by extrapolation, or by calculation from azeotropic data, utilizing these equations. The slope of the curve on a n y z us. x t plot is at its highest value when xz -+ 0. This characteristic can contribute to possible serious error in the evaluation of terminal activity coefficients when any of these methods are utilized. Orye and Prausnitz (1965) introduced a somewhat different expression for the excess Gibbs energy of mixing as proposed 1 Present
by Wilson (1964), who expresses g E as a logarithmic function of the liquid composition. This method enables accurate calculation of terminal activity coefficients whenever accurate binary data are available. However, because binary data are required to evaluate the parameters used in the relation, this method cannot be used when there are no available binary mixture data. Barker (1952), Pierotti et al. (1959), and Black (1958) have devised models which are claimed to give reasonably good results. but in general, these methods require either phase equilibrium data or a large number of empirical parameters which are difficultly predicted for many systems. T o complicate the matter further, there is still not enough knolvn about intermolecular forces in polar-polar and polar-nonpolar solutions to allow an accurate calculation of Gibbs excess energy of mixing from molecular properties such as polarizabilities and ionization potentials. Thermodynamic Model
An extension of the regular solution model of Scatchard and Hildebrand (Hildebrand and Scott, 1946. 1962; Scatchard, 1931) appears to provide a means of calculating infinite dilution activity coefficients while keeping empiricism to a minimum. \\'eimer and Prausnitz (1965) extended the original Scatchard-Hildebrand equation to include the effect of a polar solvent. The original Scatchard-Hildebrand relation is
where CII and C22 are the pure component cohesive energy densities, C12 is the interaction cohesive energy density, o1 and 02 are volume fractions, V I and Vz are molar volumes, and x1 and xz are liquid compositions. Weimer and Prausnitz (1965) expressed the energy of vaporization of the solvent, A U I = C11V1, as being composed of two parts, one resulting from dispersion interactions, and the other including the dipole-dipole interactions.
address, HumMe Oil &. Refining Co., Baytown, Tex. VOL. 7
NO. 2
APRIL 1968
213
where X is the nonpolar and 7 is the polar solubility parameter. An energy term, iL12, was added to include the induction effect between the polar and nonpolar molecules, giving Equation 3.
gE =
4142(XlV1
+
+
-
X2V2)[(hl
712
- 2$12]
(3)
The nonpolar infinite dilution activity coefficient was obtained by differentiating Equation 3. T h e last term in Equation 4 was added to correct for any volume changes resulting from mixing of the pure components.
RT In
72-
= V2[(X1
+ r12-
-
2$q2]
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-P
+ (1 - V2/VdI
RT[ln(V2/Vd
(4)
This relation gives good results for nonpolar solutes in binary mixtures of solute and solvent, but does not enable an accurate prediction of terminal activity coefficients when both components are polar. T o correct for the interaction of two polar species, Weimer’s model has been extended to include polar-polar interactions. T h e Scatchard-Hildebrand equations are based on the assumptions that the mutual attractive energy of two molecules is dependent only upon the distance between them and their relative orientation, and not a t all on the molecular nature of surrounding molecules or the temperature of the solution, and that the change of volume while mixing a t constant pressure is negligible. Equation 4 gives the “cohesive energy” of a mole of liquid mixture when these assumptions are applied to binary solutions.
AU =
CllV12X12
+
2c12v1v2x1x2 XlVl
+ xzvz
+
c22v22x22
(5)
For pure component 1, AU = C11V1. Similarly, for pure component 2, AU = C22V2. Therefore,
c 2 2
=
=
u,
=
(XlV1
+
(7)
(CllC22)”2
X2VZ)(C11
+
+
g E = (XlVl XZVZ)(Xl - X 2 ) 2 4 1 $ 2 (14) If either species is polar, its energy of vaporization can be divided into two parts, one resulting from the nonpolar dispersion interactions and the other including the dipole-dipole and induction effects. Weimer and Prausnitz (1965) extended Scatchard’s equation by proposing a model with one of the species being polar,
where X I is the nonpolar solubility parameter and 71 is the polar solubility parameter. T o extend Weimer’s model, a relation similar to Equation 15 is written to include another polar component. A _u 2 --
gE =
c22
- 2C12)$J142
XlVl
+
x2v2
xzvz $J2
=
XlVl
+
+
(Xivi
X2v2)
[(hi
- X2)2
+
(71
+ x2Vz)[h1 - A d 2 +
= (XlV1
x2v2
- 7212 - 2 $iz]$i$z
RT In
(71
-
4dxl
7212
+
- 2h14142 In 4 d x d
x2
7 2
=
gE
RT In
=
7 2
(xlV1
‘1
In x2
+
(18)
9x1
+ RT[
x2V~)K@i$J2
XI
the solute
x2,
::+
In -
- xl{K42Vl - K41Vz - K$Jh(V1 -
[ f:
RT In - - In
-
42 xz
- $1
+ + -41 $2
v2 VI
- -42 v2
V2)
I}
+ (20)
where K = ( X I 4- (71 - 7 ~ -)2 ~$12. T o obtain an expression for the infinite dilution solute activity coefficient, the limit of Equation 20 as x2 approaches zero gives
bgE
limit - =
bx2 x2 + 0
(rl
-
T2)2
RT In
- 2 $121
72”
=
VZ[(XI -
+ RT [In
(z)+
X2)*
+ (1
-
k)]
where yz” is the infinite dilution solute activity coefficient. l & E C PROCESS DESIGN AND DEVELOPMENT
+
gE - XI 9-
Differentiating Equation 18 with respect to composition, Equation 20 is obtained.
For nonpolar species
214
(17)
Equation 19 relates g E with the activity coefficient and liquid composition of a binary solution.
(8)
(9)
(16)
7Z2
With the wide variety of possible mixtures, Scatchard’s original assumption of zero volume change upon mixing is actually in slight error. To correct for this deviation from ideal mixing behavior, terms corresponding to the FloryHuggins (Flory, 1951; Huggins, 1941) energy of mixing are added to Equation 17, yielding Equation 18, the basis of the correlation presented here. (It was found that the FloryHuggins correction terms were necessary if the molal volumes differed by more than 5%.)
x2
XlVl
’+-E-- - X I 2 f
v2
The term $12 is redefined to include polar-polar and polarnonpolar interactions. Equation 8 now becomes
where 41 and 42 are volume fractions defined in Equations 9 and 10.
41 =
-
AU~(po1ar)
Au~(nonpo~ar)
vz
RT(x1 In
I n its general form, the Scatchard-Hildebrand equation for gE, the Gibbs excess energy of a binary solution, is given by gE
ClZ = (CllC22)”2 = X l X Z (13 ) where X I and A 2 are defined as nonpolar solubility parameters. Substituting these relations in Equation 8 yields the well known Scatchard-Hildebrand equation
gE
A U2
where C11 and C22 are the pure component cohesive energy densities, C12 is the cohesive energy for the interaction of the two components, AU is the energy of vaporization, and Vi and V2 are the molar volumes. C12 is defined by Equation 7. Cl2
and
(21)
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Evaluation of Parameters
To evaluate the parameters, the concept of homomorphs is utilized. I n the original definition proposed by Bondi and Simkin (1956), the homomorph of a compound was defined as the equistructural hydrocarbon a t the same reduced temperature. Anderson (1961) discussed the possibility of requiring a homomorph to have the same molar volume as that of the polar substance as well as a similar structure and this definition of a homomorph was assumed for this work. Experimental data have verified that the properties of a series of similar liquids-aliphatics, for example-vary in a smooth predictable manner with their molar volumes. This characteristic behavior allows the use of various graphical relations of properties as a function of molar volume for prediction purposes. Thus, homomorph plots serve to predict the dispersion energy density at any molar volume and temperature. Figures 1, 2, and 3 show homomorph plots for aliphatic, naphthenic, and aromatic hydrocarbons. The properties of nonpolar hydrocarbons were used to construct these plots, with the ordinates, AU/V = X2, being calculated from vapor pressure and density data from Dreisbach (1949, 1953, 1955, 1958, 1959, 1961), Perry (1963), and Stull (1957), and from the
physical properties of hydrocarbons (American Petroleum Institute, 1953). Using the thermodynamic relation given by Equation 22
and the Clausius-Clapeyron Equation 23, bln P
- AHo
aT
RT2
(23)
AU can be expressed as a function of pressure and temperature, yielding Equation 24.
AU = RT2
b In P ~
bT
- RT
T h e vapor pressure of a compound may be conveniently expressed by Antoine's vapor pressure equation,
B
lOgP=A-- t f C
80 T,.= * 40
70
-.
60
Y
V 0
50 NA-
1
40
I
I
1
I
I
80
70
u 60
-
\ 0 V
-50
40
80
90
100
110
120
I30
140
150
160
V, cc p#nole
Figure 2.
Homomorph plot for cycloparaffin hydrocarbons VOL. 7
NO. 2 A P R I L 1 9 6 8
21 5
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V, c c lgmole
Figure 3.
or In P = 2.303
[
A
-
Homomorph plot for aromatic hydrocarbons
" I
(2G)
(T-273+C)
Differentiating Equation 26 with respect to T and substituting in Equation 24 yields the expression used to calculate AU.
AU =
+ CY - RT
2.303RT2B (t
(27)
From Equation 27 the ordinate value, AU/V, can be calculated for a given molar volume and temperature. The various curves on Figures 1, 2, and 3 represent lines of constant reduced temperature. T h e square root of the ordinate used in these plots represents the nonpolar solubility parameter, h. T h e polar solubility parameter, 7, is determined by first calculating the total change in the energy of vaporization by
Table I. Volumes and Solubility Parameters for Hydrocarbons
Hydrocarbon
n-Propane n-Butane 1-Butene n-Pentane 1-Pentene n-Hexane 1-Hexene n-Heptane Cyclopentane Cyclohexane Benzene #-Xylene 1,3,5-Trimethylbenzene 1,4-Diethylbenzene To1u en e n-Propane n-Butane 1-Butene n-Pentane 1-Pentene n-Hexane I-Hexene n-Heptane n-Decane Cyclopentane Cyclohexane Ethylcyclohexane Butylcyclohexane Benzene Ethylbenzene Butylbenzene p-Xylene 1,3,5-Trimethylbenzene 1,4-Diethylbenzene Toluene n-Butane n-Pentane 1-Pentene
v,
A, 7) Cc./G. Mole (Cal./Cc.)112(Cal./Cc.)'/2 At 0' C. 83.1 6.92 0.00
96.7 90.3 111.8 106.0 127.3 121.6 143.8 91.9 105.5 86.9 121 .o 136.5 153.1 104.0 At 25' C. 89.4 101.4 95.3 116.1 110.1 131.6 125.9 147.4 195.8 94.7 108.7 143.3 176.4 89.4 123.1 156.8 123.9 139.8 156.9 106.8 At 45' C. 106.0 120.3 113.0
7.25 7.24 7.49 7.52 7.60 7.68 7.77 8.50 8.45 9.56 9.20 9.33 9.15 9.27
0.00 1.43 0.00 1.20 0.00 1.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.82
6.54 6.95 6.90 7.16 7.23 7.34 7.40 7.46 7.72 8.20 8.12 7.94 7.85 9.19 8.84 8.78 8.84 8.81 8.76 8.90
0.00 0.00 1.32 0.00 1.09 0.00 0.91 0.00 0.00 0.00 0.00 0.35 0.27 0.00 0.18 0.15 0.00 0.00 0.00 0.20
6.77 6.94 7.02
0.00 0.00 1.oo
n-Hexane 1-Hexene n-Heptane 1-Heptene Cyclopentane Cyclohexane Benzene p-Xylene 1,3,5-Trimethylbenzene 1,4-Diethylbenzene Toluene n-Pentane 1-Pentene n-Hexane 1-Hexene n-Heptane 1-Heptene Cyclopentane Cyclohexane Benzene p-Xylene 1,3,5-Trimethylbenzene 1,4-Diethylbenzene To1u en e n-Pentane 1-Pentene n-Hexane 1-Hexene n-Heptane 1-Heptene Cyclopentane Cyclohexane Benzene 4-Xylene 1,3,5-Trimethylbenzene 1,4-Diethylbenzene Toluene ~
216
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
V.,
Cc./G. Mole
Hydrocarbon
~
At 45' C. 135.4 129.5 151.9 145.5 97.4 111.5 91.6 126.8 142.7 159.8 109.2
7.10 7.18 7.23 7.25 7.89 7.86 8.91 8.56 8.54 8.50 8.72
0.00 0.83 0.00 0.69 0.00 0.00 0.00 0.00 0.00 0.00 0.61
110.8
6.80 6.84 6.94 7.00 7.09 7.14 7.71 7.70 8.94 8.38 8.36 8.32 8.52
0.00 0.93 0.00 0.76 0.00 0.62 0.00 0.00 0.00 0.00 0.00 0.00 0.57
At 100' C. 131.4 121.6 148.0 140.7 164.0 156.8 105.2 119.4 98.8 134.1 150.8 168.6 115.9
6.58 6.62 6.60 6.69 6.68 6.79 7.30 7.29 8.29 8.00 7.95 7.90 8.10
At 60' C. 122.9 115.9 138.7 132.4 154.3 148.4 99.4 113.6 93.4 128.7 144.8 162 . p
~~
~
0.00
0.75 0.00
0.64 0.00 0.44 0.00 0.00 0.00 0 .oo
0.00 0.00 0.48
Equation 27, next predicting the nonpolar solubility parameter from the appropriate homomorph plot, and then using Equation 28 to calculate the polar solubility parameter, 7.
Table 111.
Molar Volume and Solubility Parameters for Polar Solvents Cc./G.
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No. Table I lists the molar volume, polar, and nonpolar solubility parameters for selected hydrocarbons a t various temperatures. T h e critical temperatures of most of the polar solvents were estimated using the method of Lyderson (Reid and Sherwood, 1958). Vapor pressure and density data were taken from available literature sources. T h e molar volumes, nonpolar, and polar solubility parameters for 39 polar solvents a t 25' C. are tabulated in alphabetical order in Table 11. Values a t O', 45', 60°, IOO', 1 1 6 O , and 125' C. for several of these solvents are listed in Tables I11 and IV. T o evaluate the interaction energy, $12, in terms of known physical properties, Equation 21 was first rearranged to the form of Equation 29.
Vz[(7i
-
72)'
- 2 $121
(29)
By plotting the left side of this equality against the ordinate V2(71 - ~ 2 a) linear ~ ~ relationship was obtained. T h e terminal binary activity coefficient data of Gerster et al. (1960), Deal and Derr (1964), and Pierotti et al. (1959) were used with tabulated physical properties to obtain a plot of the infinite dilution activity coefficient data for both aliphatics and naphTable II. Molar Volume and Solubility Parameters for Polar Solvents
V,
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Solvent Acetone Acetonitrile Acetophenone Aniline Butanol Butyl acetate Butyrolactone Butyronitrile Chloropropionitrile Cyclopentanone Diethyl carbonate Diethyl ketone Diethyl oxalate Diisopropyl ketone Dimethyl acetamide Dimethyl cyanamide Dimethyl formamide Dimethyl sulfoxide Ethanol Ethyl acetate Ethyl n-butyl ketone Ethylene chlorohydrin Ethylene diamine Ethylene glycol Furfural Methyl Cellosolve Methyl ethyl ketone N-Methylpyrrolidone Nitrobenzene Nitromethane Pentanedione 1-Pentanol Phenol 1-Propanol 2-Propanol Propionitrile Pyridine Pyrrolidone Tetrahydrofuran
x,
7,
cc./
G. Mole
(Ca1.l CC.)'/Z
(Ca1.l CC.)'/2
74.0 52.6 117.4 91.5 92.8 131.5 77.0 87.9 77.7 89.2 121.9 106.4 136.2 161.9 93.2 80.3 77.4 71.3 58.7 98.5 139.8 66.9
7.68 8.02 9.57 9.83 7.79 7.65 9.59 7.98 8.41 8.88 7.86 7.72 8.14 6.74 8.28 8.06 8 35 8.46 7.80 7.60 7.88 8.05
6.00 8.90 3.94 6.62 8.40 3.40 7.54 6.07 9.12 4.58 4.38 4.77 6.45 4.57 7.25 7.49 7.57 9.40 10.70 4.52 3.63 9.36
67.3 56.0 83.2 79.4 90.1 96.6 102.7 54.3 103.1 108.7 89.3 75.2 77 .O 70.9 80.9 76.5 81.8
8.13 8.44 9.12 7.89 7.70 9.02 9.84 8.22 8.54 7.87 9.88 7.79 7.63 7.98 9.90 9.82 8.36
9.32 15.30 7.53 7.69 5.36
...
4.62 9.77 5.28 7.18 6.36 9.22 9.30 7.18 3.87 6.89 3.64
Solvent
Mole
At 0' C. 1 2 3 8 9 11 12 13 15 17 23 25 27 28 30 36 37 39
Acetone Acetonitrile Acetophenone Butyronitrile Chloropropionitrile Diethyl carbonate Diethyl ketone Diethyl oxalate Dimethylacetamide Dimethylformamide Ethylenediamine Furfural Methyl ethyl ketone N-Methylpyrrolidone Nitromethane Propionitrile Pyridine Tetrahydrofuran
72.3 51.1 115 .O 85.4 75.5 118.6 103.3 132.7 90.7 75.5 65.6 81.4 87.3 94.5 53.1 68.7 78.7 79.3
7.88 8.28 9.91 8.25 8.70 8.16 8.00 8.73 8.59 8.64 8.34 9.46 7.98 9.39 8.47 8.24 10.16 8.65
iO:i4 7.40 4.53 3.95
1 2 3 8 9 11 12 13 15 17 23 25 27 28 30 36 37 38
At 45' C. Acetone 76.2 Acetonitrile 54.4 Acetophenone 119.8 Butyronitrile 90.1 Chloropropionitrile 79.7 Diethyl carbonate 124.8 Diethyl ketone 108.9 Diethyl oxalate 139.3 Dimethylacetamide 95.3 Dimethy lformamide 79 . O Ethylenediamine 68.7 Furfural 84.8 Methyl ethyl ketone 92.6 N-Methylpyrrolidone 98.6 Nitromethane 55.3 Propionitrile 72.9 Pyridine 82.9 Pyrrolidone 77.4
7.44 7.83 9.30 7.77 8.20 7.63 7.52 7.88 8.07 8.14 7.94 8.91 7.36 8.75 8.04 7.75 9.57 9.90
5.82 8.55 3.90 5.90 8.79 4.29 4.61 6.28 6.95 7.26 8.98 7.27 5.15 3.73 9.48 7.06 3.20 6.52
7.28 7.70 9.36 7.96 8.10 7.24 7.48 7.75
6.28 8.46 6.39 7.42 9.15 4.32 3.65 9.28
7.76 8.76 7.59 7.34 8.70 9.42 7.88 . ..7.46 7.26 7.62 9.37
8.86 7.35 7.50 5.16 6.37 4.27 8.99 .. . 8.76 8.97 6.88 3.04
6.94 7.36 8.92 7.64 7.78 7.37 7.43 8.28 7.22 6.93 8.28 8.90 7.54 8.92 7.24 8.84
5.81 7.98 5.96 6.92 9.01 8.46 8.53 7.05 7.86 4.88 6.00 4.43 8.23 6.78 6.71 3.23
1 2 4 17 18 20 21 22
23 25 26 27 28 29 30 34 35 36 37
1 2 4 17 18 22 23 25 26 27 28 29 30 33 36 37
At 60' C. 78.1 Acetone 55.5 Acetonitrile 94.3 Aniline 80.2 Dimethylformamide 73.8 Dimethyl sulfoxide 103.3 Ethyl acetate 146.0 Ethyl n-butyl ketone 68.6 Ethylene chlorohydrin 69.7 Ethylenediamine 86.9 Furfural 82.3 Methyl Cellosolve 94.5 Methyl ethyl ketone 99.6 N-Methy lpyrrolidone 105.5 Nitrobenzene 56.3 Nitromethane 77.8 1-Propanol 80.5 2-Propanol 74.4 Propionitrile Pyridine 83.9 At 100' Acetone Acetonitrile Aniline Dimethylformamide Dimethyl sulfoxide Ethylene chlorohydrin Ethylenediamine Furfural Methyl Cellosolve Methyl ethyl ketone N-Methylpyrrolidone Nitrobenzene Nitromethane Phenol Propionitrile Pyridine
VOL. 7
C. 83.4 58.9 97.9 83.8 77.2 77.9 72.9 89.4 86.0 100.0 103.3 109.1 59.3 95.2 79 .O 87.4
NO. 2
6.32 9.29 4.92 6.28 9.67 4.67 5.10 6.34 7.88 7.89 9.71 7.88 5.56
~
APRIL 1 9 6 8
217
Table IV. Molar Volume and Solubility Parameters for Polar Solvents at Elevated Temperatures
V,
Cc./G.
Solvent
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1-Butanol Bum1 acetate Diisbpropyl ketone 1-Pentanol
t , O C. 116.1 116.1 125 .O 125.0
Mole 101.7 147.5 161.9 123.2
A, (Ca1.l Cc.)'/Z
6.94 6.72 6.74 6.88
7,
(Gal./
Cc.)1/2
6.87
-
2.66
4.57 6.47
thenes, aromatics, and olefins in polar solvents. $12 will vary for the three classes of hydrocarbons, saturated, unsaturated, and aromatic. Figure 4 shows a plot of the limiting activity coefficient data for saturated hydrocarbons in polar solvents over a temperature range of 0' to 125' C. Forty-eight hydrocarbon-polar solvent systems were used in constructing this correlation, with 34 solvents varying in polar solubility parameter from tetrahydrofuran to ethanol and 11 hydrocarbons ranging in molar volume from n-butane to butylcyclohexane. The slope of the saturated hydrocarbon curve is 0.202, corresponding to $12 = 0.399 (71 ~ 2 ) ~ Weimer . and Prausnitz (1965) reported that most of their data were fitted to within i = l O o J , of In 72"
-
Figure 4.
218
-
Saturated hydrocarbon correlation
v2 (ri
Figure 5.
for a similar correlation. The data in Figure 4 have an average error in In 7 2 " of 5.8%, with an actual average value of the absolute error in y2" of 11.6%. A similar correlation for unsaturated hydrocarbons (see Figure 5) using the I-pentene terminal activity coefficient data of Gerster et al. (1960), has a slope of 0.224, corresponding to $12 = 0.388 (71 ~ 2 ) ~ Because . of limited data, this relation covers a temperature range of only 0' to 45' C., but should be valid over a much broader range. Eighteen polar solvents ranging in polar parameter from acetophenone to nitromethane were used in the correlation. The average error in y2" for the 18 systems reported is 8.5%. Figure 6 shows the results obtained for aromatic hydrocarbons using the aromatic-polar solvent data of Deal and Derr (1964) and Pierotti et al. (1959). Seventeen hydrocarbon-polar solvent systems were used in this correlation, with 14 polar solvents varying in polar solubility parameter from pyridine to ethylene glycol. A temperature range of 25' to 100' C. is covered by these data. These data yielded an even smaller slope, 0.106, corresponding to $12 = 0.447 (71 ~ 2 ) ~ .The average error in ~ 2 "for the 17 systems reported is 13.5%. The prediction of selectivity using this correlation can be
-
r2f
Unsaturated hydrocarbon correlation
l & E C PROCESS D E S I G N A N D DEVELOPMENT
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y ('1 Figure 6.
v,
Cc./G. Mole 156.1 149.7 125.0
x,
(Cal./Cc.)1/2 5.72 5.72 6.71
7 1
(Cal./Cc.)'I* 0.00 0.77 5.91
illustrated by considering the system n-hexane-1-hexene in Cellosolve a t 135' C. The experimental data, which were not used in any of the author's correlations, were taken from Suryanarayana and Van Winkle (1966). The molar volumes and solubility parameters of n-hexane, 1-hexene, and Cellosolve at 135' C. are listed in Table V. From Equation 21 the following results are obtained. 72" = 4.68
(n-hexane)
(30)
72" = 3.57
(1-hexene)
(31)
T h e experimentally determined selectivity a t 135' C. is
S"
=
T21L
Aromatic hydrocarbon correlation
Table V. Properties and Parameters of the System n-Hexane-1-Hexene in Cellosolve at 135' C.
Hydrocarbon n-Hexane I-Hexene Cellosolve
-
p(n-hexane) = 1.33 7"(1-hexene)
correlation. Calculated and experimental activity coefficients at other concentrations agree within the limits of experimental accuracy. The correlation is valid for a wide temperature range, 0' to 125' C. Appendix
Calculation of Parameters for the System 1-Propanol-Ethyl Acetate at 60" C. I-Propanol Ethyl Acetate
T, = 536.7' K. To = 523.1'K. VI = 77.8 cc./g. mole VZ = 103.3 cc./g. mole AHu = 10,900 cal./g. mole AHu = 8000 cal./g. mole Xi2 = 55.6' Xz2 = 52.48 RT = 662.0 R T = 662.0 A U / V i = 132.4b A U / V z = 71.0b r I 2 = 76.8 rz2 = 18.6 7 1 = 8.76' 7 2 = 4.325 Xi 7.46 = 7.24 a From aliphatic homomorph plot. a From Equation 22. From Equation 28.
Nomenclature
Antoine's vapor pressure correlation constants Gibbs free energy of mixing enthalpy of mixing constant in Equation 20 pressure gas law constant selectivity at infinite dilution absolute temperature temperature, ' C. total energy of vaporization molar volume mole fraction in the liquid phase activity coefficient incremental change nonpolar solubility parameter volume fraction polar-polar and polar-nonpolar induction energy polar solubility parameter
The calculated selectivity, given by Equation 33, (33) agrees with that from the experimental data surprisingly well. Such excellent agreement cannot be expected in all cases. Conclusions
The proposed infinite dilution activity coefficient correlation possesses good accuracy and is a convenient way of predicting binary terminal activity coefficients. T h e correlation was developed for, and is applicable to, saturated, unsaturated, and aromatic hydrocarbons, based on the cohesive energy density concept. This method is especially useful in that infinite dilution activity coefficients for all three basic binary systemsnonpolar-nonpolar, nonpolar-polar, and polar-polar-may be predicted from one equation using only pure component physical properties. Infinite dilution activity coefficients for 83 binary hydrocarbon-polar solvent systems were used in developing the
SUBSCRIPTS C = critical conditions = component i, componentj, i # j = reduced conditions 1, 2 = component number
?'
VOL 7
NO.
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APRIL 1968
219
SUPERSCRIPTS E = excess = infinite dilution
co
=
U
vaporization
literature Cited
American Petroleum Institute Project 44, “Selected Values of Properties of Hydrocarbons and Related Compounds,” 1953. Anderson, R., Ph.D. dissertation, Department of Chemical Enrineerinc. Universitv of California. Berkelev. 1961. BaikeYr, J. A.,”J. Chem. Phis. 20, 1526 (1952). Black, Cline, Znd. Eng. Chem. 50,403 (1958). Bondi, A., Simkin, D. J., J . Chem. Phys. 25,1073 (1956). Carlson. H. C.. Colburn, A. P., Znd. Ene. Chem. 34. 581 (1942). Deal, C. H., Derr, E. ‘L.. IND. EN;. CHEM.‘PROCESS DESIGN DEVELOP. 3. 394 (1964). DreGbach, R.’R., ‘(P-V-T Relationships of Organic Compounds,” 3rd ed., Handbook Publishers, 1958. Dreisbach, R. R., Adv. Chem. Ser., Nos. 15, 22, 29 (1955, 1959, /
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1 oh1 ’i
Downloaded by NANYANG TECHNOLOGICAL UNIV on August 28, 2015 | http://pubs.acs.org Publication Date: April 1, 1968 | doi: 10.1021/i260026a010
Dreisbach, R. R., Znd. Eng. Chem. 41, 176 (1949). Dreisbach, R. R., “Physical Properties of Chemical Substances,” Dow Chemical Co., Midland, Mich., 1953.
Flory, P. J., J . Chem. Phys. 9, 660 (1951). Gerster, J. A,, Gorton, J. A,, Eklund, R. B., J . Chem. Eng. Data 5 , 423 (1960). Hildebrand, J. H., Scott, R. L., “Regular Solutions,” Prentice Hall. Endewood Cliffs. N. J.. 1962. Hildebrandv, J. H., Scott, R. L., “Solubility of Nonelectrolytes,” 3rd ed.. Dover Publications. New York. 1946. Huggins, ’M. L., J . Chem. Phys.’9,440 (1941). Orye, R. V., Prausnitz, J. M., Znd. Eng. Chem. 57, 18 (May 1965). Perry, J . H., “Chemical Engineer’s Handbook,” 4th ed., McGrawHill, New York, 1963. Pierotti, G. J., Deal, C. H., Derr, E. L., Znd. Eng. Chem. 51, 95 (1959). Reid, R. C., Sherwood, R. K., “Properties of Gases and Liquids,” McGraw-Hill, New York, 1958. Scatchard, G., Chem. Revs. 8, 321 (1931). Stull, D. R., Znd. Eng. Chem. 39, 517 (1957). Suryanarayana, Y. S., Van Winkle, Matthew, J. Chem. Eng. Data 11, 7 (1966). Van Laar, 1906. Weimer, R. F., Prausnitz, J. .M., Hydrocarbon Process. Petrol. Refiner 44, 237 (1965). Wilson, G. M., J.Am. Chem. SOC.86, 127 (1964). RECEIVED for review March 16, 1967 ACCEPTED October 13, 1967
LIQUID-LIQU ID AND VAPOR-LIQUID EQUILIBRIA FOR BINARY AND TERNARY SYSTEMS WITH DIBUTYL KETONE, DIMETHYL SULFOXIDE, n=HEXANE, AND 1-HEXENE H. RENO“ AND J. M. P R A U S N I T Z Department of Chemical Engineering, Uniuersity of California, Berkeley, Calif.
To facilitate a study of extractive separation using a mixed solvent, phase equilibrium data were obtained for mixtures of dibutyl ketone and dimethyl sulfoxide (DMSO) with n-hexane and with 1 -hexene. To characterize the binary solvent mixture, total vapor pressure data were obtained at 60”,70°,and 80” C.; to characterize ketone-hydrocarbon interactions, total vapor pressures were measured over the same temperature range for the binary systems ketone-hexane and ketone-hexene. Mutual solubilities with DMSO were obtained for both hydrocarbons. Liquid-liquid equilibrium measurements at 25” and 60” C. were made for the two ternary systems containing two solvents and one hydrocarbon. Data reduction utilized the nonrandom, two-liquid (NRTL) equation for excess Gibbs energy. While addition of dibutyl ketone to DMSO decreases the solvent-hydrocarbon ratio required for separation, the corresponding decrease in solvent selectivity is too large for any signifrcont economic advantage.
EQurD-liquid extraction and extractive distillation processes usually utilize only one solvent. I n the separation of olefins from paraffins, solvents which are highly selective unfortunately dissolve only small quantities of hydrocarbon and as a result, large solvent-hydrocarbon ratios are required to operate separation process equipment (Stephenson and Van Winkle, 1962). To lower this undesirably large ratio, one may add another solvent having more favorable solubility characteristics; however, such solvents tend to lower solvent selectivity. 1 On leave of absence from Institut F r a n p i s d u Pttrole, Rueil-Malmaison, 92, France
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I&EC PROCESS DESIGN A N D DEVELOPMEN1
To obtain increased understanding of phase relations in a mixed-solvent system, we have studied the separation of nhexane-1-hexene mixtures with dimethyl sulfoxide (DMSO) and dibutyl ketone. Experimental Apparatus and Procedure
Vapor-Liquid Equilibria. STATICMETHOD.The apparatus, shown schematically in Figure 1, consists of an isothermal bath containing the vapor-pressure cell and a differential manometer, a mercury manometer, a sampling section, degassing equipment, and a high-vacuum system. I n part, it is similar to the equipment used by Hermsen and Prausnitz (1963) and Orye and Prausnitz (1965). A glass cell is used, and the contents of the cell are: transferred to a sampling
