Ind. Eng. Chem. Res. 1992,31, 2603-2619 (26) Sincovec, R. F.; Erieman, A. M.; Yip, E. L.; Epton, M. A. Analysis of Descriptor Syatsm Using Numerical Algorithms. IEEE Trans. Autom. Control 1981,AC-26 (l), 139-147. (27) Wilkinaon, J. H.Linear DifferentialEquation13and Kronecker’s Canonical Form. Recent Advances in Numerical Anolyeis. Academic: New York, 1978; pp 231-265.
2603
(28) Yip, E. L.; Sincovec, R. F. Solvability, Controllability,and Olmervability of Continuous Descriptor System. ZEEE %M. Autom. Control 1981, AC-26 (S), 702-707.
Received for review July 16, 1992 Accepted July 31,1992
Statistical Thermodynamic Model for Viscosity of Pure Liquids and Liquid Mixtures Weihong Cao: Aage Fredenelund,* and Peter Rasmuseen Engineering Research Center IVC-SEP, Institut for Kemiteknik, The Technical University of Denmark, DK-2800 Lyngby, Denmark
On the basis of statistical thermodynamics, local compositions, and Eyring’s absolute rate theory, a new viscosity model for pure liquids and liquid mixtures has been developed. The model can be used to describe the viscosity of pure liquids a t different temperatures and of liquid mixtures at different compositions and temperatures. Correlation of viscosity data of 314 pure liquids and of 215 binary systems and prediction of viscosities for 14 ternary systems and 1 quaternary system have been carried out. The pure liquids include water, alcohols, organic acids, ketones, ethers, acetates, aldehydes, amines, aromatics, and other hydrocarbons, and the binary and multicomponent systems include mixtures with nonpolar + nonpolar, polar + polar, and nonpolar + polar components. The overall average MRSD (mean relative standard deviation) of the correlations of the pure liquid viscosities is 1.13%, and that of the binary systems is 0.80%. The overall average MRSD of the predictions of the multicomponent systems is 2.90%.
Introduction Information on the viscosity of pure liquids and of liquid mixtures is important in applications in chemical engineering, such as in the determination of flow in pipelines, mass-transfer operations, etc. Viscosity data of pure liquids and liquid mixtures at different temperatures, pressures, and compositions have been reported in the literature. Some of the viscosity data are published in the collection by Viswanath and Natarajan (1989) and by Stephan and Hechenberger (1988). A thorough review on models for viscosities of liquids may be found in Reid et al. (1987). The principle of corresponding states (Helfand and Rice, 1960; Gubbins, 1973; Teja and Rice, 1981) and Eyring’s absolute rate theory (Glasstone et al., 1941) have been widely used to describe the viscosity of pure liquids and liquid mixtures, see Hwang and Whiting (1987) and Wei and Rowley (1985). Moat of the correlation equations for viscosity of pure liquids are accurate but empirical and are not valid for the viscoeity of liquid mixtures. Models for viscositiea of liquid mixkvee have been reported in the literature and reviewed by Irving (1977a,b) and Reid et al. (1987). Most of the equations are based on the principle of cormponding state and Eyring‘s absolute rate theory. McAllister’s model (McAuister, 1960) is baeed on Eyring’s absolute rate theory including three-body or four-body interactions. It is widely umd to correlate the experimental viscosity data of liquid mixtures, but the parameters in McAllister’s model are Present address: DeDartment of Chemistry. Tsinahua
strongly dependent on temperature (Asfour et al., 1991). In 1986, Wu developed a group contribution method for predicting the viscosities of liquid mixtures. The method is a combination of Eyring’s absolute rate theory for pure components with the UNIFAC model. The purpose of this paper is to develop a viecosity model to be umd for correlating the viscosities of pure liquids and of binary systems, and from these results to predict the viscoeities of multicomponent systems. The model is b a d on statistical thermodynamics and on Eyring’s absolute rate theory. The concept of local compoeition is introduced into the model. The correlation of viscosities of 314 pure liquids, including water, alcohols, organic acids, ketones, ethers, acetates, aldehydes, amines, aromatics, and hydrocarbons,and for 216 binary systems, including nonpolar + nonpolar, polar + polar, and nonpolar + polar components, and the predictions for 14 ternary system and 1 quaternary system have been carried out. Good agreement between experimental and predicted results is obtained.
Statistical Thermodynamic Model On the basis of lattice theory (Guggenheim, 1952), the partition function of a pure liquid i can be written as
For a liquid mixture, following Abrams and Prausnitz (1975),we represent a molecule as a set of segments, using Staverman’s model (1950) as the boundary condition, and 0 1992 American Chemical Society
2604 Ind. Eng. Chem. ReB., Vol. 31, No. 11, 1992
we introduce local composition. The partition function of the liquid mixture is obtained from eq 1:
in the liquid. The work for movement to activation s t a b is given by ea
where Q is the partition function of the mixture, oi is the number of distinguishable configurations of lattice i, variables with superscript s are those of Staverman’s model, n is the number of components in the liquid mixture, Ni is the number of molecules of component i, mi is the mass of a molecule i, Tis the temperature, h is Planck’s constant, k is Boltzmann’s constant, and U, is the potential energy of the lattice i in the mixture:
= f&(&/2)
(8)
where f is the shear force per unit area, l2 and la are the distances between two equilibrium positions of neighbor molecules in the same molecular layer, and it is assumed that the activation energy barrier is symmetric between two neighbor equilibrium positions. If a molecule movea in the forward direction of the ahear force, it will obtain the work. The frequency of this direction is
(3) In this expression, z is the coordination number of the lattice, qi is the area parameter of molecule i, Vii is the interaction potential energy between sites i and j , and eji is the local composition: (4)
If a molecule movea in the backward direction of the shear force, it will overcome the work. The frequency of this direction is
For a pure liquid i, based on the following reaction process:
Ni.(i) T~~is the interaction parameter and ei is the average area fraction of component i in the liquid mixture:
x i is the molecular fraction of component i in the liquid
mixture:
=)
Ni.(i),
where ( i ) and (i), are molecule i at normal state and at activation state. The frequency of the pure liquid i can be obtained from eq 7:
For a liquid mixture, an equivalent expression is obtained by postulating the following reaction scheme:
EN,+)
3
CN;*(i),
The frequency of the liquid mixture can be obtained from eq 11:
Viscosity Equations for Liquid Mixtures Based on Eyring’s absolute rate theory (Glasstone et al., 1941), there is an activation energy barrier between two nearest equilibrium positions of molecules in a liquid. If a molecule in the liquid moves from an equilibrium site to another, the molecule has to overcome an energy barrier. If there is a shear force on the liquid, the molecular movements from one balance position to another in different directions of the liquid are different. If the shear force is equal to zero, the movements in different directions of the liquid are the same, and the frequency of these movements can be expressed as k, = kT Qa exp( h Q
g)
(7)
where k, is the movement frequency of one molecule, Q, is the partition function of activated state, and U, is the activation energy of a molecule. If there is a shear force, the movements in the forward and backward directions of the shear force are different because work is done by the shear force to the molecules
where N is the number of molecules in the liquid mixture (N = C N J . Eyring et al. (Glasstone et al., 1941) have for a number of systems compared the deviations of the observed energy of activation for flow in mixtures from the linear additive law with the deviation from Raoult’s law. The comparison shows a close relationship between the energy of activation and the free energy of mixing. Eyring et al. determined the energy of activation from the internal energy of vaporization at the normal boiling point multiplied by a general constant. Wu (1986) determined the energy of activation from the free energy of mixing multiplied by a general constant. Here we assume that the activation energy is directly proportional to the potential energy of molecule i in the liquid mixture
U, = niUoi
(13)
Ind. Eng. Chem. Res., Vol. 31, No. 11,1992 2606
and there are two degrees of freedom of molecular movement at the activation state because of the minimum energy limitation:
Mi,Vi, 7 j i , V , and M are the same. The interaction parameter,
is
T~~
(;
ujLTuii)
= exp -- -
~ j ;
and approximately that kT >> ea and l1 = l3 The defintion of dynamic viscosity of a Newtonian liquid can be written 8L8
f = -dAu/4)
(15)
In this equation, f is the shear force per unit area, u is the velocity of a molecular layer, ll is the distance between two molecular layers, Au/ll is the local velocity gradient, 7 is the dynamic viscosity of the liquid, and Au is the difference of velocity of molecdar layers and can be shown to be -Au = &(kf - kb) (16) Substitutions invohing eqs 3,8-10, arid 12-16 reedt in the following expression for the dynamic viscosity of pure liquid i:
Comparison to Other Models New viscoaity equations of pure liquids and liquid mixhues may be compared with some well-known viscoeity equations. The relationship between the viscosity of liquids and the temperature was proposed as the following expreasion: ln(d = A
+ (B/T)
by de Guzman (1913). Modifications of eq 25 have been reported to improve ita correlation accuracy; many include some function of the liquid molar volume in either A or B ( h i d et al., 1987). If we let
zqiniUii B = - 2R
2uRTMi ‘I2 A=(F)
The dynamic viscosity equation of the liquid mixture becomes
(18) Here vi is the dynamic viscosity of the pure liquid i, Vi is the molar volume of the pure liquid i, Mi is the molecular weight of component i, 9 is the dynamic viscosity of the liquid mixture, V is the molar volume of the liquid mixture, and R is the gas constant. Combining the definition of kinematic viscosity v = 9/P
(19)
where p is the density, the kinematic viscosity equation of the pure liquid i,
tl=
and the kinematic viscoeity equation of the liquid mixture can be written as n
n
n
In the viscoeity equations, all parameters, such as z, qi, nil
exp(
g)
Comparing it with eq 18, the expression of AG* given by McAllister is very similar to the expression in eq 18 if twdmdy interaction is assumed. The main difference is the P6in the first part of the two new viscosity eqs 17 and 18. Because the parameters in McAlliater’s equation are strongly dependent on temperature, the P6term is very interesting. On the basis of the free volume theory, Dymond and Brawn (1977) presented a liquid viscosity equation: 9
are obtained. In these equations, vi is the kinematic viscosity of the pure liquid i, Y is the kinematic viscosity of the liquid mixture, and M is molecular weight of the liquid mixture. For liquid mixtures, it is convenient to combine eq 18 with eq 17 and eq 21 with eq 20. Then the dynamic viscosity equation of the liquid mixture becomes
(26)
then the viscosity equation obtained in this paper, eq 17, reduces to eq 25 but A includes temperature and molar volume and B is slightly dependent on temperature. The widely used viscosity equation by McAlhter (1960) is based on the following viscosity expression obtained from Eyring’s absolute rate theory (Glasstone et al., 1941):
-= (A(MT)0.6
and the kinematic viscosity equation of the liquid mixture
(21)
(25)
52 ln V ) + B-v vo - v,
(28)
Comparing it with eq 17, both contain the term !P6. Irving (1977) recommended the one-parameter Grunberg-Nissan viscosity correlation in his review. For binary systems, the equation is
Md
= xi
U d + x2 In (92) + xixzG12
(29)
If we let Vi = V2
GI2
=
-41Q2
(
n1721 h ( 7 2 1 )
41x1
+ 42x2721
+
n2712 h(7iz) 41x1712
+ 4222
)
(30)
then eq 22 is reduced to eq 29. Reid et al. (1987) reviewed the new developments of the one-parameter GrunbergNissan correlation which are (1)the parameter has become a function of temperature; (2) the parameter is a function of composition, and (3) the parameter is estimated by group contribution. In this work, the parameter G12 of the new viscosity equation is a function of temperature and composition.
2606 Ind. Eng, Chem, Res., Vol. 31, No. 11, 1992 0.0100
Wei and Rowley (1985) proposed a new viscosity equation of liquid mixtures:
J
I . . . .
exp
- cal.
0.0080
sv = (sV)1m exP(-$
-
where ( T V ) is ~ local ~ viscosity. If we let
$0.0060
( q ~ ) , ,= f i ( T i ~ ~ ) x ini = u is1
( a i)~
(32)
then eq 22 is reduced to eq 31. Thus the new viscosity equations can be reduced to or compared with some well-known viscosity equations for pure liquids or liquid mixtures.
6 Y
0.0040 0
0.0020
Correlations of Viscosity Data of Pure Liquids The new viscoeity equations for pure liquids, eq 17 and eq 20 can be used to correlate viscosity data of pure liquids at different temperatures. In the two equations, qi is calculated from the surface area of the UNIFAC group (Hansen et al., 1991), Vi and Mi are obtained from DIPPR data bank (Daubert and Danner, 1989), and z is calculated from the following equation (SkjoldJolrge~senet al., 1980): z = 35.2 - 0.1272T
+ 0.00014P
Figure 1. Correlation of dynamic viscosity of ethyl propyl ether at different temperatures: h(n) = A,, + AIT + A2F.
0 . 0
0.04
(34) 0.03
where the coefficients Bj are determined from the molar heat of vaporization of the pure liquid i which am obtained from DIPPR data bank, based on the following equation: (35)
In the equation, A,.&m(,) is the molar heat of vaporization of the pure liquid i. The obtained coefficients of 314 pure liquids are listed in Table I. The last pure-componentparameter to be determined is nit and it is obtained by correlating the experimental viscosity data as a function of temperature: ln(ni) = CAjTJ j=O
The objective function used is
F=C
VISCOSITY& - VISCOSITY,, QVISCOSITY
where m is the number of experimental data,subscript cal and exp are calculated and experimental viscosity data; Q is the standard deviation of viscosity correlation and the values are given as u1 = lo-' for dynamic viscosity ( P a d u,
= 10-lo
:
(33)
Uii is a temperature function which is shown as the following equation:
(zqi/2)uii = RT - &va#m(i)
f
for kinematic viscosity (m2/s)
To examine the applicability of the new viecosity equations for pure liquids, the experimental viscosity data of 314 pure liquids including water, alcohols, organic acids, ketones, ethers, acetates, aldehydes, amines, aromatics, and other hydrocarbons have been correlated. All experimental viscosity data of the pure liquids were obtained from the DIPPR data bank. Then the coefficients of ni in eq 36 for the 314 pure liquids are obtained, and the viscosity data of the pure liquids at any temperature are calculated.
1
* MRSD of each system average MRSD
1
0.02
0.01
0.00 0 NUUBERS OF PURE WUlDS
Figure 2. Overall MRSD of the correlations of 314 pure liquids.
Figure 1 shows aa an example the calculated and experimental viscoeity data of ethyl propyl ether. Figure 2 shows the deviations between calculatedand experimental resulta for the 314 pure liquids. MRSD is the mean relative standard deviation and defined by MRSD = VISCOSITYd - VISCOSITY,, (38) m l VISCOSITY,,,
(If(
)"
The detailed correlational resulta for the 314 pure liquids, such as number of experimental pointa, temperature range, coefficients of ni in eq 36,and MRSD of each pure liquid are listed in Table 11. The overall average MRSD is 1.13%. The results show the new viscosity equations of pure liquids can be used to correlate viscosity data of pure liquids over a large temperature range and with good accuracy. Correlations of Viscoeity Data for Binary Systems In the new viscosity equations for liquid mixtures, eqe
Ind. Eng. Chem. Res., Vol. 31, No. 11,1992 2607 Table I. Coefficients of 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 40 41 42 43 44 45 46 47 48 49 50
51 52 53 54 55
56 57 58
59 60 61 62 63 64 65
66 67 68 69 70 71 72 73 74 75
76
77 78 79 80 81 82 83 84 85 86 87
U i.. i
Equation of Pure Substanceea -
name
no.
pinta
water
62
wtmn tetrachloride tribromomethane chloroform dibromomethane dichloromethane formaldehyde formic acid methyl bromide methyl chloride formamide nitromethane methane methanol methylamine tetrachloroethylene trichloroethylene pentachloroethane
30
1,1,2,2-tetrabromoethane 1,ldichloroethylane 1,1,1,2-tetrachloroethane 1,1,2,2-tetrachlorate l,l,l-trichloroethane acetonitrile ethylene 1,2-dibrornomethane 1,l-dichloroethane 1.2-dichloroethane acetaldehyde acetic acid methyl formate bromoethane ethyl chloride acetamide N-methylformamide nitroethane ethane dimethyl ether ethanol dimethyl sulfoxide ethylene glycol dimethylamine ethylamine acrylonitrile 1,2,3-trichloropropane propionitrile cyclopropane propylene 1,2-dichloropropane acetone n-propionaldehyde ethyl formate methyl acetate propionic acid 1-bromopropane 2-bromopropane isopropyl chloride n-propyl chloride NJV-dimethylformamide 1-nitropropane 24tropropane propane 2-propanol methyl ethyl ether n-propanol trimethylamine divinyl ether n-butyronitrile isobutyronitrile 2-pyrrolidone 1-butene cis-2-butene t~m-2-butene cyclobutane l,&dichlorobutane n-butyraldehyde isobutyraldehyde methyl ethyl ketone n-butyric acid 1,4diorane ethyl acetate methyl propionate n-propyl formate 1-bromobutane 2-bromobutane n-butyl chloride eec-butyl chloride
31 35 28 35 34 22 32 31 32 36 20 69 32 48 40 21 32 34 31 28 40 40 26 33 37 63 23 33 21 38 15 15 31 35 35 12 25 5 32 40 32 33 31 42
12 31 33 13 35
22 25 13 12 35 20 33 31 35 37 40 68 23 27 34 31 34 32 30 33 19 19 33 28 32 31 35
12 32
44 22 22 20 30
40 33
temperature 273.10-594.30 250.30-503.10 281.20-626.40 266.10-482.80 220.60-649.90 178.00-469.00 181.10-367.20 273.10-553.20 179.50-420.30 175.40-374.60 275.70-693.90 244.60-529.30 90.70-184.70 175.50-503.10 179.70-387.00 173.10-571.80 188.40-514.00 253.60-435.10 273.10-741.60 150.60-433.80 202.90-561.60 229.40-580.50 242.80-490.50 229.30-491.00 104.00-266.50 283.10-585.10 176.20-470.70 237.50-504.90 155.40-410.90 293.10-503.10 174.10-483.10 154.60-453.40 134.80-333.10 354.10-513.80 269.4M48.90 183.60-533.70 89.90 131.60-333.10 273.10-503.10 298.10-462.10 260.10-647.70 181.00-393.90 192.10-410.50 189.60-481.50 258.50-586.80 180.30-508.00 145.60-300.00 87.90-333.10 172.70-514.80 178.40-373.10 193.10-446.40 193.60-493.10 175.10-493.10 273.10-553.20 163.10-352.40 184.10-478.80 163.60-308.90 150.40-452.80 212.70-582.30 169.20-544.50 181.80-534.60 85.40-367.30 185.30-494.00 232.60-394.00 148.90-523.20 156.10-389.90 172.10-416.70 161.20-524.00 201.70-608.50 298.10-712.80 87.80-399.80 134.30-300.00 167.60-394.30 182.50-413.90 235.90-576.90 176.W472.50 208.1&456.50 186.50-499.80 273.10-553.20 285.00-528.30 189.60-470.90 185.60-513.20 180.20-523.20 178.70-519.30 161.20-510.30 150.10-483.30 141.90-468.50
MRSD 0.0118
0.0067 0.0089 0.0093 0.0115 0.0111 0.0132 0.0123 0.0117 0.0079 0.0145 0.0104 0.0144 0.0215 O.OO90
0.0170 0.0129 0.0014 0.0131 0.0059 o.Oo60
0.0174
0.0067 0.0124 0.0080 0.0120 0.0115 0.0154 0.0138 0.0094 0.0101 0.0136 0.0082
O.OOO9 0.0072 0.0147
0.0096 O.Oo40
0.0120 0.0001 0.0134 0.0116 0.0089 0.0194 0.0098 0.0157 0.0022 0.0163 0.0079 0.0125 0.0121 0.0165 0.0148 0.0149 0.0033 0.0141 O.OOO4
0.0133 0.0092 0.0106 0.0111 0.0171 0.0101 0.0183 0.0124 0.0130
0.0068 0.0093 0.0126 0.0075 0.0140 0.0017 0.0150 0.0092 0.0077 0.0168 0.0148 0.0175 0.0159 0.0113 0.0114 0.0178 0.0206 0.0091 0.0102 0.0133 0.0159
10-1& -3967.897 000 -3634.634000 -4962.981 900 -3830.417 200 -4844.995 100 -4033.875000 -2624.993 900 -18592.709000 -3133.647 200 -2472.945 100 -5517.614 300 -4608.367 200 -2157.551000 -8876.460000 -3027.588 100 -4333.459000 -3297.962200 -5753.999000 -12488.860 400 -4733.842 300 -5443.247 100 -7716.761 200 -4180.808 100 -4577.698 700 -2558.228000 -2830.432 100 -4221.955 100 -4137.388 200 -3407.752000 1685.653930 -5272.368 200 -4346.015 100 -3610.988000 -9663.772 500 -5944.110 400 -4441.438000 -1854.992 070 -2424.490000 -5230.425 300 -14621.190400 -6221.442 400 -3626.296 900 -3382.512 200 -4359.907 200 -4697.746 100 -5611.210900 -2843.614000 -2495.883 100 -4029.293 000 -4355.466 300 -3281.363000 -6201.712900 -7435.626 000 2528.288 100 -4845.703 100 -3901.143 100 -4002.885 300 -4144.743.200 -5315.446 800 -5281.890 100 -4477.564000 -1350.760010 -7924.120600 -8424.517 600 -7634.480000 -4075.619 900 -3599.092 300 -5294.056 200 -4429.489 700 -6721.957 000 -4314.953 100 -3783.832 000 -2803.598 100 -2823.563 200 -4760.992 200 -5728.314 900 -6376.331 100 -4233.095 200 3302.444 100 -2490.445 100 -4704.521 000 -7134.856400 -6444.126 500 -5086.371 100 -4093.117 200 -4878.856 OOO -3994.082 000
lOB, -479.882110 -131.281601 36.845 852 44.240681 293.546 300 213.265396 -142.011 093 18159.611300 155.460907 -141.279602 -896.735600 145.716995 3128.847 900 4313.337 900 -279.772 800 -105.516 197 -401.495 390 472.787900 2122.833000 882.807 310 336.002 870 1089.948 970 143.733 002 473.224 180 1685.099000 -788.842.160 278.104710 31.856051 8.157600 -1991.967040 1788.234990 620.075880 360.421 480 1562.239940 -161.534805 -119.886795 52.653 488 -237.326 294 1426.724 980 4849.228000 -532.697 690 8.676 358 -174.&2499 321.251 500 -219.868607 818.208500 276.716490 88.245 132 -94.142639 406.372 990 -248.183716 2455.782000 3500.561300 -2952.319 100 705.054 080 174.402802 370.807 500 318.964420 -3.091 787 221.531298 -76.127449 -2824.111 100 2775.086 200 2896.395000 2106.262000 736.424 800 30.017 099 364.213810 -84.381 927 -163.578888 1820.482040 593.114 870 -174.074 402 -121.046402 -189.788 815 898.036 740 1399.166020 -11.066290 -3842.793 400 -993.280030 156.247391 2586.579 100 2212.442900 219.431 702 -117.448502 452.815520 148.990799
1OBBs 141.300308 114.341202 78.324 158 90.913979 51.318050 81.797768 137.373596 -7038.290000 66.980949 139.657 898 227.636 398 63.722 290 -2464.218000 -1282.304080 192.306 290 105.105 698 145.596 688 20.294519 -100.034 203 -33.473919 57.049 320 -14.452 820 82.736244 9.429 376 -863.630 130 168.982 407 62.652470 88.154892 121.072296 267.133880 -517.110410 -1.810111 43.104488 -132.027 893 106.298096 107.020401 130.345901 172.263199 -661.497 130 -548.706 480 171.351303 149.322998 165.168900 37.820499 116.494 400 -22.373 541 64.880 588 123.281097 108.600899 28.264 420 142.644 699 -725.409 120 -1034.194950 393,857 700 -23.370 979 66,428 2& 43.913300 62.432812 96.708 755 61.918 541 98.597 862 2647.661 900 -880.578 670 -268.379000 -615.167050 -2.143 566 120.126396 48.734 562 117.819901 100.377 800 -604.982 360 5.356 465 159.613 998 122.759 796 116.213906 -14.769 230 -89.619 400 115.971703 490.293 580 215.511612 101.365501 -673.795410 -599.145690 79.747 169 118.078300 45.200790 75.068 832
1@Bo
1O'BI
1150.708980
-66.32861
730.908 810 147.281204
199.593704
72.491 859
108.314308
91.787 453 121.641296
-906.470 760 121.567 398 87.707 726
93.375931
78.995 750 72.844009
113.898 201
2608 Ind. Eng. Chem. Res., Vol. 31,No. 11,1992 Table I no. 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155
(Continued) name tert-butyl chloride pyrrolidine N,h'-dimethylacetamide n-butane isobutane n-butanol sec-butanol tert-butyl alcohol diethyl ether isobutanol 1,4butanediol 2,3-butanediol pyridine cyclopentene valeronitrile cyclopenbe 1-pentene cia-2-pentene trans-2-pentene 1,5-dichloropentane diethyl ketone methyl isopropyl ketone 2-pentanone n-butyl formate ethyl propionate isobutyl formate isopropyl acetate methyl n-butyrate n-propyl acetate 1-chloropentane isopentane neopentane n-pentane 2,2-dimethyl-l-propanol ethyl propyl ether 2-methyl-1-butanol 3-methyl-1-butanol methyl see-butyl ether methyl tert-butyl ether 1-pentanol 2-pentanol 3-pentanol 1,bpentanediol n-pentylamine 1,3,&trinitrobenzene rn-chloronitrobenzene o-chloronitrobenzene p-chloronitrobenzene rn-dichlorobenzene o-dichlorobenzene p-dichlorobenzene rn-dinitrobenzene o-dinitrobenzene p-dinitrobenzene bromobenzene monochlorobenzene rn-chlorophenol o-chlorophenol p-chlorophenol nitrobenzene benzene rn-chloroaniliine o-chloroaniline phenol 1,2-benzenediol 1,3-benzenediol 1,2,3-benzenetriol aniline 156 2-methylpyridine 157 3-methylpyridme 158 4-methylpyridme 159 cyclohexene 160 cyclohexanone 161 hexanenitrile 162 cyclohexane 163 1-hexene 164 methylcyclopentane 165 cyclohexanol 166 2-hexanone 167 3-hexanone 168 methyl ieobutyl ketone 169 n-butyl acetate 170 sec-butyl acetate 171 tert-butyl acetate 172 ethyl n-butyrate 173 .. ethyl isobutyrate 174 n-hexanoic acid
pointa 33 33 30 39 33 40 38 31 33 30 30 30 37 36 30 36 39 33 33 30 37 16 38 28 17 32 31 16 22 39 29 34 59 31 34 30 30 30 35 46 47 33 30 31 21 24 30 30 33 35 33 30 30 30 36 48 30 30 31 30 41 32 35 64 31 30 30 30 9 12 34 37 40 30 24 31 38 34 32 16 32 40 30 30 34 32 34
temperature 247.M56.30 215.30-511.70 253.10-592.20 170.00-400.00 113.50-366.50 184.50-506.60 158.40-482.40 298.00-455.60 156.90-420.00 165.10-470.40 293.00-600.20 280.w549.90 231.50-558.00 143.10-493.10 176.90-542.70 179.30-460.40 107.90-418.30 121.M28.30 132.90-427.80 200.40-596.70 234.20-504.90 202.20-497.70 196.30-505.00 202.20-485.10 273.10-503.10 183.80-371.40 205.10-361.60 373.10-523.20 298.10-523.20 174.10-511.20 113.20-430.00 213.10-402.80 143.40-433.10 327.10-495.00 145.W-450.20 298.10-508.50 155.90-521.50 150.00-448.20 164.60-447.40 195.60-529.30 274.60-496.80 204.10-492.30 257.20-605.70 218.10-499.50 398.40-747.40 317.60-595.40 306.10-681.30 356.60-675.90 248.40-624.60 256.10-634.50 298.10-625.50 364.00-724.50 390.10-747.90 446.60-722.70 242.40-603.10 227.90-569.10 306.00-656.10 282.00-607.50 316.00-664.20 278.90-617.10 273.10-533.10 262.80-675.90 271.00-619.80 314.10-624.80 377.60-687.60 382.00-729.00 407.00-747.00 267.10-673.20 298.10-402.50 298.00-417.30 298.10-581.50 173.10-513.20 242.00-554.90 205.10559.80 273.10-537.00 133.40-453.60 130.70-479.50 296.60-562.60 217.40-528.30 298.10-396.60 189.10-514.30 199.60-521.20 300.90-385.10 283.10-490.50 175.10-513.90 185.00-497.80 270.10-600.30
MRSD
1O-'Bo -2566.206 100 -6195.991 200 -4489.630400 -2356.293000 -3210.386000 -5998.392 100 -6898.970 200 -5480.019 000 -4833.817 400 -11037.370 100 -4125.407 700 -5994.294 900 -5639.944 800 -2485.864000 -6457.269000 -3659.712200 -4284.216300 -4232.721 200 -3857.737 100 0,0096 -5668.266 100 0.0110 -4076.018 100 0.0124 -5104.873 000 0.0151 -2908.002 900 0.0185 -4966.257 300 -4111.509300 0.0125 -5559.263 200 0.0035 -5266.614 700 0.0021 0.0073 -760.607 910 0.0149 -2526.018 100 -4998.066 900 0.0091 0.0184 -3557.128200 0.0113 -2287.583 000 0.0177 -3946.830 800 0.0082 -7513.018 100 0.0154 -6734.247 600 -12445.790000 0.0082 0.0162 -7627.527 300 0.0095 -3773.895000 0.0123 -3544.001 200 0.0165 -9385.704 100 -6414.844 200 0.0085 0.0133 -5401.753400 0.0187 -7749.329 600 0.0167 -4030.736 100 -7913.989700 0.0010 -5605.200 200 0.0040 0.0134 -5224.095 200 0.0047 -6089.491 200 0.0136 -4279.205 100 0.0198 -7296.335 900 0.0110 -5062.673 800 0.0061 -8626.759 800 0.0061 -8564.204 100 0.0041 -6768.860 800 0.0058 -5248.125 000 0.0080 -4309.028 800 0.0136 -3490.935 300 0.0141 -2741.063200 0.0096 -3719.351 300 0.0075 -5748.540 000 0.0063 6629.145600 -8037.770 600 0.0184 0.0049 -6967.884 300 0.0040 -8435.347 700 0.0084 -4863.409 200 0.0059 -8924.088 900 0.0171 -66.481 003 0.0165 -13185.109400 -5912.2690 00 0.0005 -5864.151 400 0.0014 0.0085 -5058.731 900 0.0182 -3559.357 900 0.0187 -6714.360400 -6616.772000 0.0089 0.0063 8050.583000 0.0154 -4457.173800 0.0139 -4557.690 900 0.0120 -6867.246100 0.0114 -4644.636 200 -5761.805200 0.0021 0.0139 -7932.635 300 -5119.418000 0.0092 0.0001 -5747.323200 0.0031 -3424.432 100 -4822.571 300 0.0136 -3929.344 200 0.0122 0.0125 -8219.710000 0.0074 0.0095 0.0114 0.0190 0.0132 0.0168 0.0177 0.0036 0.0104 0.0165 0.0162 0.0144 0.0134 0.0153 0.0142 0.0098 0.0164 0.0141 0.0137
lOBl l@Bp 1@B, -564.138 310 185.427 505 897.974 790 -4.394625 -485.612920 149.396805 -425.885 010 199.309311 236.342 300 96.681786 -259.001 710 199.135498 265.004 910 154.545990 -491.942900 280.502 720 638.911 070 29.465 040 2303.661 900 -108.827 400 -1610.422 120 250.903900 -460.643 620 143.879898 40.631 409 467.466 580 1342.273930 -1874.702 030 -340.560 390 753.802 860 2.573963 91.527443 77.143822 593.692 990 25.927 780 461.170810 47.991 173 240.896 606 80.633 301 -14.085 850 98.720062 -217.946 198 131.200 104 293.645 900 74.414 726 -807.902 830 204.540 894 36.754841 320.209 900 179.514496 -388.888 790 54.928 577 458.994 290 44.801 487 482.571 410 328.648800 -1824.474000 269.758 300 -1167.463010 52.222 977 341.818510 117.690895 81.728775 204.099 899 -490.701 720 254.175 293 87.486732 541.563960 108.539902 -115.194 496 1623.101070 2657.103 000 -139.425903 274.721 310 151.436005 -103.479 202 135.952805 -145.457 291 137.958099 1239.646000 16.641579 -177.132 095 202.391 998 222.869 507 -476.694 610 -233.598 404 113.532700 -390.013 400 163.149292 30.955 071 89.107 040 74.032 173 -136.996 002 103.018600 -379.250 430 133.655594 -414.658020 136.147308 -446.170380 1522.714970 -312.133 700 33.362488 -85.964 279 94.941 116 -133.719391 113.811600 -270.758 790 122.716003 -783.757 390 170.024200 137.524 506 68.461 967 -153.969604 104.610397 -874.026430 147.243805 -859.966 800 145.199295 151.255203 -876.421 450 100.794395 -127.027 397 -11919.239 30 5045.937 000 -901.077030 557.795 590 34.368519 40.920952 398.896 120 6.392 929 903.843 690 -601.098570 109.070503 -50.257 240 107.697304 -2M.289 100 297.734 710 4901.244 100 -1001.867980 80.431442 606.7327 90 11.315890 471.228970 29.128571 37.021812 84.464149 -261.982 300 135.777 588 901.615840 -30.593 790 350.058 230 76.694964 -13461.23050 5729.711900 -1038.366930 373.963010 58.831 902 48.572777 400.474 580 -193.935516 184.01s091 -238.133 102 140.845200 488.056 180 38.641 033 1625.286990 -95.911 346 119.527000 -21.015011 48.733 101 485.694 400 -575.947 390 189.696 198 95.180367 45.756 538 -405.075 100 160.361099 -28.259600 155.446 503
107~~
32.89040
60.692 780
71.143898
Ind. Eng. Chem. Res., Vol. 31,No. 11,1992 2609 Table I (Continued)
no. 176 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256
257 268 269 260 261
name isobutyl acetate n-propyl propionate 2,2-dmethylbutane 2,3-dimethylbutane n-hexane
2-methylpentane 3-methylpentans n-butyl ethyl ether di-n-propyl ether 1-hexanol 2-hexanol 2-methyl-I-pentanol l,&hexanediol diethylene glycol dimethyl ether triethylamine 2,4,&trinitrotoluene 2,6dinitrotoluene benzaldehyde benzoic acid benzyl chloride o-chlorotoluene p-chlorotoluene m-nitrotoluene o-nitrotoluene p-nitrotoluene toluene anisole benzyl alcohol m-cresol o-cresol p-cresol benzylamiine m-toluidine o-toluidine p-toluidine cycloheptane 1-heptene methylcyclohexane 2-heptanone diiipropyl ketone n-heptanoic acid n-pentyl acetate n-propyl n-butyrate 2,2-dimethylpentane 2,3-dimethylpentane 2,ddmethylpentane n-heptane 2-methylhexane 3-methylhexane 2,2,3-trimethylbutane 1-heptanol methyl benzoate ethylbenzene m-xylene o-xylene p-xylene phenetole Nfl-dimethylaniline 1,l-dimethylcyclohexane
cis-1,2-dimethylcyclohe~e tra~-1,2-dimethylcyclohe~e cis-1,3-dimethylcyclohexane tMM-1,3-dimethylcyClOhexane
cis-1,ddimethylcyclohexane trans-1,4-dimethylcyclohexane ethylcyclohexane 1-octane 2-octanone n-butyl n-butyrate isobutyl isobutyrate n-octanoic acid 2,2-dimethylhexane 2,5-dimethylhexane 3,3-dimethylhexane 2-methylheptane n-octane di-n-butyl ether di-tert-butyl ether 2-ethyl-1-hexanol 1-octanol 2-octanol diethylene glycol diethyl ether benzyl acetatc ethyl benzoate m-ethyltoluene 0-ethyltoluene p-ethyltoluene
points 33 36 35 41 43 39 38 35 67 30 36 31 32 30 39 31 30 35 31 31 31 31 30 30 30 99 37 32 30 30 30 30 32 30 25 34 33 33 31 32 18 31 31 34 34 35 28 34 37 34 34 27 39 68 70 89 34 22 34 31 34 34 34 34 34 38 39 31 30 33 34 30 34 34 38 42 30 34 30 30 30 31 32 27 34 34 32
temperature 174.30-504.90 107.20-520.20 174.30-439.90 145.20-450.00 273.10-488.70 119.60-447.80 110.20-454.00 170.10-477.90 149.90-477.50 228.60-550.20 223.00-527.60 288.10-523.80 298.1M3.00 210.8M32.90 158.M1.60 354.00-715.50 339.00-693.00 247.10-625.50 395.50-675.90 234.10-617.40 236.60-590.40 280.60-594.00 289.2&660.60 270.M8.00 324.80-662.40 178.20-546.00 236.60-577.50 257.90-609.30 285.40-635.30 304.20-627.80 307.90-634.20 273.W615.20 242.80-638.20 269.M24.70 318.10-633.20 265.10-543.90 154.30-480.00 146.60-515.00 238.100-550.40 204.80-518.40 373.30-576.20 209.70-422.40 177.90-534.60 149.30-468.50 203.10-483.60 153.90-467.80 273.10-513.20 154.90-477.30 153.80-481.70 248.60-478.00 239.10-568.70 260.80-586.20 267.00-487.00 225.30-582.00 248.00-6 12* 00 286.40-557.20 243.60-582.40 292.70-618.40 239.70-532.00 256.50-545.50 185.00-536.50 197.60-532.00 183.10-538.20 185.70-538.30 236.20-531.10 161.80-548.20 171.40-510.00 252.90-561.60 181.10-554.40 192.40-541.80 289.60-0.0184 152.00-494.80 182.00-495.00 147.10-505.80 164.20503.70 216.40-512.00 177.90-522.90 195.00-495.00 203.10-576.20 257.60-587.20 241.60-573.40 228.90-561.60 230.50-486.60 238.40-687.80 177.60-573.40 192.40-586.00 210.80-576.10
MRSD
lO-'Bo
0.0168 0.0139 0.0102 0.0132 0.0171 0.0160 0.0160 0.0151 0.0161 0.0124 0.0147 0.0108 0.0149
-5123.917500 -4348,834000 -3864.698.000 -4226.978 000 -2115.251 000 -4234.032 700 -5279.071 300 -4850.998 100 -5408.564900 -7699.614 300 -7029.021 000 -2134.979000 09010.411 100 -7646.918000 -3958.563000 -6554.897 000 -8596.311 500 -5094.592 300 -5658.346 200 -4608.548 800 -4755.745 100 -5774.707 000 -2486.896 200 -5325.722 200 -1423.399 050 -4923.835 900 -5538.071 300 -9962.318 400 -10703.540000 -8472.315400 -11428.250 000 -5454.927 200 -5615.917 500 -7108.968000 -2731.898 200 -4746.640 100 -5303.362 300 -5402.430 200 6111.657200 -5509.495 100 -17693.880900 -7172.249 500 -5168.938 000 -4217.044900 -4034.002000 -4755.192 900 -3280.380 100 -6406.329 100 -4916.952 100 -3448.134000 -11530.549800 -7265.915 500 -5540.016 100 -4627.206 100 -9436.497 100 -4402.773900 -5712.916000 -6096.705 100 -4375.921 400 -4301.345200 -4827.552 200 -4733.313000 -4904.687 000 -4821.763 200 -4337.433 100 -5258.575 200 -6010.541 000 -8648.704 100 -6024.919400 -5753.660 200 -10941.850 600 -5442.685 100 -5341.138200 -5384.787 100 -5442.826 200 -4282.207 OOO -5511.604 000 -4595.214 800 -17455.570300 -12052.020500 -11790.339 800 8482.928 200 -7569.236 800 -5161.105000 -5642.809 100 -5027.448 700 -5752.212400
O.OOO9
0.0111 0.0063 0.0076 0.0199 0.0047 0.0135 0.0114 0.0104 0.0159 0.0159 0.0140 0.0150 0.0109 0.0041 0.0123 0.0120 0.0122 0.0065 0.0119
0.0065 0.0085 0.0092 0.0145 0.0142 O.Oo40
0.0151 0.0031 0.0098 0.0108 0.0061 0.0110 0.0133 0.0140 0.0172 0.0136
0.0068 0.0187 0.O008 0.0035 0.0196 0.0127 0.0093 0.0133 0.0132 0.0079 0.0068 0.0124 0.0113 0.0133 0.0131 0.0083 0.0140 0.0157 0.0117 0.0109 0.0100 0.0184 0.0153 0.0134 0.0158 0.0150 0.0110 0.0107 0.0050 0.0161 0.0031 O.Oo60 0.0078 0.0084 0.0080 0.0177 0.0106
0.0148
lOBl 95.124451 -372.939 420 202,716293 326.184 080 -1042.669 920 287.207 790 872.757 020 55.878 441 550.013060 274.737 490 47.554 832 -2132.675000 -235.431 900 752.844 120 153.187897 -292.332 890 -146.716904 -230.552 811 -574.390930 -414.656 920 -194.797001 209.114 304 -1285.491 940 -329.313 510 -1670.467 040 242.687 210 137.666794 1202.428960 1541.687010 865.693 910 1882.874020 -254.070 496 -232.955 093 337.521 210 -1519.094970 147.648804 556.590 820 634.006 840 293.883 910 276.853 000 3667.585 200 871.675480 -32.865 070 129.833099 -85.967 880 380.206 790 -649.353 330 626.092 650 355.202 210 -250.201 401 1652.606080 541.632 390 394.169 370 -148.680 801 3504.167000 -198.747 192 -2.177549 27.520371 -41.650 120 -177.197 403 165.756 500 104.661 705 136.454 193 105.781304 -66.405 403 270.780 700 633.752380 723.327 700 89.771 729 98.026 436 710.336 240 505.625 790 404.893 980 486.116700 374.813600 -332.267 700 18.946 430 52.081 291 4268.861 300 1739.774050 1829.916990 -132.315399 464.726 720 -321.008910 119.974 297 -182.473 602 179.605408
l@B, 100.019997 163.834 306 81.685960 64.774 460 262.521 610 71.413 826 -12.100 150 113.510605 43.191 830 127.090607 165.714600 389.500 400 153.655090 32.671 993 131.239700 112.589005 124.725403 113.981300 147.327606 134.320602 112.543800 70.498 611 184.832 794 110.572 197 213.593491 tx.290733 77.591 270 -16.775 190 -41.896790 12.723080 -84.060631 124.104500 114.035500 61.524048 256.889 190 75.393 394 34.525 349 18.054 239 78.397 758 75.533 310 -215.108093 -3.393 639 110.923096 92.806 808 121.705704 62.108231 204.411 194 30.268 570 64.484 299 137.733902 -10.119 590 35.116222 42.673 492 115.712601 -789.147520 116.619 202 101.956 703 96.293 060 105.487694 122.516998 78.878380 90.198761 87.659943 90.623466 109.031 204 68.328 407 30.896601 73.274 139 104.509804 109.829201 83.560699 46.846 882 61.478909 43.397 110 64.627 121 155.848 206 120.743500 104.994 400 -293.474610 -20.813061 -27.978 109 142.172 195 52.255 852 111.303001 90.620 895 122.776802 82.025 223
I@Ba
71.938805
IO'&
2610 Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 Table I (Continued) no. name 262 meaitylene 263 n-propylbenzene 1,2,8trimethylbemne 264 265 benzyl ethyl ether I-nonene 266 267 n-nonanoic acid 268 2-methyloctane 1-nonanol 269 270 n-nonane 271 tripropylamine n-butylbenzene 272 273 m-diethylbenzene 274 o-diethylbenzene 275 p-diethylbenzene iaobutylbenzene 276 1,2,4,6tetramethylbenzene 277 278 1-decene 279 n-decanoic acid 280 n-decane 281 l-dmol 282 1-undecene 283 n-undecane l-undecanol 284 n-decanoic acid 286 286 n-dodecane l-dodecanol 287 1-dodecene 288 289 n-tridecane 1-tridecanol 290 291 benzyl benzoate 292 dibenzyl ether 293 I-tetradecene n-tetradecanoic acid 294 296 n-tetradecane 296 1-tetradecanol 297 1-pentadecene 298 pentadecanoic acid 299 n-pentadecane 300 1-hexadecene 301 n-hexadecanoic acid 302 n-hexadecane 303 1-hexadecanol 304 n-heptadecane 305 1-heptadecanol 306 1-&decem 307 n-&decane 308 l-octadecanol 309 I-nonadecene 310 nonadecanoic acid 311 n-nonadecane 312 I-eicosene 313 n-eicosane 314 1-eocisanol
pointa 37 30 36 30 33 30 34 30 36 31 46 33 34 34 34 33 35 30 39 36 32 32 30 30 32 32 33 51 31 30 30 31 30 31 30 22 20 21 17 30 31 30 24 30 25 21 31 22 20 35 32 32 31
temperature 228.50-673.60 173.60-674.50 247.80-698.10 283.10-695.80 191.80-532.80 286.60-632.70 192.80-628.10 268.10-606.70 219.60-636.10 179.60-619.80 193.10-623.20 189.rn596.70 241.90-601.20 230.30-692.20 221.70-585.10 298.10-607.60 206.90-555.30 304.80-641.70 243.50-666.90 280.00-621.00 224.00-674.20 247.60-574.80 289.00-633.60 317.00-660.60 263.60-592.40 297.00-648.90 237.90-591.30 267.80-608.20 303.80-657.90 292.50-738.00 276.80-699.30 260.30-622.80 327.50-680.40 279.00-623.20 310.60-666.90 287.80-637.20 343.90-689.40 300.80-636.10 298.10-649.80 355.70-698.40 291.3CH48.50 322.40-684.90 298.10-660.00 327.00-693.00 369.90-673.20 298.10-670.70 331.00-699.30 298.10-684.00 360.60-729.00 298.1-30 298.1H93.90 309.60-690.30 338.50-7 12.80
MRSD 0.0124 0.0165 0.0123 0.0106 0.0169 0.0118 0.0078 0.0095 0.0102 0.0089 0.0131 0.0155 0.0112 0.0103 0.0087 0.0193 0.0058 0.0069 0.0149 0.0163 0.0136 0.0142 0.0121 0.0026 0.0058 0.0111 0.0042 0.0157 0.0104 0.0082 0.0176 0.0156 0.0014 0.0142
0.0083 0.0099 O.OO60 0.0086 0.0107 0.0155 0.0148 0.0162 0.0177 0.0041 0.0085 0.0178 0.0158 0.0125 0.0054 0.0148 0.0176 0.0190 0.0114
1O-'B0 -5622.077 100 -6368.196 300 -4619.837 400 -5304.169 200 -6673.696 300 -14794.670300 -6489.622000 -16274.210000 -4662.906300 -5474.125000 -7117.177200 -6377.471200 -5789.532 800 -6070.436 OOO -&%1.397000 -5875.520 000 -6414.700 200 -27829.941 400 -4467.485800 -13496.080 100 -8609.336 000 -8331.339800 -18451.330 100 -18656.300800 -7160.202 600 -16801.271 500 -8111.378 900 -7692.974 100 -17454.080 100 -9571.083 000 -4419.481 900 -10914.260700 -17778.791 000 -11088.639 600 -19242.580 100 -9619.446 300 -13725.710000 -9253.405300 -10222.040 000 -5714.376 500 -11164.889600 -22345.669 900 -11612.970700 -14898.820 300 -17730.271 500 -13243.669800 -13370.780 300 -12395.799800 -14987.030 300
-12960.500000 -15878.090800 -10537.1104400 -18030.679 700
40verall number of pure liquide and average MRSD 314; 1.14%.
22 and eq 23, V and M are calculated by the following equations: is1
106&
I@& 83.132294 32.982 269 130.990601 108.280396 37.747 688 -71.406367 104.612 198 -139.367 096 163.197403 120.836098 -249.898 300 73.083 954 101.757698 78.500443 56.015 862 99.665 085 80.542770 -444.349 120 191.334610 -42.935 112 -1.047 168 20.396 720 -220.160096 -119.918098 106.719498 -122.670700 52.373461 94.417603 -130.743 103 69.918 144 293.243 930 -19.868429 -90.832 962 -16.811 831 -164.098404 60.258629 44.763 828 77.463 348 56.633 400 182.856 308 18.274 342 -234.860 306 17.487640 84.046783 -156.947 189 -44.704033 143.981689 28.481 610 35.886 021 20.018 250 -55.6734 20 119.315 102 45.925331
10'&
29.781 990
,
1
n
n
M = CMixi
0.00057
10Bl 113.906403 648.279 170 -393.494 690 -162.006096 628.990910 2211.966800 99.357 208 2908.836900 -413.600710 4.044 709 1276.036030 278.133 210 8.456012 176.048096 326.925 200 -39.011 669 298.561 890 6683.322 300 -661.369800 1986.463010 1059.547000 880.546 670 3847.273900 2988.098 100 128.804 398 2914.963 100 607.130 370 202.541 016 3048.882 100 301.828 090 -1813.403080 1370.650880 2561.715 100 1374.323970 3491.263 200 622.164670 1040.446040 467.748 170 699.854430 -1 192.358030 1057.790040 4328.367 200 1108.451050 1084.908940 3112.560 100 1687.543950 393.450 900 1060.717040 1137.510990 1196.408940 2070.366900 103.644600 1650.037960
V=
i=l
Viri
(39)
The interaction potential energy parameters, Vii - Vi, are unknown. They are obtained by correlating experimental viscosity data for binary systems. For the binary systems, there are two interaction potential energy parameters, U2, - Ul, and U12- U22.They are determined by fitting eqs 22 and 23 to the experimental viscosity for binary systems. The objective function of the computation of these parameters is as same as eq 37. To examine the applicability of the new viscosity equations to liquid mixtures, the experimental viscosity data of 216 binary systems including nonpolar + nonpolar, polar + polar, and nonpolar + polar components have been correlated with the equations. All experimental viscosity data of the binary systems were obtained from the Journal of Chemical and Engineering Data. Figure 3 shows the calculated viscosity data and the experimental viscosity data for the chloroform-toluene binary system. Figure 4 shows the calculated kinematic viscosity and the corresponding experimental data for the 1,2-dichloroethane-
0.00053 0.00
0.20
0.40
0.60
0.80
1.00
YOUR FRAYON OF F!UST CONPONENT
Figure 3. Correlation of dynamic viecosity of chloroform-toluene at 298.15 K.
benzene system. Figure 5 shows the correlation deviations of the 215 binary systems. The detailed correlational re-
Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 2611
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 40 41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58
59 60 61 62 63 64
66 66 67
68 69 70 71 72 73 74 75 76 77
78 79 80 81 82 83 84 85 86 87
water
carbon tetrachloride tribromomethnue chloroform dibromomethane dichloromethane formaldehyde formic acid methyl bromide methyl chloride fonnamide nitromethane methane methanol methylamine tetrachloroethylene trichloroethylene pentachloroethane
1,1,2,2-tetrabrornoethane 1,l-dichloroethylene 1,1,1,2-tetrachloroethane 1,1,2,2-tetrachlorothane l,l,l-trichloroethane acetonitrile ethylene l,2-dibromoethane 1,l-dichloroethane 1,2-dichloroethane acetaldehyde acetic acid methyl formate bromoethane ethyl chloride acetamide N-methylformamide nitroethane ethane dimethyl ether ethanol dimethyl sulfoxide ethylene glycol dimethylamie ethylamie acrylonitrile 1,2,3-trichloropropane propionitrile cyclopropane propylene l,2-dichloropropane acetone n-propionaldehyde ethyl formate methyl acetate propionic acid 1-bromopropane 2-bromopropane isopropyl chloride n-propyl chloride Nfl-dimethylformamide 1-nitropropane 2-nitropropane propane 2-propanol methyl ethyl ether n-propanol trimethylamine divinyl ether n-butyronitrile imbutyronitrile 2-pynolidone 1-butene cb-2-butene trons-2-butene cyclobutane 1.4-dichlorobutane n-butyraldehyde isobutyraldehyde methyl ethyl ketone n-butyric acid 1,4-diowe ethyl acetate methyl propionate n-propyl formate 1-bromobutane 2-bromobutane n-butyl chloride see-butyl chloride
56 49 11 19 20 18 11 17 6
18 17 10 16 21 14 12 10 16 10 11 12 22 17 9 29 29 29 19 19 30 13 19 14 11 8 11 26 11 47 10 35 7 11 14 11 21 12 15 11 21 9 14 38 36 29 12 20 7 8 12 11 26 20 11 25 10 11 9 11 12 9 7 7 11 8 8 10 41 16 8 28 20 18 8 4 11 8
263.10-453.10 279.50-349.60 210.10-353.20 273.10-370.40 208.40-373.90 181.10-251.10 280.80-373.10 213.10-313.10 230.00-400.00 278.10-393.10 288.10-369.50 88.20-163.10 233.10-333.10 179.70-333.00 273.10-390.20 273.10-348.10 244.10-424.10 284.10-513.20 150.60-300.60 202.9rk402.90 273.10-453.10 261.20-423.10 288.10-343.10 103.10-210.00 273.10-404.50 176.20-327.70 244.30-310.90 273.20-293.50 288.10-385.70 273.10-303.10 173.10-309.20 233.10-373.10 354.10-494.10 288.10-353.10 276.10-381.60 100.00-250.00 131.60-230.00 270.00-423.10 293.10-403.10 260.90-449.80 239.60-308.10 192.10-289.70 253.10-350.10 258.50-428.50 273.10-370.20 145.60-318.30 123.20-300.00 172.70-362.70 223.10-323.10 228.50-321.00 273.60-311.20 273.50-413.10 273.10-413.10 273.10-343.10 273.10-328.10 273.10-306.20 273.10-313.10 278.10-363.10 276.10-333.10 181.80-391.80 123.20-300.00 187.40-323.10 200.00-300.00 233.10-368.10 239.60-308.10 172.10-292.00 291.10-391.10 201.70-371.70 299.80-365.50 168.10-238.10 213.10-333.10 213.10-333.10 182.50-367.90 235.90-426.90 291.50-348.00 208.10-336.10 188.70-410.90 276.40-428.90 288.10-333.10 273.10-473.10 273.10-349.00 273.10-353.10 273.10-373.10 274.10-328.10 288.10-343.10 288.10-333.10
0.0098 0.0174 0.0119 0.0130 0.0152 0.0095
0.0046 0.0077 0.0161 0.0128 0.0171 0.0072 0.0144 0.0164 0.0167 0.0194 0.0189 0.0201 0.0176 0.0111 0.0211 0.0129 0.0072 0.0278 0.0174 0.0074 0.0087 0.0127 0.0168 0.0091 0.0179 0.0139
0.0085 0.0082 0.0167 0.0133
0.0046 0.0123 0.0070 0.0117 0.0069 0.0068 0.0105 0.0068 0.0139 0.0155 0.0166 0.0035 0.0067 0.0019 0.0050 0.0072 0.0139 0.0111 0.0175 0.0104 0.0050 0.0197 0.0113 O.OO40
0.0267 0.0189 0.0069 0.0181 0.0013 0.0050 0.0164 0.0146 0.0141 0.0176 0.0095
0.0374 0.0114 0.0134 0.0019 0.0063 0.0128 0.0224 0.0127 0.0187 0.0103 0.0094 0.0083 0.0019 0.0077 0.0041
-5.720626 -6.188258 -5.640479 -5.942 578 -5.402 640 -4.96896 -21.44 175 -4.851 145 -1.766 957 -6.484166 -5.727 593
12.763 230 15.538 350 14.812 530 16.311201 14.547020 14.799230 207.076096
13.933710 -25.985 550 18.061560 16.088 239 -6.448607 90.044411 -5.667 490 17.244211 -5.664 015 23.568 331 -6.336 572 15.888400 13.855690 -5.680377 27.175211 -7.589 079 -9.502 471 31.642649 -6.617 062 25.661 999 -7.615 747 29.985409 -7.861 691 27.705740 -5.675 526 11.390280 -6.777 309 18.047079 -5.827 879 44.610 104 6.148882 -4.977 797 20.628 670 -6.258 722 13.860610 -5.668495 10.802340 -4.660 581 -3.441 481 7.467 683 14.974000 -5.423 497 16.848311 -5.748 392 14.700450 -5.279941 18.108969 -7.199040 16.313040 -6.349 298 -4.888 308 5.422 827 37.315571 -5.617 75 25.207 560 -5.597 802 -6.712249 22.739 059 -5.863 972 3.649 904 -12.46 191 74.802 264 10.240 160 -4.825 993 22.784 720 -6.081 016 -5.571 629 15.429 350 -5.865 969 8.964 558 -6.168166 17.631701 -5.305 640 22.007 080 -6.033 055 33.140 739 -7.435 773 34.235672 -5.701 565 15.715400 -5.236 766 12.642 720 -5.674 418 14.624 890 -7.013 785 27.500 519 -2.644424 -5.134 485 -6.099 655 16.948649 -2.000038 -23.615 231 14.991150 -5.681 471 -5.744 536 14.964 110 171.759399 -2122.4661 -6.427 888 16.606869 -7.167 057 30.079 722 10.712 160 -5.169 305 -8.290 129 30.975 821 -6.311 489 17.588800 -7.279 157 21.650 591 -5.483 184 14.456 280 -6.194026 20.745 089 17.599270 -6.481 708 -6.028720 15.017 201 64.738449 -12.556 350 18.026550 -5.686 169 15.369289 -5.520 953 10.854060 -4.956513 16.477 030 -5.321 248 10.414 331 -6.191 004 17.084 780 -6.346 384 17.880480 -6.447 559 24.294371 -f;.561455 -26.349 400 -1.401 061 14.629 200 -5.828 858 -6.204 794 15.524060 -8.150717 15.475630 -6.086827 15.358030 15.878201 -6.369 306 14.397970 -6.030 736 -6.148703 15.423960 -6.117304 15.779911
0.147 589 -9.717 462 -7.441 331 -10.409 530 -8.055 851 -6.194 764 -816.11 139 -6.169 246 204.856 308 -13.588571 -10,409619 -607.025 210 -11.623590 -45.186 623 -10.133 150 -6.853 137 -66.036 537 -48.569 252 -44.684 460 -78.664 200 -57.101 433 5.538 289 -13.514 791 -184.894 211 17.965950 -27.642 271 -8.037 994 1.127222 -1.409 336 -7.193 156 -10.360 129 -8.029 530 -4.164092 -11.292410 21.869480 -164.470 901 -60.769730 -37.106873 46.958 488 -236.333801 3.412853 -39.438053 -8.997 671 12.353 050 -12.087 461 -36.947 830 -110.520 203 -108.119797 -9.093 088 -3.338 524 -7.144233 -48.868488 35.877 441 -11.214970 123.803299 -6.919015 -6.768 364 9607.64 750 -11.079289 -87.535 507 71.802 246 -53.749 068 -5.862 624 -26.121 302 -3.976055 -32.824 150 -12.247490 -8.221921 -146.906 403 -13.278740 -6.699 551 2.471 844 -16.778469 8.127 512 -10.276 050 -11.095280 -58.956 482 121.533600 -8.366 508 -8.050 785 -8.440 839 -8.576 745 -9.383 756 -7.137 952 -7.928318 -8.857 523
-9.081 612
1484.50891 -498.20 761
-1021.50897 461.003 690
1732.71204 58.466419 126.760696 48.631 878 46.334751 164.698 196 97.178 207 -15.012 599
-113.068 199 -33.286079
418.752590 -28.528 889 24.162941
-152.757 004
-131.527 100 -81.242210
-17.637 880 -32.512658 434.051 090 94.425 880 34.377 622 -73.258 003 397.778 200
-397.739 110
-271.792 390
47.106491 -24.428570 48.089 161 252.344 193 230.263 596
-181.367 407 -197.804611
44.814709 -36.924950 -149.026 51 -19202.590 182.64189 -370.806 30 45.979 980
1439.1699 -158.379 913 568.484 500
18.073389 38.177 197 127.378998
17.426510 -20.288 071 121.175903 -195.402710
-103.427696 106.647697
2612 Ind. Eng. Chem. Rea., Vol. 31, No. 11,1992 Table I1 (Continued) no.
88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168
169 170 171 172 173 174
name tert-butyl chloride pyrrolidine N,h'-dimethylrrcetamide n-butane ieobutane n-butanol sec-butanol tert-butanol diethyl ether isobutanol 1,Cbutanediol 2$-butanediol pyridine cyclopentene valeronitrile cyclopentane 1-pentene cis-bpentene trans-2-pentene 1,bdichloropentane diethyl ketone methyl isopropyl ketone 2-penbone n-butyl formate ethyl propionate isobutyl formate isopropyl acetate methyl n-butyrate n-propyl acetate 1-chloropentane isopentane neopentane n-pentane 2.2-dimethyl-1-propanol ethyl propyl ether 2-methyl-1-butanol 3-methyl-1-butanol methyl rec-butyl ether methyl tert-butyl ether 1-pentmol 2-pentanol 3-penhol l,&pentanediol n-pentylamine 1,3,btrinitrobenzene m-chloronitrobenzene o-chloronitrobenzene p-chloronitrobenzene rn-dichlorobenzene o-dichlorobenzene p-dichlorobenzene m-dinitrobenzene o-dinitrobenzene p-dinitrobenzene bromobenzene monocldorobenzene m-chlorophenol o-chlorophenol p-chlorophenol nitrobenzene benzene rn-chloroaniline o-chloroaniline phenol 1,2-benzenediol 1,3-benzenediol 1,2,3-benzenetriol aniline 2-methylpyridine 3-methylpyridine Cmethylpyridine cyciohexene cyclohexanone hexanenitrile cyclohexane 1-hexene methylcyclopentane cyclohexanol 2-hexanone 3-hexanone methyl isobutyl ketone n-butyl acetate see-butyl acetate tert-butyl acetate ethyl n-butyrate ethyl isobutyrate n-hexnnoic acid
points 7 16 11 49 27 13 10 21 7 35 7 11
18 7 10 13 11 11
11 9 30 9 20 8 23 11 11
34 18 9 12 13 12 12 32 14 13 8 8 20 18 10 8 11
5 21 11 11 13 13 10 7 11 11 23 39 11 18
12 10 37 13 12 29 9 9 11 17 9 3 4 12 11 9
7 14 44 11 14 11
9 10 10 11 24 10 18
temperature 288.10-323.10 215.40-334.80 298.10-363.10 180.00-360.00 200.00-360.00 293.10-388.10 288.10-373.10 298.10-451.20 233.10-373.10 222.00455.40 399.40-468.10 280.80-450.80 273.10-388.40 259.70-405.60 291.80-413.10 248.10-323.10 183.10-273.10 121.80-310.10 132.90-309.50 200.40-375.40 273.10-373.10 217.10-361.10 273.50-372.00 289.50-370.30 273.10-363.10 289.20-370.10 215.80-359.80 273.10-373.10 273.10-473.10 214.10-374.10 233.10-303.10 258.10-303.10 213.10-308.10 327.10-382.10 273.10-333.40 273.10-403.10 273.40-401.20 204.W330.00 219.20-449.90 253.10-403.10 258.10-343.10 222.10-384.10 306.60-4 18.10 229.90-370.00 398.40-500.40 315.20-419.00 306.10-516.20 356.60-506.60 265.10-373.00 265.10-394.10 328.50-403.10 402.60-573.20 390.10-590.10 446.60-566.60 243.10-384.90 273.10-513.20
306.00-486.00 283.10-447.10 371.90-491.10 273.50-373.60 283.10-446.00 262.80-492.80 271.00-481.00 291.50-453.10 394.10-505.10 414.10-533.20 407.00-577.00 273.10-457.10 273.10-353.10 293.10-333.10 274.10-333.10 273.10-333.10 274.10-339.00 240.90-432.90 290.00-350.00 218.10-333.10 248.10-353.10 303.10-431.60 217.40-397.40 217.50-387.50 245.90-393.10 288.10-360.00 225.00-369.00 283.10-363.10 288.10-393.10 204.00-375.00 288.10-363.10
MRSD
A0
0.0027 0.0146 0.0169 0.0119 0.0174 0.0039 0.0062 0.0173 0.0128 0.0139 0.0029 0.0098 0.0133 0.0156
-5.629693 -7.885 483 -6.356 034 -5.765 623 -6.192 850 -7.215208 -7.756 835 -11.3024% -5.825044 -10.252441 -8.921 359 -8.567 883 -6.362 684 -6.549 221 -5.532 093 -5.610839 -5.982 202 -7.231 027 -7.015 021 -7.331 570 -6.150308 -6.344281 -5.900 484 -6.711 655 -6.180 107 -6.711 728 -6.510532 -5.398 593 -5.893 539 -6.499 420 -5.689 208 -5.379 661 -5.764 256 -8.016023 -6.663 565 -8.710362 -7.814 144 -5.956 842 -6.051 526 -8.038 999 -8.333 667 -8.015 331 -9.614 122 -6.479 208 -9.372 292 -7.574 293 -3.535 437 -8.205 252
O.Oo60
0.0026 0.0153 0.0137 0.0106 0.0181 0.0074
0.0088 0.0142 0.0088 0.0096 0.0125 0.0073 0.0117 0.0067 0.0151 0.0078 0.0052 0.0062 0.0013 0.0100 0.0117 0.W 0.0170 0.0121 0.0140 0.0089 0.0167 0.0154
0.0068 0.0112 0.0141 0.0080 0.0166 0.0143 0.0166 0.0076 0.0034 0.0047 0.0061 0.0167 0.0157 O.OO90
0.0164 0.0039 0.0171 0.0112 0.0171
0.0086 0.0193 0.0146 0.0158 0.0123 0.0094 0.0029 O.oo00
0.0071 0.0166 0.0124 0.0134 O.OOO4
0.0150 0.0048 0.0181 0.0147 0.0139 0.0176 0.0089 0.0106 0.0029 0.0171 0.0168 0.0110
-6.440468
-6.916 134 -6.960569 -12.38706 -3.766 570 -13.804 32 -6.467 859 -3.789472 -6.670 857 -11.28862 -7.955000 -34.301 311 -4.972 424 -6.879 374 -6.502 773 -8.409 030 -8.494 365 -14.939 11 -12.89077 -11.29962 -6.469 769 -6.112255 -6.329 814 -5.905 559 -7.241 679 -6.413416 -11.46403 -6.105 244 -6.124783 -22.336 189 -6.316578 -6.563 357 -7.172 784 -6.652 509 -6.999 307 -6.276085 -6.801 987 -6.444 340 -7.755 123
1@Al @A2 12.826 360 -3.673 684 32.182 850 -60.212357 15.109000 -9.551 640 20.453909 -36.701 210 23.680 569 -42.634 769 17.425930 -10.492420 20.200 298 -13.169 980 -103.692 001 51.113 331 14.484 210 -4.809713 46.342 201 -122.589 798 24.878870 -22.941 231 21.196390 -12.266 930 18.226421 -12.999 379 24.391 220 -39.687 580 5.964 171 23.628 840 14.072920 -5.537 123 16.257 330 -8.478 697 36.539 177 -131.252 899 33.721 218 -114.492500 20.738 260 -26.402 760 14.797 060 -8.055 113 15.671000 -8.669940 13.666740 -6.786 276 17.682 591 -12.775650 13.972070 -6.144 053 17.029 190 -10.607 860 16.274 410 -9.404 728 10.947 290 -3.430111 12.727631 -5.040 379 16.238 119 -9.951 126 13.408 290 -2.872 483 11.758390 0.621 679 13.757 210 -3.920419 20.232 180 -13.166 531 17.825029 -10.520080 23.539450 -17.656 269 19.218370 -12.563041 14.022490 -5.428001 15.205990 -10.087 600 20.494 240 -14.440681 22.776 199 -17.941 969 23.695 721 -29.490 709 26.454809 -24.454 029 15.521 040 -8.698 352 26.487211 -25.280 520 20.820 730 -18.310829 -18.586 840 121.899 193 23.147 781 -20.878 941 15.991160 -11.116860 18.288580 -14.213810 18.716459 -14.740 270 47.516731 -72.505 959 -24.493 898 150.007004 56.226471 -90.202 522 16.978251 -11.948430 -9.429810 86.807 663 14.113540 1.658497 68.311 333 -219.978210 23.514780 -21.735010 352.393 22 -1541.912 96 7.149444 17.818371 13.235290 5.290 758 11.450790 9.369 188 -22.648401 25.476219 25.567 989 -24.226 080 63.027 641 -101.494202 51.144 779 -80.291 481 58.269 390 -155.802 307 17.403061 -12.034320 14.941430 -8.386 509 16.432 100 -10.957 320 13.977 861 -6208 153 19.897070 -15.562621 11.127760 7.915857 81.090 332 -312.905400 14.862980 -6.679 518 15.373250 -7.704573 167.159012 -581.491 640 13.139 700 -1.409651 14.617 680 -3.285 131 18.923920 -13.251 920 15.426 180 -8.751 995 16.614851 -10.166 550 14.055 719 -6.524 205 16.939 350 -11.313280 14.962 10 -8.270 147 18.494 150 -13.619 260
lODAs 55.184761
10''Al 55.184 761
51.860 100 56.052 841 90.339417 209.508499
-153.331 696
-8.322 329 35.746040 -36.451 439 318.205320 269.526 790 18.108921
-300.773 500 -246.715286
6.204 110 19.296421
-216.043 40
121.127800
35.993 820 -267.47690 47.908 630
154.165405
-158.26831 -18.669010 375.M 39 3094.29690 -27.467 720 -21.721 781 -24.988 611
90.319977 -258.854 920 -2342.76590
54.241 440 40.770 729 234.730 194
-153.580 307
-20.570 499 629.078250
-487.538 7 w
972.161 930 -8.531 695 -8.618481
-625.213 870
Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 2613 Table I1 (Continued) no. name
points 9 10 10 ~
175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206
207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254
255 256 257
258 259 260 261
imbutyl acetate n-propyl propionate 2,2-dimethylbutane 2,t-dimethylbutane n-hexane 2-methylpentane Bmethylpentane n-butyl ethyl ether di-n-propyl ether 1-hexanol 2-hexanol 2-methyl-1-pentanol 1,B-hexanediol diethylene glycol dimethyl ether triethylamine 2,4,6trinitrotoluene 2,bdinitrotoluene benzaldehyde benzoic acid benzyl chloride o-chlorotoluene p-chlorotoluene m-nitrotoluene o-nitrotoluene p-nitrotoluene toluene &le benzyl alcohol m-cresol o-cresol p-cresol benzylamine m-toluidine o-toluidine p-toluidine cycloheptane 1-heptene methylcyclohexane 2-heptanone diisopropyl ketone n-heptanoic acid n-pentyl acetate n-propyl n-butyrate 2,Zdimethylpentane 2,3-dimethylpentane 2,ddimethylpentane n-heptane 2-methylhexane Bmethylhexane 2,2,3-trimethylbutane 1-heptanol methyl benzoate ethylbenzene m-xylene 0-xylene p-xylene phenetole N,h'-dimethylauiline 1.1-dimethylcycloheue
cis-1,2-dimethylcyclohexane trons-1,2-dimethylcyclohexane cis-1,3-dimethylcyclohexane trans-l,3diiethylcydohexane cis-1,ddimethylcyclohexane trans-1,ddiethylcyclohexane ethylcyclohexane lsctene B-octanone n-butyl n-butyrate imbutyl imbutyrate n-octanoic acid 2,2-dimethylhexane 2,6dimethylhexane 3,3-dimethylhexane 2-methylheptane n-octane di-n-butyl ether di-tert-butyl ether 2-ethyl-1-hexanol l-octanol 2sctenol diethylene glycol diethyl ether benzyl acetate ethyl benzoate m-ethyltoluene 0-ethyltoluene p-ethyltoluene
5
19 20 11 9 22 15 11 15 11 9 7 6 11 11 3 11 11 18 4 9 23 33 8 7
13 13 12 9 9 21 18 11 20 33 16 11 14 10 8 8 9 9 20 26 9 9 7 6
19 14 21 14 21 10 11 5 9 10 9 9 11 34 14 11 4 9 4 9 5
3 9 32 10 6 9 14 8 9 10 14 11 11 21
temperature 293.00-372.50 216.20-387.20 269.30-320.10 273.10-303.10 203.10-343.10 257.50-333.10 266.60-332.70 208.10-360.10 273.70-362.10 278.10-418.10 278.10-378.10 278.10-413.10 315.10-515.20 247.10-423.10 293.10-343.10 354.00-494.00 339.00-609.00 247.10-447.10 396.60-423.10 234.10-444.10 308.50-432.10 283.10-434.90 343.10-373.10 273.10-353.10 320.10-373.10 248.10-383.10 287.70-425.40 293.10-323.10 303.10-463.10 303.10-463.10 313.10-463.10 271.10-455.10 273.10-403.10 283.10-473.00 318.10-473.40 265.10-475.10 273.10-368.10 248.10-373.10 274.10-393.10 204.80-394.80 290.60-363.10 288.50-417.60 273.10-333.10 227.30-409.30 192.00-360.00 191.90-343.90 213.10-373.10 273.10-363.10 195.80-363.80 268.60-348.60 288.10-449.00 288.10-303.10 248.10-412.10 273.10-393.10 268.10-418.10 288.10-403.10 273.10-353.10 283.10-371.10 239.70-389.70 273.10-313.10 227.00-395.00 216.60-387.60 225.10-393.00 227.70-395.70 236.20-386.20 248.10-383.10 273.10-388.10 252.90-442.90 273.10-298.10 236.4Cb412.50 293.10-363.10 196.00-372.00 273.10-313.10 273.10-313.10 208.20-384.20 217.10-398.10 246.70-412.50 219.20-372.00 230.00-457.80 288.10-363.10 304.M1.50 228.90-444.90 247.60-481.60 284.10-343.10 177.60-427.60 192.40-432.40 283.10-353.10
MRSD
A,,
WA,
10BAS
0.0112 0.0167 0.0111 0.0017
-6.683 118 -6.553 166 -5.947 759 -6.090 860 -5.894 076 -5.996070 -6.373 371 -6.464961 -6.569888 -8.136 437 -8.492 698 -7.303 685 -10.57451 -6.687 333 -6.192 798 -8.631 532 -2.827 272 -5.666 796 -12.73871 -5.742 431 -5.415 269 -5.625 875 -6.494 840 -7.053 466 -6.383379 -6.280 610 -5.638 540 -7.749 939 -8.769 023 -8.302 164 -8.885620 -5.962 167 -9.236 659 -10.76 210 -5.853689 -5.932 438 -6.623614 -6.661 502 -7.090 610 -7.866 321 -8.736569 -6.381 357 -6.798649 -6.296 655 -6.676 382 -6.901 950 -6.158821 -6.622 797 -6.571 281 -6.165 266 -9.040 551 -7.345 572 -6.007 268 -6.511 118 -7.178 944 -6.572 173 -7.053 363 -7.107863 -6.222 569 -6.872 694 -6.382 147 -6.506747 -6.440 565 -6.380367 -6.573 361 -6.835 244 -7.023 966 -6.887 685 -7.721084 -6.763 238 -8.620 930 -7.066 225 -6.738 299 -6.779 537 -6.862 488 -6.883021 -6.482518 -7.024 787 -10.74 700 -9.028 923 -8.497 653 -6.789 903 -6.777 958 -7.199702 -7.924 963 -7.740 491 4.848220
15.845289 15.116660 13.539390 14.393900 15.151150 13.862 580 15.994 539 15.153980 15.893411 20.399210 22.624 670 18.594080 30.296 990 11.129951 13.917 090 23.529 711 -30.325 640 7.572018 45.116909 9.719 505 6.859 049 7.820 487 16.466 011 18.367 140 16.341589 16.214071 7.356717 18.750071 26.026 379 24.515989 26.570679 8.651 592 35.488 251 54.339039 8.963059 9.884 269 16.500 870 17.010370 17.189 140 30.429 930 21.222509 9.099 558 15.484 660 13.610 189 17.892 561 19.606 249 13.337 430 16.972 730 15.814019 13.821330 23.700060 18.439 621 10.729 530 16.183579 19.978930 16.712730 17.833 460 17.537 951 11.973740 17.231588 13.080811 14.418410 13.463 639 12.983709 15.649069 16.746679 17.287 239 10.932 130 20.159 060 12.467240 21.035940 18.041580 15.515120 15.790 319 16.196661 15.162 050 10.807 160 16.763350 41.282 478 22.649 729 17.732269 10.483300 12.026690 17.570 120 31.363089 29.253 149 16.554 430
-9.319280 -8.483 291 -3.944 716 -5.519764 -16.179 100 -4.950 103 -8.029 252 -7.688 110 -8.524 758 -15.014 600 -17.753069 -13.653 280 -30.595 779 9.097 096 -6.040 006 -21.482990 164.522598 15.267650 -47.364 880 9.643 593 17.906 330 16.439 320 -13.102840 -14.742 100 -13.633471 -9.999 358 17.934441 -12.839 820 -22.815 480 -21.412399 -23.512 482 13.844420 -60.741 859 -154.328 705 10.078570 10.421161 -9.802 219 -10.485 270 -11.595480 -83.408 203 -15.598540 15.267 901 -9.125 151 -1.803 100 -17.917481 -21.896071 -5.454 013 -8.586 011 -8.641 792 -5.838 846 -19.025 580 -13.506411 8.475462 -10.633 660 -16.143 440 -11.518291 -13.050221 -12.779 230 2.830485 -11.826 220 0.433 920 -4.249 275 -0.982 221 0.436638 -9.211 560 -10.792 130 -11.242 170 9.186712 -17.239790 3.001 532 -16.884901 -14.807 111 -8.244 988 -8.779 389 -9.601 484 -8.650 535 6.901 092 -10.261 200 -101.015 198 -17.491 961 -1.504 415 8.112381
0.0099
0.0192 0.0058 0.0128 O.Oo40
0.0155 0.0186 0.0073 0.0157 0.0105 O.OOO9
0.0200 0.0099
0.0098 O.oo00
0.0180 0.0016 0.0092 0.0011
0.0066 0.0076 0.0194 0.0027 0.0116 0.0176 0.0170 0.0131 0.0044 0.0163 0.0137 0.0070 0.0104 0.0198 0.0123 0.0192 0.0025 0.0057 0.0047 0.0021 0.0112 0.0164 0.0108 0.0167 0.0088 0.0198 0.0019 0.0199 0.0023 0.0083 0.0160 0.0150 0.0173 0.0113 0.0045 0.0065
0.0094 0.0115 0.0139 0.0118 0.0117 0.0184 0.0154 0.0147 0.0085 0.0094 0.0117 0.0136 0.0194 0.0022 O.oo00 0.0199 0.0181 0.0132 0.0198 0.0128 0.0109 0.0035 0.0191 0.0139 0.0163 0.0114 0.0096
0.0026
1.434952 .. ._ .. -
-13.349 -87.427 -77.340 -10.975
330 177 431 930
lOeA8
1O"Ad
17.222551
4.523 264 -22.410832 -283.67520 -27.334669
161.529907
-22.224 781 -29.531 330 -28.848 440
-30.219 141
-26.704090 42.078 892 251.048782 -22.031 839 -21.863 621
-172.803604
168.463 898
-143.556886
-28.960 470 -6.308684 12.092 670 16.258530
-21.105970
-12.948800 -11.344 240 -5.867 825 -9.560478 -11.014530
-21.330401 -14.455 561 5.861 231
-17.436260 175.062 195
-136.720093
-15.366 449 -20.171299 -22.572 960 173.621399 150.674698
-146.768911 -126.472801
2614 Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 Table I1 (Continued) no. name 262 merritvlene 263 n-propylbenzene 264 1,2,3-trimethylbenzene 265 benzyl ethyl ether 266 1-nonene 267 n-nonanoic acid 268 2-methyloctane 269 1-nonanol 270 n-nonane 271 tripropylamine 272 n-butylbenzene 273 m-diethylbenzene 274 o-diethylbenzene 275 p-diethylbenzene 276 isobutylbenzene 277 1,2,4,5tetramethylbenzene 278 1-decene 279 n-decanoic acid 280 n-decane 281 1-d-01 282 1-undecene 283 n-undecane 284 1-undecanol 285 n-dodecanoic acid 286 n-dodecane 287 l-dodecanol 288 1-dodecene 289 n-tridecane 290 1-tridecanol 291 benzyl benzoate 292 dibenzyl ether 293 1-tetradecene 294 n-tetradecanoic acid 295 n-tetradecane 1-tetradecanol 296 1-pentadecene 297 298 pentadecanoic acid 299 n-pentadecane 300 1-hexadecene 301 n-hexadecanoic acid 302 n-hexadecane 303 1-hexadecanol 304 n-heptadecane 305 l-hpetadecanol 306 1-octadecene 307 n-&decane 308 1-octadecanol 309 1-nonadecene 310 nonadecanoic acid 311 n-nonadecane 312 1-eicosene 313 n-eicosane 314 1-eicosanol
points 10 22 9 11
14 8 9 5 35 10 28 11 11 11 11 11
33 13 45 9 14 38 10 13 43 9 14 16 11 8 5 14 4 21 11 24 11
14 14 12 29 3 39 11 12 46 11 19 10 39 13 47 11
temperature 248.50-428.50 248.10-423.10 287.80-447.80 283.10-453.10 273.10-388.10 293.10-363.10 236.M-412.80 288.10-328.10 223.10-423.10 278.10-423.10 248.10-423.10 189.30-449.30 241.90-451.90 230.30-450.30 221.70-441.70 352.40-462.40 273.10-413.10 304.80-534.80 240.10-448.10 293.10-358.10 273.10-388.10 248.10-488.10 293.10-358.10 323.10-433.10 262.10-486.10 293.10-363.10 273.10-388.10 268.10-403.10 303.60-543-80 278.10-373.10 280.50-308.10 273.10-388.10 333.10-363.10 279.10-413.10 310.60-550.70 273.10-388.10 325.70-605.70 273.10-388.10 278.10-388.10 343.10-469.10 293.10-558.20 323.10 303.10-573.20 327.00-597.00 293.10-388.10 303.10-588.20 331.00-601.00 298.10-388.10 341.20-620.20 303.10-598.20 328.10-388.10 308.10-548.20 338.50-628.50
MRSD
A0
0.0105 0.0115 0.0024 0.0029 0.0173 0.0134 0.0112 0.0038 0.0057 0.0138 0.0113 0.0153 0.0152 0.0073 0.0071 0.0149 0.0098 0.0099 0.0123 0.0058 0.0140 0.0160 0.0050 0.0192 0.0176
-6.238254 -6.380257 -5.836058 -5.927 630 -7.317991 -9.043963 -6.573 777 -9.294419 -8.047 010 -6.838771 -6.864 192 7.932045 -6.515 765 -7.352621 -7.620 288 -8.161 830 -6.723 103 -6.241432 -7.866 002 -9.582 189 -7.967491 -8.208676 -10.135 78 -10.081 76 -7.307 669 -10.079 63 -8.032 813 -8.225713 -6.814 892 -10.880 66 -8.527 975 -8.656 465 -10.191 92 -8.816 399 -6.766 692 -8.619800 -5.013 239 -8.620 058 -8.827 496 -9.520 259 -5.415 169 -14.514 23 -4.799 728 -6.216 571 -9.650461 -5.484 203 -6.284429 -9.379 635 -5.900 992 -5.364 626 -9.786 621 -5.791 068 -7.747 159
O.Oo60
0.0103 0.0158 0.0113 O.Oo90
0.0067 0.0103 0.0022 0.0197 0.0097 O.Oo90 O.OO80
0.0087 0.0084 0.0209 0.0169
O.oo00 0.0108 0.0058 0.0075 0.0147 0.0067 0.0036 0.0129 0.0141 0.0015 0.0117 0.0155
@A1 10.172 180 11.277659 7.441 262 7.942 966 17.664040 21.896 179 11.364930 22.635 600 30.290 840 12.820450 14.340&10 27.935 400 10.704 520 21.299641 24.834 219 22.353699 10.718440 -12.469 570 25.614691 24.044 880 18.923931 22.908001 25.612841 24.830 830 11.882711 24.950 789 18.554 630 18.845 129 -9.178009 39.995 522 22.577 660 19.988621 24.628 811 20.603 350 -12.096490 19.437 321 -24.123 510 19.306 511 19.824629 23.196230 -16.347651 47.752 850 -23.366871 -18.988461 21.735970 -18.549391 -18.660709 20.871 580 -19.336571 -20.664 091 21.903040 -15.849430 -8.998006
l@A, 10.075629 7.906769 16.352 240 15.858681 -12.006 340 -17.357870 5.492 403 -16.822 790 -82.910355 1.106461 -1.882 559 -68.859 543 8.825 187 -39.568619 -54.563 950 -19.318010 8.314 155 111.025200 -60.308 781 -19.588 360 -13.874 270 -39.405991 -20.917 139 -21.197 569 5.945 596 -20.547 350 -13.722870 -14.517 300 106.646 599 -71.743370 -22.395990 -15.498 110 -21.190001 -16.366850 117.874397 -15.139540 150.172897 -15.049510 -15.692460 -21.581 171 121.245903 -53.571 190 146.380096 141.305603 -17.233540 130.816201 139.630600 -17.057 890 134.337204 137.986603 -18.055 121 118.021301 109.685600
@As -22.953 159 -21.335 150 -28.466 190 -28.800880
10*9~,
-16.424480 160.768600 -12.114680 -12.401 691 131.508606 -21.980 570 74.081 268 103.604 500
-130.994598 -111.900505 -70.550 629 -92.586 929
-20.428001 -197.37929 111.875 21
107.114899 -92.738 541
66.029 480
-60.760021
-19.711 409
-203.87000 51.062363
118.808006
-221.714 20
128.925201
-266.544 10
152.942795
-221.46050
127.810097
-260.615 20 -261.57629
150.275696 154.736404
-237.083 10 -259.29401
136.151 108 153.544 800
-243.328 29 -249.122 12
139.862 198 144.208206
-216.50490 -215.83060
124.981209 129.265305
"Overall number of pure liquids and average MRSD: 314; 1.13%. 6.SE-007
,
0.05
0.04
ooo3
1
MRSD of each system
- - average MRSD
i
O'O2I 0.01
55E-007
** * *
I
'
' '
6-
1,,,,~,,,,,,,~,,,,,,,,,,,,~,,,,,,~,,,,,,,,,,,,,,,,
0.00
0.20
0.40
0.60
0.80
1
YOUR FRICIWN OF FIRST C O Y W E N T
Figure 4. Correlation of kinematic viscosity of 1,2-dichloroethanebenzene at 303.15 K.
Figure 5. Overall MRSD of the correlations of 215 binary system.
sults of the 215 binary systems, such as number of experimental points, temperature or temperature range, in-
teraction potential energy parameters, and MRSD of each binary system, are listed in Table III. The overall average
NUMBER OF BINARY SYSTEMS
Ind. Eng. Chem. Rea., Vol. 31, No. 11, 1992 2616 Table 111. Correlation Results of 215 Binary Systems0 no. name 1 carbon tetrachloride (+benzene (2) 2 water (1)-methanol (2) benzene (l)-cyclohexane (2) 3 4 benzene (1)-n-hexane (2) 5 n-heptane (1)-benzene (2) 6 n-hexane (1)-toluene (2) 7 n-heptane (Wethano1 (2) 8 benzene (Wethano1 (2) cyclohexane (l)-ethyl acetate (2) 9 carbon tetrachloride (l)-cyclohexane (2) 10 benzene (l)-ethyl acetate (2) 11 ethyl acetate (l)-carbon tetrachloride (2) 12 benzene (1)-toluene (2) 13 n-hexane (1)-1-hexanol (2) 14 methyl ethyl ketone (l)-cyclohexane (2) 15 n-hexane (1)-methyl ethyl ketone (2) 16 methyl ethyl ketone (1)-n-heptane (2) 17 n-pentane (1)-n-butyl chloride (2) 18 n-butyl chloride (1)-n-decane (2) 19 acetone (lkmethanol (2) 20 chloroform (+toluene (2) 21 chloroform (1)-benzene (2) 22 chloroform (1)-acetic acid (2) 23 chloroform (1)-n-propanol (2) 24 carbon tetrachloride (1)-bromobenzene (2) 25 carbon tetrachloride (1)-methyl ethyl ketone (2) 26 carbon tetrachloride (1)-n-hexane (2) 27 carbon tetrachloride (1)-2-propanol (2) 28 tribromomethane (l)-carbon tetrachloride (2) 29 carbon tetrachloride (1)-n-propyl acetate (2) 30 carbon tetrachloride (1)-n-butyl acetate (2) 31 carbon tetrachloride (l)-ethyl n-butyrate (2) 32 benzene (1)-n-propyl acetate (2) 33 benzene (l)-ethyl n-butyrate (2) 34 tribromomethane (l)-cyclohexane (2) 35 tribromomethane (1)-bromobenzene (2) 36 tribromomethane (l)-ethyl acetate (2) 37 ethanol (l)-cyclohexane (2) 38 ethanol (1)-1,2-dichloroethanne (2) 39 n-propanol (1)-acetone (2) 40 acetone (1)-n-hexane (2) 41 n-butanol (l)-ethyl acetate (2) 42 n-butanol (1)-p-xylene (2) 43 n-butanol (l)-ethylbenzene (2) 44 toluene (l)-ethylbenzene (2) 45 ethylbenzene (1)-methyl ethyl ketone (2) 46 l,2-dichloroethane (1)-benzene (2) 47 1,2-dichloroethane (1)-toluene (2) 48 1,2-dichloroethane (1)-p-xylene (2) 49 methanol (l)-ethanol (2) 50 2-propanol (1)-n-propanol (2) 51 2-propanol (1)-methanol (2) 52 2-propanol (l)-ethanol (2) 53 n-butanol (1)-methyl ethyl ketone (2) 54 1,2-dichloroethane (l)-cyclohexane (2) 55 acetone (1)-1,2-dichloroethane (2) 56 acetone (l)-cyclohexane (2) 57 acetone (1)-benzene (2) 58 acetone (1)-acetic acid (2) 59 methyl ethyl ketone (1)-n-nonane (2) 60 methyl ethyl ketone (1)-benzene (2) 61 n-hexane (1)-n-heptane (2) 62 n-butyl acetate (1)-methyl ethyl ketone (2) 63 benzene (1)-p-xylene (2) 64 benzene (1)-n-decane (2) 65 benzene (l)-o-xylene (2) 66 toluene (l)-o-xylene (2) 67 toluene (1)p-xylene (2) 68 o-xylene (1)-n-hexane (2) 69 o-xylene (1)-n-decane (2) 70 p-xylene (1)-n-hexane (2) 71 p-xylene (1)-n-decane (2) 72 n-hexane (1)-n-nonane 92) 73 n-heptane (1)-n-nonane (2) 74 n-octane (1)-n-nonane (2) 75 n-octane (1)-n-decane (2) 76 77 n-octane (l)-n-dodecane (2)
points 9 9 11 10 11 36 10 9 9 7 14 14 8 36 5 9 15 9 9 8 8 8 16 15 10 5 8 8 14 15 15 16 16 16 10 10 3 8 36 9 8 8 7 8 7 8 10 8 11
8 30 27 9 9 7 13 8 40 44 7 12 9 9 5 9 5 5 5 5 5 5 5 9 9 9 18
3
temperature 298.15 373.00 298.15 298.15 298.15 303.15-333.15 298.15 298.15 293.15 298.15 293.15-318.15 293.15-318.15 298.15 303.15-333.15 318.15 297.85 273.15-297.85 298.15 298.15 298.15 298.15 298.15 298.15 303.00-319.00 298.15-318.15 318.15 298.15 298.15 298.15-318.15 303.15-313.15 303.15-313.15 303.15-313.15 303.15-313.15 303.15-313.15 298.15-318.15 298.15-318.15 318.15 298.15 303.15-333.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.15 303.15 303.15 298.15 283.15-303.15 303.15-323.15 293.15 309.15 303.15 303.15 298.15 293.15-323.20 293.15-323.15 293.15 293.15-298.15 298.15 308.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 293.15-298.15 298.15
u,, - VI, -51.771 481 454.816410 -334.826 200 -381.253 910 -209.972 702 -64.066 410 -516.812 500 -500.537 110 -652.158 200 -359.988 310 -343.871 090 -347.867 190 -14.703 130 -648.687 500 -55.253 910 1199.616940 -252.761 703 336.718810 414.898 410 -350.882 810 130.121094 -252.277 298 30.994 141 -567.918030 -192.007 797 711.353520 -370.222 690 -560.324 220 234.214 798 -192.085 907 701.087 890 708.257 810 -258.175 810 771.017 580 663.804 690 64.687 500 758.152 280 -503.453 090 11.640630 -875.793 030 577.187 500 -1093.538 940 -784.050 780 464.378 910 561.835880 15.335 940 -147.767 593 1275.491940 868.750000 130.593 796 -64.132 812 -702.949 220 -429.359 410 -667.750000 -224.599 594 299.199 190 -40.337 891 -311.550810 921.078 120 215.888702 -120.585 899 -89.929 688 -380.488 310 431.289 090 1117.214970 615.275 390 -171.714798 46.734 379 -277.304 690 792.277 280 1127.055 050 990.691410 162.912 094 63.921 879 256.734410 92.734 383 374.984 410
Um-Um 122.798798 600.035 220 -500.632 810 -287.517 610 -366.029 300 -234.097 702 -185.640 594 -243.851 593 -271.609410 922.664 120 558.166020 995.390620 -48.828 129 45.835941 -513.128 910 -314.939 510 829.699 220 -253.236 298 1059.336060 -325.765 590 365.878 910 706.902 280 -227.404 297 229.914093 392.058 590 -223.496 094 -169.273 407 -447.378910 -176.976 593 220.953 094 -474.007 810 -483.703 090 306.160 190 -528.109 380 -414.064 690 315.140590 826.064 510 1171.126950 83.746094 -630.406 310 -446.630 890 -732.246 090 -773.035 220 -810.429 690 -250.316406 181.425797 -273.669 890 -457.683 590 -528.808 590 229.835 907 79.000 000 501.699 190 -252.464 798 -278.169 890 -548.611 330 -79.580078 -480.408 200 541.562 500 -26.998051 585.781 310 -106.285 202 304.574 190 588.474 610 -353.246090 -724.511 720 -478.437 500 279.662 600 -4.480 469 -182.341 797 -533.773 380 -399.810 610 -570.703 120 482.539090 98.011 719 -182.355 499 65.824 219 602.234380
MRSD 0.0012 0.0014 0.0019 0.0016 0.0032 O.Oo80
0.0069 0.0033 0.0073 0.0025 0.0036 0.0095 0.0005 0.0193 0.0062 0.0087 0.0071 0.0032 0.0042 0.0018 0.0014 0.0039 0.0079 0.0210 0.0026 0.0029 O.OOO6
0.0099 0.0070 0.0028 0.0035
0.0046 0.0039 0.0030 0.0141 0.0050 0.0255 0.0142 0.0083 0.0489 0.0059 0.0378 0.0187 0.0221 0.0025 0.0017 0.0022 0.0034 0.0051 0.0013 0.0044 0.0180 0.0017 0.0210 0.0021 0.0063 0.0064 0.0029 0.0091 0.0055 0.0047 0.0013 0.0137 O.OOO6
0.0103 0.0018 0.0002 0.0003 0.0002 0.0025 0.0037 0.0o4O 0.0015 0.0003 0.0021 0.0007 0.0007
2616 Ind. Eng. Chem. Res., Vol. 31, No.11, 1992 Table 111 (Continued) no. name 78 n-nonane (1)-n-decane (2) 79 n-nonane (1)-n-dodecane (2) 80 n-decane (1)-n-dodecane (2) 81 n-decane (1)-n-tetradecane (2) 82 n-dodecane (1)-n-tetradecane (2) 83 n-dodecane (1)-n-hexadecane (2) 84 n-hexadecane (1)-n-tetradecane (2) 85 n-heptane (1)-n-decane (2) 86 n-heptane (1)-n-octane (2) 87 n-hexane (1)-n-decane (2) 88 n-hexane (l)-n-odane (2) 89 p-xylene (l)-o-xylene (2) 90 p-xylene (1)-rn-xylene (2) 91 rn-xylene (1)-0-xylene (2) 92 toluene (1)-n-heptane (2) 93 ethanol (1)-methyl ethyl ketone (2) 94 ethanol (l)-ethyl acetate (2) 95 n-heptane (l)-cyclohexane (2) 96 ethyl acetate (11-0-xylene (2) 97 ethyl acetate (1)-p-xylene (2) 98 n-hexane (1)-monochlorobenzene (2) 99 propionic acid (1)-n-propylbenzene (2) 100 propionic acid (l)-ethylbenzene (2) 101 propionic acid (1)-toluene (2) 102 propionic acid (1)-benzene (2) 103 ethylbenzene (1)-n-octane (2) 104 toluene (1)-n-dodecane (2) 105 toluene (1)-n-decane (2) 106 toluene (1)-n-octane (2) 107 toluene (l)-ethylbenzene (2) 108 anisole (l)-cyclohexane (2) 109 anisole (1)-nitrobenzene (2) 110 anisole (1)-1,2-dichloroethane (2) 111 anisole (1)-monochlorobenzene (2) 112 anisole (l)-carbon tetrachloride (2) 113 monochlorobenzene (l)-dimethyl sulfoxide (2) 114 pyridine (l)-dimethyl sulfoxide (2) 115 methyl ethyl ketone (l)-dimethyl sulfoxide (2) 116 acetonitrile (1)-toluene (2) 117 cyclohexane (1)-acrylonitrile (2) 118 benzene (1)-acrylonitrile (2) 119 p-xylene (1)-acrylonitrile (2) 120 mesitylene (1)-acrylonitrile (2) 121 acetonitrile (1)-methyl benzoate (2) 122 carbon tetrachloride (1)-NJV-dimethylformamide (2) 123 dimethyl sulfoxide (1)-nitromethane (2) 124 carbon tetrachloride (1)-nitromethane (2) 125 benzene (1)-nitromethane (2) 126 p-xylene (1)-nitromethane (2) 127 mesitylene (1)-nitromethane (2) 128 benzene (1)-nitroethane (2) 129 p-xylene (1)-nitroethane (2) 130 mesitylene (1)-nitroethane (2) 131 benzene (1)-2-nitropropane (2) 132 p-xylene (1)-2-nitropropane (2) 133 mesitylene (1)-2-nitropropane (2) 134 l,4-dioxane (l)-ethanol (2) 135 benzene (1)-1,4-dioxane (2) 136 benzene (1)-2-methylheptane (2) 137 toluene (l)-a-methylheptane (2) 138 n-heptane (1)-2-methylheptane (2) 139 ethyl acetate (1)-1,4-dioxane (2) 140 trichloroethylene (1)-l,4-dioxane (2) 141 trichloroethylene (1)-methyl ethyl ketone (2) 142 trichloroethylene (ll-diethyl ketone (2) 143 trichloroethylene (1)-methyl isobutyl ketone (2) 144 trichloroethylene (l)-cyclohexane (2) 145 benzyl acetate (1)-1,4-dioxane (2) 146 benzyl acetate (1)-aniline (2) 147 benzyl acetate (1)-rn-cresol (2) 148 nitromethane (l)-carbon tetrachloride (2) 149 nitroethane (l)-carbon tetrachloride (2) 150 anisole (1)-methanol (2) 151 anisole (1)-benzene (2) 152 ethanol (1)-l,l,l-trichloroethane (2) 153 ethanol (1)-1,1,2,2-tetrachloroethane(2) 154 n-butanol (1)-methyl isobutyl ketone (2)
points 9 3 3 3 3 3 9 18 18 18 18 41 36 63 17 16 20 10 7 7 36 11 9 9 13 39 40 45 40 7 27 36 36 36 36 44 44
44 27 6 6 6 6 8 5 10 10 8 9 9 9 9 9 9 9 9 45 10 11 24 9 7
18 24
18 9 27 7 7
5 27 27 36 36 36 36 9
temperature 298.15 298.15 298.15 298.15 298.15 298.15 293.15 293.15-298.15 293.15-298.15 293.15-298.15 293.15-298.15 288.15-303.15 288.15-303.15 273.15-303.15 293.15-298.15 293.15-298.15 293.15-298.15 298.15 313.15 313.15 303.15-333.15 308.15 308.15 308.15 308.15 293.15-313.15 293.15-313.15 293.15-313.15 293.15-313.15 298.15 298.15-313.15 298.15-313.15 298.15-313.15 298.15-313.15 298.15-313.15 298.15-328.15 298.15-328.15 298.15-328.15 288.15-308.15 307.40 307.40 307.40 307.40 323.00 318.15 298.15-318.15 298.15-318.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 288.15-308.15 293.15-298.15 293.15 293.15-298.15 298.15 313.15 298.15-308.15 298.15-318.15 308.15-318.15 318.15 298.15-318.15 313.15 303.15 313.15 303.15-318.15 303.15-318.15 298.15-313.15 298.15-313.15 303.15-333.15 303.15-333.15 313.15
Uzl - VI, 52.101 559 159.574 203 1.593750 258.582 000 -43.753 910 277.269 500 158.820 297 180.585907 27.226 561 417.023 410 68.449 219 -246.214 798 -114.195297 -260.058 590 -308.371 090 -685.894 470 -730.613 280 -192.554 703 200.474 594 136.123001 -368.609 410 1604.859010 -423.064 510 -388.828 090 -433.720 700 -200.789 093 585.738 280 699.187 500 -354.097 690 561.839 780 -141.359406 1028.265 990 623.765620 -12.296880 -289.296 910 121.109398 43.527 340 331.697 300 -435.044 890 -722.007 810 403.443 390 267.464810 727.199 220 -115.009 804 706.109 380 -232.648 407 -77.152 344 1355.692 990 493.871 090 628.117 190 -307.523 410 709.339 780 820.828 120 -285.996 090 -385.273 410 1140.636960 -489.882 810 554.943 420 -367.377 010 -121.171 898 217.265594 -137.898 407 -361.371090 219.167999 284.660 190 321.611 300 -117.857 399 74.718 750 507.125 000 -467.777 310 -312.347 690 -143.863 297 684.535 220 875.453 120 190.789093 275.992 190 -806.660 220
Uiz- Ua -14.246090 264.898410 215.671 906 736.148 380 246.296 906 386.437 600 2.414 063 218.273407 12.113280 705.871 090 146.671906 376.578 090 156.906 296 600.886690 1218.297000 -489.578 090 -436.675 810 -387.748 110 -134.636 703 -82.738281 480.191 410 -642.800 780 301.418000 -21.175 779 -71.328 133 -171.816406 551.976620 -528.613 280 834.496 090 -250.316406 -575.490 170 -475.406 310 -162.769501 255.625 000 709.335 880 -199.027 298 -482.812600 -363.742 190 1340.504030 1295.875000 -290.763 700 393.328090 672.658200 -665.937 500 451.902310 82.539 062 272.093 810 -400.726 590 168.050797 686.843 810 -231.875000 -264.722 690 70.457 031 -306.117 190 -63.015629 -245.199 203 -808.039 120 -326.808 590 -269.261 690 -298.539 090 -144.554 703 -355.171 910 1209.823970 348.197 300 66.976 562 -98.949 219 -255.906 296 441.539090 51.484379 1492.593990 1113.291020 -138.464 798 760.570 310 269.304 690 165.015 594 527.668 030 -612.308590
MRSD 0.0003 0.0010 O.OOO9
0.0082 0.0033 0.0001 0.0005 0.0008 0.0007 0.0047 0.0022 0.0020 0.0018 0.0045 0.0144 0.0226 0.0166 0.0098 0.0007 0.0008 0.0057 0.0149 0.0036 0.0050 0.0061 0.0035 0.0038 0.0035 0.0025 0.0025 0.0118 0.0064 0.0088 0.0074 0.0048 0.0181 0.0130 0.0087 0.0198 0.0201 0.0066 0.0053 0.0107 0.0157 0.0068 0.0094 0.0102 0.0172 0.0063 0.0290 0.0018
0.0066 0.0041 0.0058 0.0027 0.0117 0.0102 0.0087 0.0051 0.0064 0.0007 0.0019 0.0107 0.0083 0.0086 0.0012 0.0081 0.0089 0.0024 0.0063 0.0097 0.0126 0.0374 0.0239 0.0135 0.0149 0.0212
Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 2617 Table 111 (Continued) no. 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215
name n-butanol (1)-2-methyl-l-butanol (2) methyl isobutyl ketone (l)-l-pentanol(2) methyl isobutyl ketone (1)-2-rnethyl-l-butanol (2) n-butyl acetate (1)-3-methyl-l-butanol (2) tetrachloroethylene (1)-benzene (2) tetrachloroethylene (l)-carbon tetrachloride (2) tetrachloroethylene (1)-toluene (2) tetrachloroethylene (l)-cyclohexane (2) 2-bromobutane (1)-n-hexane (2) acetone (1)-trichloroethylene (2) acetone (l)-dichloromethane (2) acetone (1)-tetrachloroethylene (2) toluene (1)-acetone (2) methyl isobutyl ketone (1)-acetic acid (2) n-butyl acetate (l)-a-hexanone (2) n-butyl acetate (1)-n-pentyl acetate (2) methyl isobutyl ketone (l)-diethyl ketone (2) methyl isobutyl ketone Wa-hexanone (2) methyl isobutyl ketone (1)-n-heptane (2) methyl isobutyl ketone (1)-toluene (2) methyl isobutyl ketone (1)-p-xylene (2) methyl isobutyl ketone (l)-ethylcyclohexane (2) methyl isobutyl ketone (l)-cyclohexanone (2) methyl isobutyl ketone (1)-l,l,l-trichloroethane (2) methyl isobutyl ketone (1)-n-butyl acetate (2) nitrobenzene (l)-cyclohexane (2) methylcyclohexane (1)-n-heptane (2) isopropyl acetate (l)-cyclohexane (2) benzene (l)-cis-l,2-dimethylcyclohexane (2) toluene (1)-methylcyclohexane (2) 2-methylheptane (1)-n-hexane (2) methylcyclohexane (1)-n-hexane (2) cis-1,2-dimethylcyclohexane(1)-n-hexane (2) 3-methylpentane (1)-n-decane(2) methylcyclohexane (1)-n-decane (2) 2,2-dimethylpentane (1)-n-decane (2) 2-methylheptane (1)-n-decane (2) 2,2-dimethylhexane (1)-n-decane (2) benzene (l)-ethylbenzene (2) benzene (l)-2-propanol (2) benzene (1)-n-butanol (2) benzene (1)-1-hexanol (2) methanol (1)-benzene (2) 1,Zdichloroethane (1)-n-butanol (2) 1,2-dichloroethane (1)-1-pentanol (2) 1,2-dichloroethane (1)-n-propanol (2) methanol (1)-1,2-dichloroethane (2) carbon tetrachloride (l)-ethanol (2) carbon tetrachloride (1)-1-hexanol (2) acetone (l)-chloroform (2) acetone (l)-carbon tetrachloride (2) acetone (l)-ethanol (2) n-hexane (+ethanol (2) n-hexane (l)-cyclohexane (2) acetone (1)-2-propanol (2) cyclohexane (1)-2-propanol (2) triethylamine (1)-monochlorobenzene (2) dimethyl sulfoxide (1)-methanol (2) n-hexane (l)-chloroform (2) methyl acetate (1)-n-hexane (2) methyl acetate (l)-chloroform (2)
points 9 9 9 9 8 7 7 7 9 12 13 10 36 36 8 7 8 8 8 8 8 8 8 8 8 36 20 22 5 5 5 5 5 5 5 5 5 5 30 18 9 9 24 7 32 24 36 9 9 18 8 8 8 8 8 8 8 8 8 8 8
temperature 309.15 313.15 313.15 308.15 303.15 303.15 303.15 303.15 298.15 303.15 303.15 303.15 293.15-318.15 293.15-318.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15-313.15 293.150-298.15 298.15-308.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15-338.15 293.15-303.15 298.15 298.15 293.15-323.15 303.15 303.15-333.15 303.15-333.15 303.15-333.15 298.15 298.15 298.15-308.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15
Uzl - VI, -53.816 410 -653.831 970 -696.343 810 -653.609 380 -144.660 202 423.363 310 644.121090 -198.628 906 -404.121 090 781.863 280 316.290990 268.863 310 120.679 703 -25.433 590 260.371 090 30.898 439 217.449 203 -158.839 798 109.960 899 -426.421 910 -287.043 000 386.890 590 -315.058 590 -352.015 590 120.886 703 -597.183 590 -251.953 094 -329.269 500 -201.675 797 -169.613 297 464.238 310 880.101 620 -382.472 690 501.121 090 217.566 406 251.267 593 132.191406 111.507 797 444.810610 -734.923 830 -643.789 120 -428.357 390 216.882 797 -649.857 420 -588.968810 -633.398 380 -12.867 190 1009.936 970 1415.558960 784.456 970 137.841797 -467.646 510 -514.324 200 -152.584000 -562.375000 -638.613 280 992.970 700 -351.613310 -451.843 810 -164.064 499 756.593 810
Uiz- Uz 144.808594 -886.625 000 -750.902 280 -861.656 310 -191.769 501 -220.654 297 -292.398410 229.996 094 807.781 310 562.581 970 92.074 219 823.531310 207.476 593 146.720703 -181.968796 35.437 500 -91.648 438 294.125000 -338.929 690 741.187 500 426.933 590 -614.921 880 -487.371 090 668.142 580 -67.550 781 1689.614 990 678.746 090 -514.259830 -370.347 690 -329.222 690 -130.707001 -368.759 800 -49.595699 702.152 280 -81.378906 381.589810 75.824 219 81.968750 -383.011 690 -961.828 120 -574.191 410 -436.750000 776.902 280 -595.956 970 -747.269 470 -648.121 090 1022.875 000 -94.171 883 -418.093 810 596.748 110 69.781 250 -824.828 120 -271.918000 -474.183 590 -1264.218990 -610.339 780 -219.394501 899.300780 796.896 480 -151.820 297 549.537 110
MRSD 0.0079 0.0217 0.0278 0.0095 0.0031 0.0016 0.0033 0.0012 0.0026 0.0162 0.0031 0.0044 0.0029 0.0049 0.0011 0.0015 0.0011 0.0010 0.0011 0.0020 0.0005 0.0029 0.0033 0.0037 0.0014 0.0158 0.0082 O.OO90
0.0003 0.0003 0.0014 0.0042 O.OOO9
0.0073 0.0005 0.0005 0.0013 0.0002 0.0039 0.0313 0.0270 0.0095 0.0256 0.0168 0.0257 0.0195 0.0219 0.0172 0.0357 0.0337 0.0186 0.0122 O.OO90 0.0044
0.0235 0.0083 0.0094
0.0067 0.0052 0.0017 0.0261
Overall number of binary systems and average MRSD 215; 0.80%.
MRSD of the correlations is 0.80%. Predictions of Viscosity Data for Multicomponent Systems For multicomponent systems, the new viscosity equations for liquid mixtures, eqs 22 and 23, can be used to predict the viscosity data of multicomponent systems if all parameters in the equations have been obtained from the relevant pure liquids and binary systems. To examine the reliability of the new viscosity equations for liquid mixtures and the parameters obtained above, the Viscosity data of 14 ternary systems and 1quaternary system in-
cluding nonpolar + nonpolar, polar + polar, arid nonpolar + polar components have been predicted and compared with the experimental data. All parameters, ni and Uji Uii,used in the predictions for multicomponent aptem are obtained from the correlations of viecoeity data for pure liquids and binary systems. They are listed in Tables 11 and III. All experimental viscosity data of the multicomponent systems were obtained from the Journal of Chemical and Engineering Data. Figure 6 shows the prediction deviations of the 15 multicomponent system. The detailed prediction results, such as number of experimental points, temperature, and MRSD of each
-
2618 Ind. Eng. Chem. Res., Vol. 31, No. 11,1992 Table IV. Viscosity Prediction Results of Multiconmonent systems name ethanol-benzene-n-heptane n-heptane-2-methylheptane-toluene 2-propanol-ethanol-methanol carbon tetrachloride-n-hexane-benzene ethanol-acetone-c yclohexane acetone-n- hexanethanol acetoneethanol-methanol acetone-n-hexane-cyclohexane n-hexane-cyclohexanethanol methanol-ethanol-2-propanol aceton~thanol-2-propanol ethanol-cyclohexane-2-propanol acetone-carbon tetrachloride-cyclohexane carbon tetrachloride-cyclohexane-2-propanol ethanol-benzene-n-heptane-cyclohexane
no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
points 24 15 9 14 12 12 12 12 12 12 12 12 12 12 35
overall average MRSD
MRSD new model UNMSC 0.0309 0.0316 0.0204 0.1271 0.0290 0.1421 0.0053 0.0378 0.0202 0.0325 0.0179 0.0336 0.0775 0.0789 0.0079 0.0495 0.0209 0.0175 0.0154 0.0166 0.0299 0.0565 0.0680 0.0177 0,0606 0.0239 0.1067 0.0174 0.0438 0.0508 0.0290
0.20
0.0568
0.001 MRSD of the new - average MRSD of 0 0 0 0 0 MRSD of UNlVlSC - - average MRSD of 9 . 0 . -
0.15
temp 298.15 298.15 303.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15
model the new model model UNlVlSC model
-
-
0
0.001
0
g 0.10
1
1
0.00 0.00 ,
I
\ /
I
/
I
I
I ,
/
,
5.00
I
,
I
I
I
I
I
J
J
I
10.00
I
J
I
I
I I
I
I
I
I
I
15.00
I
I
1
/
I
I
10
T
20
3
NUMBER OF MULTICOMPONENT SYSTEMS
Figure 6. Overall MRSD of the predictions of 15 multicomponent systems.
multicomponent system, are listed in Table IV. The overall average MRSD of the predictions is 2.90%. The viscosity data of the 15 multicomponent systems have been predicted by the UNIVISC model (Wu, 1986) and compared with the experimental data. The prediction deviations are listed in Table IV and shown in Figure 6. The overall average MRSD of UNMSC model is 5.68%. The results show the new viscosity equations for liquid mixtures can be used to predict viscosity data of multicomponent systems with good accuracy.
Conclusion Based on statistical thermodynamic model, local composition, and Eying‘s absolute rate theory, a new viscosity model for pbre liquids and liquid mixtures has been developed, and the new dynamic and kinematic viscosity equations for pure liquids and liquid mixtures are obtained. The equations can be used to correlate the viscosity data of pure liquids as a function of temperature. For binary systems, the equations can correlate viscosity data even if the data are at different temperatures. Figure 7 shows the correlation of viscosity data for the 1,Cdioxane-ethanol system at different temperatures, using one set of binary parameters which are temperature independent. The equation can be used to predict viscosity data of multicomponent systems. The correlation of 314
Figure 7. Correlation of viecosity of 1,4-dioxan~thanol at different temperatures: 288.15,293.15,298.15,303.15,and 308.15 K.
pure liquids, including water, alcohols, organic acids, ketones, ethers, acetates, aldehydes, amines, aromatics, hydrocarbons, etc., and of 215 binary systems and the predictions of 14 ternary systems and 1quaternary system, including nonpolar + nonpolar, polar + polar, and nonpolar + polar components, have been carried out. The overall average MRSD of the correlations of the pure liquids is 1.13%, that of the binary systems is 0.80%, and that of the predictions of the 15 multicomponent systems is 2.90%.
Nomenclature f = shear force per unit area h = Planck’s constant baSm(i) = molar heat of vaporization of the pure liquid i k = Boltzmann’s constant k, = frequency without shear force k b = frequency at backward direction of shear force kf = frequency at forward direction of shear force l1 = distance between two molecular layers 4, & = distances between two balanca poeitions of the neighbor molecules in the same molecular layer m = number of experimental data mi = masa of a molecule i M = molecular weight of the liquid mixture Mi = molecular weight of component i MRSD = mean relative standard deviation n = component numbers of the liquid mixture
Ind. Eng. Chem. Res., Vol. 31,No. 11, 1992 2619 ni = proportion constant of component i N = number of molecules in the liquid mixture Ni = number of molecules of component i qi = external area parameter of molecule i R = gas constant, 8.3143 J*mol-’.K-’ T = temperature, K U,= activation energy Uji = interaction potential energy between sites i and j Uoi= potential energy of the lattice i u = velocity of molecular layer V = molar volume of the liquid mixture Vi = molar volume of pure liquid i z = coordination numbers of the lattice Greek Symbols
= work done by the shear foce on a molecule = dynamic viscosity, P a s vi = dynamic viscosity of pure liquid i , Pa-s Oji = local composition Y = kinematic viscosity, m 2 d vi = kinematic viscosity of pure liquid i, m 2 d u = deviation of viscosity correlation rji = interaction parameter wi = number of distinguishable configurations Q = partition function = partition function of activation state c, 7
Superscript
s = Staverman’s model Subscripts
cal = calculated data exp = experimental data Supplementary Material Available: A complete list of the applied references from the Journal of Chemical and Engineering Data for experimental viscosity data can be obtained from the authors.
Literature Cited Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Ehpreesion for the &cess Gibbs Energy of Partly or Completely Miscible Systems. AZChE J. 1976,21 (l), 116-128. Aefour, A.-F. A.; Cooper, E. F.; Wu, J.; Zahran, R. R.Prediction of McAUister Model Parametera from Pure Component Properties
for Liauid Binarv n-Alkane Svetems. Znd. EM. Chem. Res. 1991. 30, 1&1669. Daubert, T. E.; Danner, R.P. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation; Hemisphere: New York, 1989. de Guzman, J. An. SOC.Esp. fia. quim. 1913,11,363. Dymond, J. H.; Brawn, T. A. Viscosity Coefficienta of Liquids under Pressure. Proceeding of the Seventh Symposium on Thermophysical Properties; ASME. New York, 1977;pp 660-667. Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hilk New York, 1941;Chapter 9,p 477. Gubbins, K. E. In Specialist Periodical Reports in Statistical Mechanics; T h e Chemical Society: London, 1973; Vol. 1, p 194. Guggenheim, E. A. Mixtures; Clarendon Presa: Oxford, 1962. Hansen, H. K.;Rasmussen, P.; Fredenalund, A. Vapor-Liquid Equilibria by UNIFAC Group Contribution. 6. Revision and Extension. Znd. Eng. Chem. Res. 1991,30,2362-2366. Helfand, E.; Rice, S. A. Principle of Corresponding State for Transport Properties. J. Chem. Phys. 1960,32,1642-1644. Hwang, M.J.; Whiting,W. B. A Corresponding Statea Treatment for the Viscosity of Polar Fluids. Znd. Eng. Chem. Res. 1987, 26, 1768-1766. Irving, J. B. ‘Viscosities of Binary Liquid Mixtures: A Survey of Mixture Equation”; NEL Report No. 630;National Engineering Laboratory, East Kilbridge, Glaegow, Scotland, February 1977. Irving, J. B. ‘Viscosities of Binary Liquid Mixtures: The Effectiveness of Mixture Equations”; NEL Report No. 631;National Engineering Laboratory, East Kilbridge, Glasgow, Scotland, F e b ruary 1977. McAllister, R.A. T h e Viscosity of Liquid Mixtures. AZChE J. 1960, 6,427-431. Reid, R. C.; Prauenitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hilk New York, 1987;Chapter 9, pp 388-490, Skjold-Jargeneen, S.; Rasmussen, P.; Fredenslund, A. On the Temperature Dependence of the UNIQUAC/UNIFAC Models. Chem. Eng. Sci. 1980,35,2389-2403. Staverman, A. J. The Entropy of High Polymer Solutione. Recl. Trav. Chim. Pays-bas 1960,69,163. Stephan, K.; Hechenberger, T. Therm1 Conductivity and Viscosity Data of Fluid Mixtures; DECHEMA: Frankfurt, 1988;pp 4043. Teja, A. S.;Rice, P. Generalized Companding State Method for the Viscosities of Liquid Mixtures. Znd. Eng. Chem. Fundam. 1981, 20,774. Viswanath, D. S.; Natarajan, G. Data Book on the Viscosity of Liquids; Hemisphere: New York, 1989;Chapter 2,pp 29-40. Wei, 1. C.; Rowley, €2. L. A Local Composition Model for Multicomponent Liquid Mixture Shear Viscosity. Chem. Eng. Sci. 1986, 40 (3),401-408. Wu, D. T. Prediction of Viscosities of Liquid Mixtures by a Group Contribution Method. Fluid Phase Equilib. 1986,30, 149-166. 1
Received for review April 1, 1992 Accepted July 23,1992
