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The Prediction of Viscosity for Mixtures Using a Modified Square Well Intermolecular Potential Model.

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Dev.Chem. Eng. Mineral Process., 11(3/4), pp. 267-285, 2003.
The Prediction of Viscosity for Mixtures
Using a Modified Square Well
Intermolecular Potential Model
J.D. Williams and W.Y. Svrcek"
Department of Chemical and Petroleum Eng., University of Calgary,
2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4
W.D. Monnery
Chem-Pet Process Technology Ltd, Calgary, Alberta, Canada
In the chemical and process industries, the viscosity of pure components and mixtures
is a required fluid property in the areas of hydraulics, heat transfer, and mass
transfir. Hence, there is a dejinite need for a reliable and accurate method for
viscosity calculations of mixtures that is applicable over the entire density range for a
wide variety of components.
The Modified Square Well Intermolecular Potential viscosity model developed by
Monnery et al. (1998) to predict pure component viscosities oflers a good
compromise between theory and applicability. In this work the square well model is
extended to mixtures. A total of 276 binary mixtures, including non-polar and polar
components, were used to regress binary interaction parameters for the mixing rules.
The predicted mixture viscosities had a 10% average absolute deviationfor the entire
density range that included the gas, liquid, and dense phases.
Introduction
Viscosity is one of the transport properties most commonly required in modeling and,
more specifically, is important in the calculations of heat and mass transfer as well as
in hydraulics. Since viscosity is critical in a wide range of areas, there is a need for a
means of obtaining viscosity, not only for pure components but also for mixtures. It is
"Authorfor correspondence.
267
J.D. Williams, W.Y. Svrcek, and W.D. Monnery
not feasible to rely on experimental viscosity data alone, particularly once mixtures
are considered since the amount of data needed increases exponentially. It is
therefore essential that a model be available which accurately and consistently
predicts viscosity for gas, liquid, and dense-phase mixtures.
Monnery et al. (1998) developed a Modified Square Well Intermolecular Potential
(MSWIP) viscosity model to predict the pure component viscosity for gases, liquids,
and dense fluids. Some of the benefits of this model include its theoretical
framework, simplicity, and predictive nature, The intent of this present work was to
extend Monnery's model to mixtures, thereby enabling rapid and accurate calculation
of viscosities for multiple phases through the use of a semi-theoretical, statistical
mechanics group contribution method.
Background
Experimental and Proper@ Database
During the course of the work, an extensive database of experimental viscosity data
for binary gas, liquid, and dense-phase mixtures was compiled. Experimental
viscosities for the binary mixtures were obtained from several sources, including
DIPMIXTM(1992), Irving (1977), Touloukian et al. (1975), Brokaw (1968), Stephan
and Heckenberger (1988), and Sutton (1976).
In total, 242 liquid binary mixtures and 34 gas and dense-phase binary mixtures
were compiled and used in this work, representing a wide range of chemical families.
Although data was available for quite a wide range of chemical families, some
mixtures had a limited number of experimental data points, with the majority of the
measurements made at atmospheric pressure and within limited temperature ranges.
In addition, the literature is abundant with duplicate measurements for certain popular
systems, but diminishes quickly for the remaining mixtures.
Density for the gas components was calculated using the Peng-Robinson cubic
equation of state (Peng and Robinson, 1976). Density for the pure liquid components
was determined using an empirical correlation from DIPPR (1998) based on the
Rackett equation (e.g. Reid et al., 1987). In the case of the dense-phase mixtures,
experimental densities were used as given in Touloukian (1975) and DIPMIXTM
( 1992).
Molar mass, critical temperature, and acentric factor were taken fiom DIPPR
(1994) pure component database, except for inorganic components and
chlorine/fluorine alkane components, which were taken from Reid et al. (1 987).
Modifled Square Well Intermolecular Potential Model (MSWIP)
Monnery et al. (1998) modified the original square well viscosity model, as shown in
Equation 1, to account for the breakdown in the assumption of only two-body
collisions and molecular chaos for velocities, as well as the inadequacy of the square
well potential b c t i o n itself by adding a correction factor, C. The key equations fiom
their work to predict pure component viscosity are as follows:
268
Prediction of Viscosityfor Mixrures
The first term in Equation 3 dominates at low densities and is negligible at high
densities. This term accounts for the inadequacy of the square well potential, with ko
as a structural correction and (kT/&)o.28correcting the temperature dependence. The
second term accounts for three-body or higher interactions and correlations of
velocities between successive collisions, dominating at high densities but becoming
negligible at low densities. This second term is necessary because the square well
potential model was developed based on the assumption of binary collisions only.
Results
Extension of MSWIP - Mixing Rules Development
The MSWIP viscosity model is a semi-theoretical model and thus has the potential to
correctly predict viscosity trends, including minima and maxima in viscosity versus
composition. This advantage would be lost if an interpolative equation was used to
mix pure component viscosities. Therefore, mixing rules were developed for the six
model parameters, including molecular weight, M,critical temperature, T,, acentric
factor, 4 and model parameters b, %, k3. These six were chosen since the parameters
k,, k2, and k4 are all fimctions of Mand m, and (dk)is a function of T,.
There are a large number of mixed parameters that may be interacting, and as such
it is infeasible to develop complex mixing rules for each one since the number of
possible combinations that would need to be tested is prohibitively large. Hence,
simple mixing rules were used for the majority, and binary interaction parameters
were used for the remaining parameter mixing rules.
A sensitivity analysis was used to determine which of the six parameters is most
sensitive, and thus requiring a binary interaction parameter. The sensitivity analysis
showed that molecular weight, critical temperature, and b parameter affect the
predicted viscosity the most, particularly in the liquid phase. It is not surprising that
the molecular weight has such a large impact since it affects the value of three other
parameters, kl,k 2 , 4 .
The number of binary interaction parameters used for the mixing rules was limited
to two in order to decrease the potential for cross correlation when generalizing.
Based on the results of the sensitivity analysis, mixing rules with binary interaction
parameters are developed for T, and b. The remaining parameters are mixed using
simple linear mixing rules, with the understanding that some error must inevitably be
absorbed by the binary interaction parameters. The molecular weight (M)is a
physically significant quantity, with accepted mixing rules available in the literature
that do not require binary interaction parameters.
269
J.D. Williams, W.Y. Svrcek, and W.D.Monnery
The mixture molecular weight, M,, and the mixture acentric factor, w m, are
calculated using simple linear mixing rules such as Equations 4 and 5:
M , = Ci X i M i
63,
=cxi
0;
i
Equations 6,7,and 8 are then used to find the parameters k,,, k b , k4, for the mixture.
k ,,=0.03072+(0.00128) M,o
,%
k,, = (0.627O)exp((-O.O0242)M,o
k,, = 1 .O + exp((-0.03895) M,w
(6)
,%)
,x)
ken, and k,, are also determined using simple linear mixing rules:
(dk),is a function of the mixture critical temperature, T,, given by:
(i]
= 0.65(Tc,)
m
where T, is defined as:
i
j
and
b, is determined using Equations 14 and 15.
2 70
(7)
(8)
Prediction of Viscosityfor Mixtures
In Equations 13 and 15, ku and ju are binary interaction parameters.
For this work, the mixture density, pm, also requires a mixing rule since pure
component densities are calculated using the methods discussed previously.
Assuming no volume change upon mixing the following will apply:
-=c1
Pm
xi
i
Pi
Binary Interaction Parametersfor Mking Rules
Binary interaction parameters are empirical parameters, with no theoretical basis, that
help to make up for the deficiencies in a model. The binary interaction parameters
from Equations 13 and I5 were regressed using experimental binary viscosity data.
The optimized parameters resulting fiom this regression are listed in Table 1. The
table states for each mixture which phases the binaries are applicable to, the number
of experimental data points used, the temperature range covered by these points, and
the average absolute deviation for the data set (%AAD). In many cases binaries could
not be regressed to cover multiple phases due to a lack of experimental data.
For the majority of the data sets, viscosity measurements of the pure components
are also included which gives a good benchmark for how well the MSWIP viscosity
model is predicting the pure components and hence how much error must be absorbed
by the binaries. One of the key successes of this work is a model that is able to
predict the correct trend in the viscosity curve versus the mixture composition. In
general, the model is able to predict mixture viscosity very well, within 10% AAD,
however there are a few exceptions.
Many of the aqueous mixtures have a very high %AAD, although this is not
surprising since water is a notoriously difficult component to model. Aminelacid
mixtures are also predicted poorly, and again this is not without precedent since acids
are associating components that can also be difficult to model. The only other
component that is poorly predicted is 172-ethanediol. The error for the pure
component data points of I72-ethanediolwas very high ranging from 19-30%, at times
worse than the water prediction, which means that the binaries had to compensate for
a large amount of pure component viscosity error. However, the data used in the
1,2-ethanediol and water mixtures was mostly given at temperatures of 298 K, which
is below the temperature range recommended by Monnery et al. (1998) for
1,2-ethanediol.
2 71
2
h,
n-Heptane
n-Heptane
n-Heptane
n-Octane
n-Octane
2,2,4-Trimethylpentane
2,2,4-Trimethylpentane
2,2,4-Trimethylpentane
2,2,4-Trimethylpentane
2,2,4-Trimethylpentane
2,2,4-Trimethylpentane
2,2,4-Trimethylpentane
n-Hexadeche
n-Heptane
Methane
Methane
Methane
Ethane
2,4-Dimethylpentane
2,4-Dimethylpentane
n-Hexane
n-Hexane
n-Hexane
Alkane
Component 1
n-Butane
Propane
Ethane
Propane
n-Dodecane
n-Hexadecane
n-Dodecane
n-Tetradecane
n-Hexadecane
n-Dodecane
n-Hexadecane
n-0ctadecane
n-Tetradecane
n-Decane
n-Hexadecane
n-Hexane
n-Nonane
n-Dodecane
n-Decane
n-Heptane
n-Hexadecane
n-Tetradecane
n-Tetradecane
Alkane
Component 2
1.12
1.15
1.13
1.11
1.19
1.17
1.01
1.1 1
1.08
1.12
1.31
1.25
1.oo
0.98
0.98
1.07
1.11
0.91
1.05
0.93
0.9 1
0.98
1.08
&ij
1.06
0.97
0.50
0.50
0.50
0.50
0.50
0.5 1
0.50
1.06
1.44
1.33
1.04
0.50
0.50
1.1 1
1.28
1.29
1.10
1.07
1.40
1.16
1S O
1,
15
12
11
12
10
12
12
14
11
6
15
3
3
28
3
67
10
51
3
206
269
76
76
No.Data
Points
Table 1. Optimizedbinary interactionparametersfor MSWIP model combining rules.
293-444
293-523
293-523
293-523
298-336
298-336
289-343
298
283-393
298-336
293-336
298-336
298-336
290-420
318-338
298
298
298
298
298
298
298
298
Temperature
Range (K)
2.32
4.07
6.96
4.12
2.47
4.93
6.82
4.38
1.41
5.27
3.80
2.21
0.18
0.12
1.32
0.85
4.23
0.13
2.56
0.88
0.07
1.65
11.48
%AAD
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
G
G
L
G,D
G,D
Phase'
2
h,
n-Hexane
n-Heptane
n-Octane
n-Nonane
n-Decane
n-Dodecane
n-Hexadecane
n-Tetradecane
n-Octane
Alkane
n-Butane
n-Pentane
2,4-Dimethylpentane
n-Hexane
n-Heptane
n-Octane
n-Decane
n-Dodecane
n-Hexadecane
n-Octadecane
n-Tetradecane
n-Hexane
n-Heptane
n-Hexane
n-Hexane
2,2,4-Trimethylpentane
Alkane
Table 1 continued.
Naphthene
Cyclohexane
Cyclohexane
Cyclohexane
Cyclohexane
Cyclohexane
Cyclohexane
Cyclohexane
Cyclohexane
Methylcyclohexane
Aromatic
Benzene
Benzene
Benzene
Benzene
Benzene
Benzene
Benzene
Benzene
Benzene
Benzene
Benzene
Naphthalene
o-Xylene
Ethy lbenzene
Toluene
Toluene
7
6
7
3
146
27
41
21
56
49
3
12
18
49
18
67
14
I .01
0.50
0.92
0.76
0.95
0.67
0.84
0.9 1
0.96
1.01
1.35
1.13
1.04
1.10
1.23
0.90
0.50
1.24
1.oo
1.06
1.oo
1.08
1.05
1.06
1.08
1.13
1 .oo
1.05
1.02
0.94
0.92
1.03
1.13
1.04
23
22
12
12
12
32
12
12
0.83
0.83
0.72
0.75
0.88
1.16
1.06
1.03
1.04
1.08
1.08
1.06
0.99
1.09
1.07
1.01
293
298
298-336
283-463
293-336
283-393
283-393
283-393
298-393
298-336
298-336
298-3 18
293-593
298-323
298-333
298
298
298
298
298
298
289-337
298
298
298
0.40
0.54
0.30
3.91
0.80
1.05
1.23
2.06
3.76
0.02
1.36
1.68
5.02
3.70
1.63
3.18
1.26
0.70
2.23
1.66
1.76
1.72
2.92
1.67
I .30
L
L
L
L
2
tv
Methane
n-Hexadecane
n-Hexane
Propane
Methane
n-Heptane
Methane
Methane
Carbon Dioxide
Oxygen
Nitrogen
Carbon Monoxide
Ammonia
CVF Alkane
Carbon Tetrafluoride
Carbon Tetrachloride
Trichloromethane
Alkane
Methane
Naphthene
Cyclohexane
Cyclohexane
Cyclohexane
Cyclohexane
Aromatic
Toluene
o-Xylene
p-Xylene
Isopropylbenzene
Ethylbenzene
Naphthalene
0-Xy lene
Isopropylbenzene
Ethylbenzene
p-Xylene
o-Xylene
Ethylbenzene
Alkane
Carbon Dioxide
Aromatic
Benzene
p-Xy lene
m-Xy lene
Toluene
Aromatic
Benzene
Benzene
Benzene
Benzene
Benzene
Benzene
Toluene
Toluene
Toluene
Toluene
m-Xy lene
Isopropy lbenzene
Inorganic
Table I continued.
0.99
1.11
1.04
1.19
1.20
1.41
1.27
0.89
110
10
8
19
3
10
76
0.50
0.95
0.50
1.50
1.08
0.96
76
0.50
1.so
204
I .24
107
106
64
28
176
62
55
44
68
34
63
5
0.95
0.50
0.84
0.78
0.93
1.10
1.10
0.75
0.97
0.94
1.11
0.67
1.02
1.16
1.06
1.06
1.02
0.98
0.98
1.07
1.01
1.03
0.96
I .07
0.98
203
27
27
45
0.83
0.75
0.70
0.79
1.03
1.06
1.06
1.06
298473
298
298
300-550
293
344
298-473
288-353
293-474
3.80
20.47
0.98
3.09
0.96
273-343
294-358
283-353
283-343
298-343
298-353
253-353
253-353
253-353
283-353
273-303
283-353
9.70
3.54
0.64
2.34
2.27
6.38
2.02
2.68
3.44
1.62
4.68
1.45
0.76
4.72
1.30
1.oo
1.90
1.oo
0.72
3.16
283-393
303-323
303-323
286-323
L
.b
2
b
Carbon Tetrachloride
Inorganic
Carbon Monoxide
Nitrogen
Oxygen
Ethylene
CUF Alkane
Carbon Tetrafluoride
Hydrogen Chloride
Methyl Chloride
Cl/F Alkane
Carbon Tetrachloride
Carbon Tetrachloride
Trichloromethane
Trichloromethane
Dichloromethane
Cl/F Alkane
Carbon Tetrachloride
Carbon Tetrachloride
ClIF Alkane
Carbon Tetrachloride
Inorganic
Carbon Dioxide
Carbon Dioxide
Argon
Carbon Monoxide
Carbon Monoxide
Carbon Dioxide
Oxygen
Table I continued.
n-Hexane
Cyclohexane
Inorganic
Nitrogen
Argon
Nitrogen
Nitrogen
Oxygen
Oxygen
Nitrogen
Naphthene
Ethylene
Ethylene
Ethylene
Ammonia
Inorganic
Carbon Monoxide
Carbon Dioxide
Carbon Dioxide
Aromatic
Benzene
Toluene
Benzene
Toluene
Benzene
Cl/F Alkane
Trichloromethane
Dichloromethane
Alkene
21
149
110
74
76
57
19
76
1.20
1S O
1.50
1.05
0.50
0.50
1.50
0.50
0.90
0.95
0.90
1.10
1.38
1.32
0.94
1.38
0.50
293-304
293-303
293-303
300-550
300-500
300
300-550
293
298-323
293-413
0.84
1.05
1.18
41
57
0.85
0.90
0.92
1.02
1.06
1.06
1.03
1.03
1.01
0.98
298-473
29 1
238-308
298
298-333
288-323
298
293-303
10
19
16
0.50
0.90
0.66
1.33
0.99
1.09
300-550
300-550
293-373
293-523
298
49
33
32
8
27
76
76
76
57
12
1.18
1.50
1.50
1.16
0.93
1.09
1.05
0.94
0.95
1.oo
6.05
4.94
1.27
15.28
1.70
3.20
0.85
0.94
2.69
1.08
8.63
0.70
0.63
0.20
0.36
1.80
0.35
0.86
4.72
5.16
2.43
1.49
0.78
G
G
G
G
G
G
G
L
L
G
L
L
L
L
L
G
G
G
G
G
G
G
L
2
F
%
5
3
>
3
2:
r,
2
%
s
3.
e
2
m
u
o\
h,
Methanol
Methanol
Ethanol
I-Propanol
2-Propanol
2-Propano1
Alcohol
Methanol
Ethanol
I-Propanol
Ethanol
I-Butanol
2-Butanol
2-Methyl-2-Propanol
1-Pentanol
2-Methyl- I-Propanol
2-Pentanol
1-Hexanol
Alcohol
Methanol
2-Propanol
Carbon Monoxide
Ammonia
Nitrogen
Oxygen
Alcohol
Methanol
Ethanol
1-Propano1
Table 1 continued.
-
1.21
298-328
298
298-333
298-328
298
298
1.10
61
8
74
49
26
9
283-323
293-333
45
27
1.09
0.76
0.99
0.80
1.12
1.27
1.23
1.07
1.09
298
7
1.08
0.96
Diethyl Ether
1.14
1.01
0.89
0.87
0.9 1
0.83
298
298
183-373
283-373
273-343
293-298
288-3 18
273-373
298-333
288-3 18
293-333
298
288-3 18
298-473
293-303
293-573
293-473
7
9
430
484
247
62
53
10
66
38
17
10
32
10
30
171
57
1.07
1.14
1.13
1.10
0.77
0.73
0.63
1.03
1.20
0.64
1.29
1S O
0.94
1S O
1S O
1SO
1.02
0.96
1.16
1.33
1.34
I .40
1.16
1.04
1.43
0.93
1.so
1.21
1.43
1.03
0.82
0.91
0.88
~~
Diethyl Ether
Diethyl Ether
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
1,CDioxane
1,4-Dioxane
Cl/F Alkane
Carbon Tetrachloride
Trichloromethane
Carbon Tetrachloride
Carbon Tetrachloride
Dichloromethane
Carbon Tetrachloride
Ether
Waier
Carbon Dioxide
Argon
Ammonia
Ammonia
~
3.02
7.40
7.00
4.52
4.27
4.94
1.46
4.62
2.04
2.82
2.29
18.15
22.16
25.82
3 1.75
8.40
17.83
28.36
I .80
14.34
3.86
44.17
1.95
1.53
6.80
3.52
-
L
L
L
L
L
L
s
8
3
i$
P
3
P
v
h
u,
Amine
Toluene
Aniline
Aniline
1-Propano1
2-Propanol
Methanol
1-Butan01
Aromatic
Alcohol
I -Butan01
1-Butanol
Ethanol
2-Methyl-1-Propano1
Alcohol
Ethanol
1-Butand
Alcohol
Methanol
Cyclohexane
Carbon Tetrachloride
Carbon Tetrachloride
Carbon Tetrachloride
Carbon Tetrachloride
Naphthene
Cyclohexane
Cyclohexane
Cyclohexane
Methylcyclohexane
Cyclohexane
Cyclohexane
Methy lcyclohexane
Cyclohexane
Methylcyclohexane
Cyclohexane
Cyclohexane
Methy Icyclohexane
Cyclohexane
Alcohol
1-Decanol
MethanoI
Ethanol
1-Propano1
1-Propano1
2-Propanol
1-Butan01
1-Butanol
1-Pentan01
1-Pentanol
2-Methyl-1-Propano1
1-Hexanol
1-Hexanol
1-0ctanol
Alcohol
1-Butan01
I-Hexanol
1-Heptanol
1-Decanol
Table 1 continued.
1.02
1.04
1.05
1.03
0.99
1.oo
0.99
1.oo
1.21
0.99
0.85
0.98
1.03
1.09
1.03
1.01
1.oo
1.oo
1
114
15
36
9
9
36
9
3
6
5
6
4
1.16
.oo
6
1.08
0.85
1.oo
0.98
1.oo
4
163
36
6
8
32
6
40
54
9
9
9
0.50
1.16
1.30
1.13
1.12
1.22
1.09
1.16
1.27
1.09
1.06
1.04
0.50
0.94
0.83
0.92
0.88
0.87
0.93
0.91
0.94
0.85
0.96
1.oo
1.10
293-353
293-298
298-3 13
298
298
298-328
298
293
298-328
298-328
303
298
298-328
303
298-328
303
303
293
303
293
293
298-328
298
298
298
10.47
8.72
5.06
1.71
1.74
1.67
3.20
0.91
1.15
1.27
0.13
0.73
1.55
43.40
6.14
1.91
1.84
13 0
1.38
1.18
1.57
3.37
1.69
2.17
1.90
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
2
g9'
%
B
B
R
0
2
9
3
(b
2
a
3.
0
h,
2
Alcohol
Alcohol
Methanol
Ethanol
Aldehyde
Benzaldehyde
Nitrile
Acetonitrile
Benzene
Benzene
1-0ctanol
1-Decanol
1-Hexanol
1-Hexanol
Benzene
0.94
0.99
1.oo
1.oo
0.94
0.88
1.20
1.15
0.94
0.90
0.95
0.82
0.86
0.89
0.86
0.86
0.52
0.83
0.88
0.83
0.91
0.85
0.91
Ethylbenzene
m-Xylene
Toluene
Benzene
Ethylbenzene
Benzene
Toluene
Ethylbenzene
Benzene
Benzene
Isopropylbenzene
Ethylbenzene
p-Xylene
Toluene
Naphthalene
Benzene
1.10
Benzene
Benzene
Toluene
Ethanol
Ethanol
1-Propano1
1-Propano1
1-Propano1
2-Propanol
I -Butan01
I-Butanol
1-Butan01
1-Butan01
1-Butan01
1-Butan01
2-Methyl-2-Propanol
1-Pentan01
Ethanol
Methanol
Methanol
Methanol
Table 1 continued.
1.04
0.99
1.oo
1 .oo
9
9
298
298
293
293
4
4
0.23
4.12
1.69
0.54
I .56
2.48
298
303-333
14
36
14
8
7
9
19
13
14
1.17
I .05
41
1.17
3.86
6.61
6.98
8.42
8.79
8.10
2.06
1.55
6.83
5.59
1.38
3.40
1.73
1.03
1.30
1.23
0.88
1.25
283-323
298-308
293
223-353
288-328
223-363
298-308
298
223-363
293-303
298-3 18
298-308
298
298
298
303-323
298
293-298
95
14
6
65
73
57
32
10
60
27
1.56
1.16
1.09
1.20
1.07
0.99
1.12
0.82
0.65
0.86
1.17
1.20
1.14
1.25
1.17
1.15
1.08
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
P
S
2
h,
Dimethyl Ether
Diethyl Ether
1,4-Dioxane
Acetaldehyde
Ether
Methyl-phenyl Ether
Diethyl Ether
Ether
Methyl-phenyl Ether
Ether
Methyl Chloride
Trichloromethane
Trichloromethane
Aromatic
Benzene
Benzene
Naphthene
Cyclohexane
CUF Alkane
Water
Phenol
3-Methylphenol
Phenol
Water
Methanol
Ethanol
Ethanol
1-Propano1
2-Propanol
I -Butan01
1-Pentanol
2-Pentanol
2-Methyl-1-Propano1
2-Methyl- 1-Propano1
1-Hexanol
1-HexanoI
1-0ctanol
I -Decanol
Aldehyde
Benzaldeh yde
Benzaldehyde
Aldehyde
n-Heptane
n-Hexane
n-Heptane
n-Heptane
n-Pentane
n-Pentane
n-Hexane
n-Hexane
n-Hexane
n-Heptane
n-Heptane
n-Hexane
n-Heptane
n-Heptane
Alkane
Alcohol
Table I continued.
1.15
1.oo
0.82
1.03
36
60
19
38
25
27
298-3 13
298-323
283-298
308-353
288-298
298
273
9
1S O
0.50
0.76
1.01
308
308
223-353
293
298
283-298
298-328
293-333
303
303
293
303-333
293
293
298
293
7
7
5
16
52
5
10
16
41
45
6
6
6
36
6
4
1.22
1.26
1S O
1.38
1.27
1S O
1.14
1.28
1.22
1.23
1.02
0.98
1S O
1.05
1S O
1S O
0.94
1.oo
1.17
1.11
1.06
1.46
0.95
0.90
1-50
0.85
0.93
1S O
0.91
0.89
0.90
0.85
0.95
0.97
1S O
0.99
1.50
1S O
1.21
1.06
1.35
7.82
1.18
1.56
16.42
3.49
4.59
17.43
4.60
12.93
77.81
4.25
2.10
2.2 1
6.54
1.36
1.69
90.15
2.28
94.18
96.52
L
L
L
G
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
t
u
0
0
n-Butanoic Acid
n-Hexanoic Acid
n-Octanoic Acid
Carboxylic Acid
Methanoic Acid
Ethanoic Acid
Propanoic Acid
n-Butanoic Acid
Isobutanoic Acid
Ethanoic Acid
1,4-Dioxane
CarbouylicAcid
Ethanoic Acid
Ethanoic Acid
Ethanoic Acid
Propanoic Acid
Propanoic Acid
n-Butanoic Acid
n-Pentanoic Acid
n-Hexanoic Acid
n-Octanoic
Propanoic Acid
Propanoic Acid
Benzoic Acid
Carboxylic Acid
Ethanoic Acid
Ether
Table I continued.
1.27
1.17
0.84
1.37
1.18
1.25
0.90
0.99
1.15
1.07
1.30
1.32
1.34
Carbon Tetrachloride
Carbon Tetrachloride
Water
Water
Water
Water
Water
Water
1 .oo
1.10
0.95
0.96
1.01
1.32
0.78
0.85
0.70
0.64
0.90
0.66
0.92
1 .oo
0.88
1.03
Trichloromethane
Carbon Tetrachloride
1.81
0.99
1S O
1.18
1S O
1.14
1.oo
1.30
1.07
1.28
1S O
0.50
0.69
1.06
0.55
1.40
0.94
Water
Benzene
Toluene
Naphthalene
Toluene
Benzene
Benzene
Benzene
Benzene
Benzene
Ethylbenzene
Propylbenzene
Benzene
CUF Alkane
Carbon Tetrachloride
Aromatic
Water
L
L
L
L
L
2.98
2.56
4.46
10.46
16.05
30.95
31.18
298
298
293-358
293-368
29 1-333
273-308
293-3 13
16
9
9
9
70
L
L
L
L
0.67
1.63
255
30
143
46
L
0.55
298
298
298
L
13
16
L
L
L
L
L
L
L
L
L
L
L
L
14.87
23.42
13.63
5.16
12.93
0.46
2.09
1.29
0.29
3.81
4.36
0.93
24.44
293-363
283-323
308-328
308
293-3 18
298
298
298
298
308
308
303-3 18
293-323
25
9
18
9
29
8
8
8
8
9
11
158
B
ru
2
Propanone
Methyl Ethyl Ketone
Ketone
Propanone
Propanone
Ketone
Propanone
Propanone
Ketone
1,2-Ethanediol
Carboxylic Acid
Ethanoic Acid
Ethanoic Acid
Ethanoic Acid
Ethanoic Acid
Ethanoic Acid
Methanoic Acid
n-Butanoic Acid
Carboxylic Acid
Ethanoic Acid
Propanoic Acid
Propanoic Acid
Propanoic Acid
Carboxyiic Acid
Benzoic Acid
Benzoic Acid
Ethanoic Acid
Diol
Toble I continued.
Alcohol
Alkane
Aromatic
Methanol
Ethanol
n-Hexane
n-Heptane
Benzene
Benzene
Water
Ketone
Methyl Phenyl Ketone
Methyl Isobutyl Ketone
Propanone
Methyl Ethyl Ketone
Methyl Propyl Ketone
Propanone
Propanone
Amine
Aniline
Aniline
n-Butyl Amine
Di-n-Butyl Amine
Alcohol
Methanol
1-Propano1
Ethanol
Water
0.68
0.60
0.9 1
1S O
1.36
1.08
1.08
0.96
0.98
1.13
1.04
1.01
0.99
0.72
1.09
37
9
17
15
18
0.90
I .08
0.52
53
71
16
16
10
78
61
18
34
9
36
54
27
27
27
27
0.99
1.16
0.50
1.49
1.50
1.50
1.09
1.12
1.1 1
0.97
0.82
1.17
1.07
1.17
0.93
0.97
1.22
1.10
1.1 1
0.97
1.oo
0.96
1.07
1.03
293-3 18
298
298
296
283-299
293-323
263-303
298-3 18
298-3 18
298
291-373
298
293-333
293-333
298
293-3 18
293-323
298-3 18
298-3 18
298-3 18
298-3 18
4.49
10.51
3.53
0.22
1.79
1.29
35.93
2.87
0.4 1
0.65
55.27
18.84
36.09
53.39
4.90
1.29
2.35
0.83
0.83
1.69
1.13
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
B
8
2
F
%
5
2
3'
n
%
g
r?
b
>
m
lu
lu
00
Propanone
Propanone
Propanone
2-Butanone
~~~
~~
Alkane
2,2,4-Trimethylpente
Water
Water
Water
Water
CWF Alkane
Carbon Tetrachloride
Inorganic
Ammonia
Triethyl Amine
Amine
Triethyl Amine
n-Butyl Amine
Diethyl Amine
Amine
Aniline
Arnine
Methylamine
l-Butanol
2-Methyl-1-Propano1
Phenol
Phenol
Ketone
Propanone
Propanone
Propanone
CIIF Alkane
Carbon Tetrachloride
Trichloromethane
Carbon Tetrachloride
Water
Water
Aromatic
Toluene
Benzene
Naphthalene
Benzene
Amine
Aniline
Aniline
Aniline
Diethyl Amine
Amine
Ketone
Ketone
Propanone
Ketone
Methyl Isobutyl Ketone
Methyl Ethyl Ketone
Methyl Propyl Ketone
Ketone
Propanone
Propanone
Table I continued.
1.02
G
273-673
209
0.81
1.04
L
8.53
298
9
1.52
15
13
0.75
1.so
1.so
L
L
L
0.76
0.52
1.so
1.45
44.77
32.33
40.17
0.50
278-293
298-328
298
L
L
L
L
L
L
L
L
49
3.85
10.45
3.56
10.91
24.4 1
5.18
2.80
0.38
L
L
L
0.49
0.3 1
0.31
L
L
L
~
6.06
4.91
2.57
L
.
3.13
298-3 13
298
308-328
293-308
273-333
~~
303-313
16
15
57
36
338
293-333
293-308
298
298
293-3 13
293-3 13
9
18
18
65
34
7
283-323
298
298
45
9
9
14
1S O
1.50
1.so
1S O
1.01
1.1 1
0.77
0.76
0.77
0.70
t .22
0.78
1.28
0.83
0.94
0.74
0.94
1.04
1.07
1.03
1.08
0.96
1.05
1.26
0.94
1.01
0.99
1.01
0.99
2
hr
Phenol
Aniline
Aniline
Benzene
Toluene
Benzene
Toluene
Toluene
Benzene
Water
1,4-Dioxane
CUF Alkane
Carbon Tetrachloride
G = Gas; L = Liquid; D = Dense Phase.
Ester
Methyl Ethanoate
Ester
Ethyl Ethanoate
Ester
Ethyl Ethanoate
Methyl Ethyl Ketone
Methyl Isobutyl Ketone
Ester
Ethyl Ethanoate
Ether
Ethyl Ethanoate
n-Hexane
Naphthene
Cyclohexane
Cyclohexane
Ketone
Methyl Ethyl Ketone
Alkane
Aromatic
Water
Phenol
4-Methylphenol
Phenol
Butyl Ethanoate
Phenol
2-Methylphenol
2-Methylphenol
4-Methylphenol
4-methy phenol
Phenol
Phenol
Phenol
Phenol
Phenol
2- Methyphenol
4- Methyphenol
Ester
Propyl Propanoate
Phenol
Amine
Table I continued.
1.07
1.37
I .oo
0.76
0.99
0.88
0.78
1.07
0.98
1.07
1.04
1.oo
1 .oo
1.14
1S O
0.94
298
8
9
7
293
3 13
298
0.44
298
9
7
0.17
298
9
0.86
2.38
0.56
1.69
2.02
12.00
308
308
9
9
2.26
2.78
1.55
10.29
10.29
0.55
7.27
32.19
2.59
20.99
328
6
18
298-323
308
308
308
283-303
293-298
283-358
308
298-323
9
11
1.57
0.87
1S O
1.13
32
9
9
84
4
10
1.07
1.09
1.45
0.61
1S O
1S O
0.96
0.74
0.97
0.95
0.79
0.72
1.06
1.39
0.87
0.81
L
L
L
L
L
L
L
L
L
L
L
L
0
%
3
E
9
30
2.
953
J.D. Williams, W.Y. Svrcek, and W:D.Monnev
Conclusions
In this work, mixing rules were developed for the Modified Square Well
Intermolecular Potential (MSWIP) viscosity model developed by Monnery et al.
(1998). The mixing rules require two binary interaction parameters that were
regressed fiom experimental viscosity data for a range of chemical families. Gas
mixture viscosity data is sorely lacking in comparison to the available liquid mixture
viscosity data, and hence only 34 gas mixtures versus the 242 liquid mixtures were
used.
The regressed binary interaction parameters give good viscosity predictions with
the exception of aqueous systems, amine/acid systems, and 1,2-ethanediol. The
MSWIP model predicted viscosities for the majority of the binary mixtures within
10% AAD, which given their application is a reasonable uncertainty.
Additionally, the MSWIP viscosity model was found to accurately predict trends
in the viscosity-composition curves, including maxima and minima. This is a
significant accomplishment and can be attributed to the theoretical framework on
which the model is based. This ability to correctly predict trends and the simplicity of
the model make it extremely attractive for industrial use. The only inputs required by
the model are molecular weight, critical temperature, acentric factor, and density,
which can all be readily obtained.
Nomenclature
B
C
Excluded volume (cm3/mol)
Square well model correction
g(o J Square well radial distribution
fimction at repulsion diameter
g(Ro 3 Square well radial distribution
function at attraction diameter
K
Boltzmann’s constant
(1.38048 x loz3J/K)
ko, k,, Model parameters
kz, 5 k4
k,
Binary interaction parameter
‘u
Binary interaction parameter
M
T
T,
X
Molar mass (kgflunol)
Temperature (K)
Critical temperature (K)
Mole firaction
Greek Letters
Viscosity (mPas)
P
Density (mol/cm3)
&
Intermolecular potential
attractive energy well depth (J)
~y1, 1y2 Square well model parameter
w
Acentric factor
References
Brokaw, R.S. 1968. Viscosity of Gas Mixtures, NASA Technical Note D-4496, Washington
D.C., April 1968.
DIPMIXTM,Dewan, A.K.; Ruggles, B.M, and Moore, M.A. 1992. DIPMH: An Evaluated
Database for Transport Properties and Related Therrno&aarnicData of Binaty Mixtures,
Thermodynamics Research Center, Texas.
DIPPR Design Institute for Physical Property Data 1998. Project 801 - Evaluated Process
Design Data, BYU-DIPPR Thermophysical Properties Laboratory.
284
Prediction of Viscosityfor Mixtures
DIPPR, Daubert, T.E. and Danner, R.P. 1994. Data Cornpilalion of Pure Compound
Properties, Version 9, NISTISRD Database 1 I .
Irving, J.B. 1977. Viscosity of Binary Liquid Mixtures: The Effectiveness of Mixture Equations,
Natl. Eng. Lab. Report No. 631, East Kilbride, Glasgow, Scotland, February 1977.
Monnery, W.D.; Mehrotra, A.K.; and Svrcek, W.Y. 1998. Viscosity Prediction of Nonpolar,
Polar, and Associating Fluids Over a Wide PpT Range From a Modified Square Well
Intermolecular Potential Model, Ind. Eng. Chem. Res. 37,652-659.
Peng, D.Y., and Robinson, D.B. 1976. New Two-Constant Equation of State, Ind Eng. Chem.
Fund. 15,59-64.
Reid, R.C.; Prausnitz, J.M.; and Poling, B.E. 1987. The Properties of Gases and Liquid,
McGraw-Hill.
Stephan, K., and Heckenberger, T. 1988. Thermal Conductivity and Viscosify Data of Fluid
Mixtures, Chemistry Data Series, Vol. X, Part 1, DECHEMA.
Sutton, J.R. 1976. References to Experimental Data on Viscosity of Gas Mixtures, Natl. Eng.
Lub. Rep. No. 613, East Kilbride, Glasgow, Scotland, May 1976.
Touloukian, Y.S.; Saxena, S.C.; and Hestermans, P. 1975. Thermophysical Properties of
Matter Volume I 1 - Viscosity,Plenum Publishing Corporation, New York.
Received: 5 December 200 1;Accepted after revision: 1 June 2002.
285
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