High Temperatures ^ High Pressures, 2002, volume 34, pages 49 ^ 55
15 ECTP Proceedings pages 1277 ^ 1283
DOI:10.1068/htwu126
Dynamic viscosity of azeotropic and quasi-azeotropic
mixtures of organic compounds
Giovanni Latini, Giovanni Di Nicola, Giorgio Passerini
Dipartimento di Energetica, Universita© di Ancona, Via Brecce Bianche, 60100 Ancona, Italy;
fax: +39 071 280 4239; email: [email protected]
Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany,
5 ^ 9 September 1999
Abstract. Azeotropic and quasi-azeotropic mixtures of organic compounds are becoming the most
effective candidates as replacement fluids. Heat and mass transfer phenomena in organic compound mixtures have been theoretically studied from several different points of view. Despite these
efforts, theoretical models are frequently inaccurate while empirical methods are usually more
accurate but they are often specialised and tuned to cover a small number of compounds and/or
a limited temperature range. Based on the development of effective prediction formulas for several
families of pure organic compounds, the problem of the evaluation of mixture dynamic viscosity
is approached from a rather different point of view. Azeotropic mixtures are treated as pure
compounds rather than a combination of several pure substances, and a single, specialised formula
for the evaluation of saturated liquid dynamic viscosity is developed. The prediction method
requires the knowledge of few equilibrium properties of the mixture to be analysed thus becoming a simple and powerful tool for exhaustive analysis of alternatives. It has been tested against
experimental data leading to deviations far below those required for engineering purposes.
1 Introduction
Organic compound mixtures can be roughly grouped as azeotropes and zeotropes (ie
non-azeotropes). Azeotropes are mixtures of fluids for which the composition in the
vapour phase and in the liquid phase does not change when in equilibrium. Zeotropes
are associated with composition and temperature glides or shifts during phase changes.
In some cases, the temperature glide (ie the difference between its temperature at the
dew point and its temperature at the bubble point) is almost negligible and the mixture is
said to be a `quasi-azeotrope', a `near-azeotrope', or `azeotrope-like'. The boundaries
between azeotropes, near azeotropes, and zeotropes cannot be easily stated. However, a
mixture with a temperature glide smaller than 1 8C is generally judged to be a nearazeotrope and a mixture with a temperature glide greater than 5 8C is almost certainly a
zeotrope (Didion 1994).
During the past years we have developed a prediction method to evaluate the
dynamic viscosity of refrigerants in their saturated liquid state. The related formulas
required the knowledge of a few equilibrium properties and were effective over a wide
range of temperatures. Each formula was able to evaluate the dynamic viscosity of each
compound belonging to a refrigerant series or to other organic compound series. Namely,
we developed specialised formulas for: methane-series refrigerants, ethane-series refrigerants, alkanes, and aromatic compounds. Few differences existed between the equations
related to the first two families, and we were already conscious of the possibility of
developing a single equation for all the refrigerants belonging to the two series. On the
other hand, the increase in the deviations between experimental data and predicted values was not justified by a negligible reduction in the number of constants.
An azeotropic mixture can be regarded, in terms of pressure, volume, temperature
( p, V, T ) behaviour, as a pure substance. We can determine a normal freezing-point
temperature and a normal boiling-point temperature as well as critical-point physical
properties. Because these properties are namely the only parameters to be introduced in
50
G Latini, G Di Nicola, G Passerini
15 ECTP Proceedings page 1278
our formulas, together with the molecular mass, it was possible to evaluate the transport
properties of azeotropic mixtures as if they were pure substances (Latini et al 1996a).
We just needed to develop new formulas to evaluate transport properties of methane
series and ethane series refrigerants and to apply them to azeotropic mixtures. For a
quasi-azeotropic mixture, we can still evaluate its properties at the normal boiling point
and at the critical point, for example by means of a refrigerant database such as
REFPROP (Huber et al 1996). We can also use such databases to evaluate the same
properties for zeotropes.
As a result, we propose a new formula to evaluate the saturated liquid dynamic
viscosity in the reduced temperature range from 0.5 to 0.9. We validated the prediction
method against pure refrigerant data and mixture data available in the literature. Mean
deviations between prediction results and experimental data are usually below 8%.
Because mixtures were not considered during the fitting of constants, it was possible to
test the predictive capability of the method. The method can therefore be considered as
a tool for an a priori investigation of the applicability of new refrigerant mixtures.
2 Pure compounds prediction method
Our prediction method is based on a model, developed by one of the present authors
(Latini et al 1987, 1990; Latini 1989) by combining the Batschinski equation (Batschinski
1913) modified by Hildebrand (Hildebrand and Lamoreaux 1972, 1973; Hildebrand 1977)
with the rule of Mathias (Reid et al 1978) which links the sum of liquid and vapour
densities with the reduced temperature and the density at the normal boiling point. The
first form of the derived equation was:
1
A
ÿB ,
ˆ
m C ÿ Tr
(1)
where m is the dynamic viscosity, A and B are constants characteristic of the fluid, C is
a constant sensitive to the molecular structure, and Tr is the reduced temperature T=Tc
(where Tc is the critical temperature).
The constants A, B, and C had to be calculated by evaluating experimental data. A
further step was performed by two of the present authors (Latini and Polonara 1994)
when they found that a new choice of C made it possible to assume B equal to A:
1
1
ÿ1 .
(2)
ˆA
m
C ÿ Tr
In the present equation, the constant C assumes a new single value of 1.35 for both the
methane and ethane series of refrigerants, provided that the constant A is calculated by
means of the new formula
A ˆ hM a Tbrb ,
(3)
where M is the molecular mass, Tbr is the reduced normal boiling point temperature,
Tb =Tc , and where h ˆ 6, a ˆ ÿ0:25, b ˆ ÿ2:85. Those values were evaluated by means of
correlation applied to a wide range of refrigerants. This makes the present method a
somewhat semi-empirical method, with the original equation derived from a theoretical
model but with experimental data used to fit constants. For each compound we have
considered all the experimental data series found in the literature because we stated that
we could not judge a priori the accuracy of one or more series based on the discrepancy
with the other ones. This new equation contains only two terms: the reduced temperature
at the normal boiling point and the molecular mass. The presence of M in the correlation
is essential to take into account both the mass and the strong relationship between
molecular structure and liquid dynamic viscosity (Latini et al 1996b), having set the
factor C to a single value.
Dynamic viscosity of organic compounds
51
15 ECTP Proceedings page 1279
Table 1. Investigated pure compounds for dynamic viscosity. Equilibrium properties are taken
from Huber et al (1996), Reid et al (1978), and Beaton and Hewitt (1989).
Fluid
Reference
M
Tb
K
Tc
K
A
ADD MAD
mPaÿ1 sÿ1
%
%
R113
R114
R115
R123
Kumagai and Takahashi (1991)
Kumagai and Takahashi (1991)
ASHRAE (1976)
Kumagai and Takahashi (1991),
Diller et al (1993),
Okubo and Nagashima (1992a)
Kumagai and Takahashi (1991)
Phillips and Murphy (1970),
Ripple and Matar (1993)
Phillips and Murphy (1970),
Oliveira and Wakeham (1993)
Phillips and Murphy (1970)
Kumagai and Takahashi (1991),
Ripple and Matar (1993),
Oliveira and Wakeham (1993),
Assael et al (1994a),
Okubo and Nagashima (1992b),
Bivens et al (1994), Krauss et al
(1993), Shankland (1990),
Laesecke et al (1999)
Kumagai and Takahashi (1991, 1993)
Van der Gulik (1993)
Kumagai and Takahashi (1991)
Kumagai and Takahashi (1991),
Phillips and Murphy (1970),
Van der Gulik (1993),
Assael et al (1994b)
Titani (1927)
Kumagai and Takahashi (1991),
Phillips and Murphy (1970),
Assael et al (1994b)
Kumagai and Takahashi (1991),
Phillips and Murphy (1970),
Assael et al (1994b)
Diller and Van Poolen (1989)
Kumagai and Takahashi (1991),
Diller and Van Poolen (1989)
Kumagai and Takahashi (1991),
Phillips and Murphy (1970)
Phillips and Murphy (1970)
Kumagai and Takahashi (1991),
Phillips and Murphy (1970),
Assael and Polimatidou (1994)
Phillips and Murphy (1970)
Phillips and Murphy (1970)
Phillips and Murphy (1970)
Phillips and Murphy (1970),
Ripple and Matar (1993),
Oliveira and Wakeham (1993),
Assael et al (1994a), Bivens et al
(1994), Laesecke et al (1999)
Landolt and Bornstein (1955)
187.38
170.92
154.47
152.93
320.7
276.8
235.2
301.9
487.5
418.8
353.2
456.9
4.9114
5.2224
5.5546
5.5619
152.93
136.48
301.2
260.0
461.1 5.7453
395.6 5.8062
5.43
2.18
8.93
5.14
120.02
224.7
339.3 5.8687
3.88
7.74
118.49
102.03
279.2
247.1
432.0 6.3137
374.3 6.1654
5.40 8.90
4.16 14.28
116.95
100.49
84.04
66.05
304.9
263.4
225.9
248.5
477.3
410.4
346.3
386.7
153.82
137.37
349.9
296.9
556.3 6.3868
471.2 6.5350
9.76 14.54
4.89 11.96
120.91
243.4
385.0 6.6823
5.52 16.07
104.46
148.91
191.7
215.5
302.0 6.8543
340.2 6.3101
14.67 14.54
3.40 10.97
119.38
334.3
536.4 6.9851
2.71
102.93
86.47
282.1
232.3
451.7 7.2037
369.3 7.3761
6.31 13.28
1.81 5.99
70.01
84.93
68.48
52.052
191.0
313.0
263.9
221.6
299.1
510.0
430.0
351.4
7.4472
7.9461
8.3858
8.3104
5.71
6.10
5.12
5.84
10.18
12.80
12.09
10.18
50.49
249.1
416.3 9.7274
2.51
5.43
R123a
R124
R125
R133a
R134a
R141b
R142b
R143a
R152a
R10
R11
R12
R13
R13B1
R20
R21
R22
R23
R30
R31
R32
R40
6.5442
6.7080
6.6973
7.42420
8.39 13.75
2.79 7.12
5.24 9.08
3.18 10.98
0.58 2.21
7.78 8.37
13.58 13.77
9.74 14.52
5.72
52
G Latini, G Di Nicola, G Passerini
15 ECTP Proceedings page 1280
Equations (2) and (3) have been tested against a large number of pure refrigerants,
and it was found that it is effective over the reduced temperature range 0.5 ^ 0.9.
Results are shown in table 1, where
X
1
mcalc
AAD=% ˆ 100
ÿ
1
n ,
m
exp
and
m
MAD=% ˆ 100 MAX calc ÿ 1 ,
mexp
with mexp and mcalc , respectively, the experimental and the estimated dynamic viscosity
values, and n the number of experimental points.
New data related to R32 and R134a (Laesecke et al 1999) were not used during
constant fitting but the deviations between our results and such data are almost the same
both for AAD and for MAD.
3 Application to mixtures
We thought that azeotropic mixtures could be regarded as pure refrigerants and this
approach could be applied to the prediction of their transport properties provided that a
single formula was originally reliable for each mixture component. The same approach
can be applied to near-azeotropic mixtures with comparable results. For both azeotropic
and near-azeotropic mixtures, only the molecular mass, the critical temperature, and the
temperature at the normal boiling point are easily available. For zeotropes we found
that our prediction method could be applied by introducing, as the normal boiling-point
temperature, the average of the dew-point temperature and bubble-point temperature.
We applied equation (2) with the constant A evaluated by means of equation (3) to
azeotropic, near-azeotropic, and small-temperature-glide non-azeotropic mixtures, as
listed in table 2. We obtained good results, with the deviations equal to or less than those
we obtained for pure refrigerants. This seems to justify the fact that a general equation
for the prediction of transport properties of pure refrigerants could be used to evaluate
the same properties of azeotropic mixtures and small-temperature-glide zeotropes.
We must point out again that, for zeotropes, we introduced a `boiling-point-like'
temperature defined as the average of the normal dew-point temperature and normal
bubble-point temperature. This temperature generally corresponds to the one calculated
as the boiling-point temperature when REFPROP (Huber et al 1996) is used to evaluate
zeotropes.
Table 2. Investigated mixtures for dynamic viscosity. Properties are taken from Didion (1994),
Refrigerant mixture
R22/R125/R290
R125/R143a/R134a
R32/R125/R134a
R32/R125
R12/R152a
R22/R115
R13/R23
R32/R115
R32/R134a
R23/R116
R32/R125
ASHRAE code
R402B
R404A
R407C
R410A
R500
R502
R503
R504
R508
R508B
Reference
Shankland et al (1988)
Shankland et al (1988)
Shankland et al (1988)
Du Pont (1996a)
Phillips and Murphy (1970)
Phillips and Murphy (1970)
Phillips and Murphy (1970)
Phillips and Murphy (1970)
Bivens et al (1994)
Du Pont (1996b)
Bivens et al (1994)
Mass fraction
of components
1st
2nd
0.600
0.440
0.230
0.500
0.738
0.486
0.401
0.482
0.250
0.460
0.600
0.380
0.520
0.250
M
98.372
100.6
88.83
86.02
99.31
111.6
87.28
79.2
89.54
106.5
79.22
Dynamic viscosity of organic compounds
53
15 ECTP Proceedings page 1281
4 Results
Results are shown in tables 1 and 2. Figure 1 shows deviations between predicted
dynamic viscosity values and experimental data. Deviations are mainly due to the
dependence of dynamic viscosity on the molecular structure of compounds. In the original prediction method for pure substances, this dependence was taken into account by
the factor C which has now been set to a single value for all refrigerants thus leading to
an expected increase of the deviations.
For pure refrigerants (table 1), mean deviations range from a few percent to 10%
while maximum deviations are usually around or above 10%. Exceptions are those for
R13 and R143a where average deviations are around 14%. However, such deviations are
constant within the reduced temperature range. We have not yet analysed such deviations.
Deviations %
20
R402B
R500
R508
R404A
R502
R508b
R407C
R503
R32/R125
R410A
R504
10
0
ÿ10
ÿ20
0.5
0.6
0.7
0.8
Reduced temperature
0.9
Figure 1. Deviation between predicted dynamic viscosity and experimental values for some azeotropic and quasi-azeotropic mixtures.
Deviations %
20
10
0
ÿ10
ÿ20
0.5
0.6
0.7
Reduced temperature
0.8
0.9
R402B
R500
R508
R404A
R502
R508B
R407C
R503
R32/R125
R410A
R504
Figure 2. Deviation between dynamic viscosity predicted by REFPROP (McLinden et al 1998)
and experimental values for some azeotropic and quasi-azeotropic mixtures.
Huber et al (1996), Latini et al (1996b), Reid et al (1978), Cavallini (1996).
Tb
or
K
Tbubble
K
(226.05/2.3)
(226.65/0.8)
(226.48/7.4)
(220.35/< 0:1)
239.7
227.8
184.5
266.2
(232.75/7.2)
(185.15/< 0:1)
221.01 (est.)
Tglide
K
Tc
K
A
mPaÿ1 sÿ1
AAD
%
MAD
%
367.95
355.8
373.6
358.1
378.7
355.4
292.7
339.6
377.5
298.6
359.6
7.5042
6.8472
7.8273
7.8896
6.9998
6.5586
7.3158
7.3065
8.0029
7.0899
8.0497
7.74
14.79
4.74
7.69
5.28
6.69
3.67
6.84
4.45
6.13
11.84
14.32
23.22
9.51
15.93
8.34
14.13
10.06
10.31
8.25
10.28
19.37
54
G Latini, G Di Nicola, G Passerini
15 ECTP Proceedings page 1282
However, based on deviations shown in table 2, we think that the predictive capability
of the prediction method for mixtures should not be affected by errors of the same
magnitude. However, we want to stress again that this method is intended for an a priori,
even almost exhaustive, investigation on the potential behaviour of mixtures in terms of
liquid dynamic viscosity. On such a basis, its results, in terms of deviations, should not be
compared with those generated by more sophisticated models that, on the other hand,
require a precise knowledge of several other fluid properties and/or their molecular
structures. Nevertheless, the values of liquid dynamic viscosity predicted by the latest
version of REFPROP (McLinden et al 1998) are shown, for comparison, in figure 2 in
terms of deviations between predicted values and experimental data. Data were evaluated
maintaining all REFPROP options preferences at their default values. Results obtained
by REFPROP are, although comparable, generally better than ours but the use of the
software is intrinsically limited to the proposed mixtures and mixtures composed of
available pure fluids.
5 Conclusions
The method for the evaluation of the dynamic viscosity of liquid mixtures presented
here shows good reliability and reasonably good precision. A statistical analysis of the
sensitivity of prediction errors with respect to the temperature glide of the mixtures is
currently being studied. In the near future this analysis could lead to the application of
the same approach to mixtures with organic components belonging to propane refrigerant families.
Acknowledgements. This work has been supported in part by the European Union in the framework of the JOULE ^ THERMIE programme, and by the Ministero dell'Universita© della Ricerca
Scientifica e Tecnologica of Italy.
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ß 2002 a Pion publication printed in Great Britain