Purdue University
Purdue e-Pubs
International Refrigeration and Air Conditioning
Conference
School of Mechanical Engineering
1992
Accurate Vapor Pressures for Refrigerants
R. C. Miller
Texas A&M University
A. Diaz Ceballos
Texas A&M University
K. R. Hall
Texas A&M University
J. C. Holste
Texas A&M University
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Miller, R. C.; Ceballos, A. Diaz; Hall, K. R.; and Holste, J. C., "Accurate Vapor Pressures for Refrigerants" (1992). International
Refrigeration and Air Conditioning Conference. Paper 187.
http://docs.lib.purdue.edu/iracc/187
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ACCURATE VAPOR PRESSURES FOR REFRIGERANT S
Reid C. Millert, Ana Diaz Ceballos:j::, Kenneth R. Hall and James C. Holste*
Department of Chemical Engineering, Texas A&M University
College Station TX 77843-3122 USA
tPennanent address: College of Engineering and Architecture, Washington State
University, Pullman WA 99164 USA
:j::Present address: Corpoven, S.A., Refineria el Palito, APDO. 102, EDO. Carobobo,
VENEZUELA
*Author to whom correspondence should be addressed.
ABSTRACT
Parameters for a new vapor pressure equation are reported for methane, ethane,
propane, n-butane, i-butane, R-11, R-12, R-22, R-23, R-32, R-123, R-134a, R-141b, R·
142b, R-143a and R-152a These parameters have been obtained using experimental
vapor pressures reported in the literature. The vapor pressure equation is based on
asymptotic behavior at the triple and critical points, and it has three fluid dependent
parameters. This equation describes the entire vapor pressure curve within the approximate accuracy of the experimental values.
NOMENCLATU RE
a;
b; =
N
""
p =
Po =
p.., =
dp =
pa
fjp<1
PC
P,
cr;(P)
cr;(T)
=
=
=
=
=
R
ss
=
t "'
T
Tc "'
T, =
W; =
parameters for vapor pressure equation
parameters for vapor pressure equation
empirical constant of vapor pressure equation
reduced vapor pressure variable
asymptotic vapor pressure behavior approaching the triple point
asymptotic vapor pressure behavior approaching the critical point
difference between experimental and calculated values of p
vapor pressure
difference between experimental and calculated vapor pressures
critical pressure
triple point pressure
variance of pressure measurement
variance of temperature measurement
universal gas constant
weighted sum of squares in statistical procedure
reduced temperature variable
temperature
critical temperarure
triple point temperarure
.
statistical weighting factor for datum i
479
INTR ODU CTIO N
for the design of process equipment,
Accurate vapor pressures are important
conditioning. Many vapor pressure
air
especially in the field of refrigeration and
in general, the equations which describe
equations have appeared in the literature, but,
the measurements are quite complex if the
experimental data within the accuracy of
point to the critical point) is described
triple
the
(from
entire vapor pressure curve
functions such as the Antoine equation can
with a single function. Alternatively, simple
d range of temperatures, and several·
limite
a
over
ately
describe vapor pressures accur
of temperatures. Recently, an equation
ranges must be used to describe a wide range
accurately over the entire vapor
ures
1
press
r
vapo
ibes
was reported which descr
eters in addition to the temper·
param
dent
pressure curve using only three fluid depen
A comparison of the new
s.
point
al
critic
and
triple
the
atures and pressures at
in Reference 1, therefore
ded
provi
is
ions
equation with existing vapor pressure equat
it is not repeated here.
Iglesias equation to a variety of fluids
This work reports the application of the
air conditioning industry, and for which
which are important to the refrigeration and
ted in the literature. The fluid dependent
experimental measurements have been repor
,
al hydrocarbon and halocarbon substances
parameters have been determined for sever
in
(with
ures
press
point
the triple and critical
and minor adjustments have been made to
to provide the best descriptions of the
ents)
urem
meas
ted
repor
the
of
acy
the accur
The parameters described in this work are
experimental measurements for each fluid.
h computes vapor pressures using the
incorporated into a computer program whic such a way that parameters for new
in
Iglesias equation. The program is structured
ng parameters for substances already in
existi
the
or
,
easily
added
be
may
ances
subst
general characteristics of this program are
the data bank may be changed easily. The
described below.
VAPOR PRESSURE EQUATION.
upon a method proposed by ChurThe Iglesias vapor pressure equation is based is very useful if the asymptotic
which
nt
3
opme
devel
lation
chill and Usagi2. for corre
of the range of variables. For the case
behavior of the function is known at the ends
ior near the triple and critical points each
of the vapor pressure, the asymptotic behav
Usagi approach, they are ·combined
chillChur
are known, and according to the
according to
liN
p(t)
=
[ [po(t) ]N
+
[p..,(t)]N]
(1)
ptotic limits approaching the triple and
where the subscripts 0 and .,., denote the asym
ures and temperatures are given by
critical points respectively. The reduced press
t
"'
and
p
=
.L:L..
(2)
l+p a.pr
Pc· Pr
(3)
Tc· Tr
480
so that 0 < t <1 and 1 < p < 2. The asymptote approaching the triple point is
(4)
where
a 1 = - (a 0 - 1) exp(a 2 - bo/R)
a 2 = b 1/RT
a3
= T,- T
T,
This result is obtained by application of the Clausius-Clapeyron equation and the
assumption that the enthalpy of vaporization varies- linearly with temperature. Details
of the derivation are provided in Reference 1. Because of the relations between the
parameters, the fluid-dependent parameters for this asymptote are b0 and bl.
The asymptote approaching the critical point is derived from the assumption of
scaling and simple background terms (see reference 1 for details) to be
Simple relations also exist 1 which give the parameters a5, a6 and a 7 in Equation (5) in
terms of a4 • These have been determined empirically to be
as = -0.11599104 + 0.29506258 as- 0.00021222 a~
a6 = - 0.01546028 + 0.08978160 a,f- 0.05322199 al
a7 =
0.05725757-0.06817687 a 4 + 0.00047188 a~
Therefore only a 4 in Equation (5) remains as a fluid-dependent fit parameter.
Walton, et al. 4 , suggest that 9 = 0.199 provides the optimal representation of
experimental data. Therefore, although scaling theory suggests that the value should
be lower, we use 9 = 0.2 for this work. Finally, Iglesias-5ilva, et al. 1, showed that the
empirical exponent N may be calculated from the reduced triple point temperature
according to
N = 87 T 1 /T,
(6)
Finally, only a 4 , b 0 and b 1 remain as parameters which must be determined from
vapor pressure data for each fluid.
481
FITTING PROCEDURE
ard nonlinear statistical procedures in
The parameters were determined using stand
package. The optimal representation
the form available in the PC-SAS statistical
ically to reflect the inaccuracies of
statist
ted
occurs when the measurements are ~eigh
are chosen by minimizing the sum of
the experimental measurements. The parameters
calculated and observed values:
the
en
betwe
the weighted squares of the differences
ss :::
i: w;(Lipi
(7)
1•1
5
One is that given by Hust and McCarty
Two methods were considered for this work.
(8)
and the other is due to Hall and Waxman
6
(9)
(8) and (9) for several substances. No
We compared results obtained using Equations
to use the Hall-Waxman method.
chose
we
so
ved.
obser
significant differences were
uracies in the e,;perimental
inacc
ated
The variances are calculated from the estim
measurements.
es the calculation of the derivative
Application of either Equation (8) or (9) requir
Because only modest accuracy is
.
rarure
of the vapor pressure with respect to tempe
fitting an Antoine equation to the experi·
required, these values are calculated by first
ne constants to calculate temperarure
Antoi
mental data, then using the resulting
ion.
derivatives during the fitting of the Iglesias equat
RESULTS
fits are listed in Table 1. These
The critical and triple point values used for these pressures have been adjusted
some
but
ure,
originally were obtained from the literat
of each) to provide better agreement in
slightly (within the experimental uncertainty
s are not available, the freezing point
value
the fits. For cases where triple point
there usually is little difference between
provides a very good reference point, because
parameters a 4 , b 0 and b 1 were deterThe
s.
the freezing and triple point temperarure
gh butane) and for those halocarbons
mined for the light hydrocarbons (methane throu
were available from the archival
ents
urem
where sufficient experimental meas
eters. The resulting values are listed
literature to provide a legitimate fit of the param
values of the deviations between the
te
absolu
the
of
in Table 2 along with the averages
the equation. Table 2 also identifies the
experimental values and those calculated from
data sources for each fluid.
482
Table 1. Critical and triple point values used for fits
Species
Formula
Methane
Ethane
Propane
i-Butane
n-Butane
190.551
CH4
305.33
Cfi:JCH3
369.85
CH3CH2CH3
C(CH3) 3
407.85
CH3(CHhCH3 425.16
R-11
R-12
R-22
R-23
R-32
CFC13
CF2Cl2
CHF2Cl2
CHF3
CHzF2
R-123
R-134a
R-141b
R-142b
R-143a
R-152a
CHC!zCF3
CH2FCF3
CFCI 2CH3
CF2ClCH3
CF3CH3
CHF2CH3
P,lkPa
T,IK
TIIK
P,tkPa
4599.2
4871.4
4247.46
3640.
3796.
90.685
90.348
85.470
113.55
134.86
471.15
384.95
369.30
299.30
351.56
4487.1
4124.
4988.
4858.
5828.
162.15
115.19
113.
113.2
137.
0.0063
0.00023
0.00024
O.OZ5
0.056
456.87
374.51
477.35
410.29
346.25
386.44
3668.
4056.
4250.
4041.
3811.
4520.
166.
172.
163.
142.
161.82
156.
0.0055
0.56
0.0029
0.014
1.18
0.100
11.696
0.0011308
1.670xlo-7
1.9481xlQ-S
6.7352x1Q-4
Typical deviations between the experimental and calculated values are shown in
Figures 1, 2 and 3, which show the results for R-32, R-134a and R-152a, respectively.
The first, R-32, is representative of the case where only one set of measurements (of
moderate quality) have been reported. For R-134a, four sets of values have been
reported, and two sets were available for R-152a at the time of fitting. For both R134a and R-152a, the data are of high quality. All three figures show that the equation
is quite capable of describing the entire vapor pressure range to within the estimated
experimental uncertainties.
COMPUTER PROGRAM
Because of the complexity of the equations, we prepared a computer program to
calculate vapor pressures according to the Iglesias equation. This program has
capability for easy alteration of existing parameters or the addition of parameters for
additional fluids as they become available through future statistical treatment and as
more experimental values are reported in the literature. The capability for additions
or changes is password protected, so that alterations may be controlled and recorded
even though a particular copy of the program may have many users.
The current version of the program operates un'der MS/DOS on PC-compatib1e
machines. It is menu driven and has the capability to provide vapor pressures at single
specific temperatures, or to generate tables where the upper and lower bounds and
intervals in temperature are specified. Output may be received on the screen, as
483
disk. Additional information about the
printed hard copy, or written to a file on
sponding author.
cone
the
program may be obtained by contacting
Table 2. Fit parameters and goodness of fit
Species
Methane
Ethane
Propane
i-Butane
n-Butane
bl
AAPE"
Reference
a4
bo
6
3.159535
4.581460
5.205689
4.999256
4.797703
"19.77081
-36.42229
-43.50273
-47.83018
-43.85128
8812.417
17877.435
24771.221
28197.481
28605.450
0.03
-42.98908
-44.25981
-45.35556
-44.54006
-40.59925
30789.076
25594.772
25645.692
20546.185
23775.126
0.03
0.06
0.09
0.26
0.22
-46.74315
-42.47784
·48.00818
-8.64520
-31.40464
-34.613687
32619.809
25799.300
32769.259
23114.129
21960.191
25294.458
0.18
0.18
0.03
0-32
0.35
0.06
7
8
9
10
R·ll
R-12
R-22
R-23
R-32
12-13
14-16
17·21
22
4.620788
4.840123
4.919967
4.563538
5.543935
R-123
R·134a
R-141b
R-142b
R-143a
R-152a
23
24·27
28
29-30
29,31
32-33
4.703437
4.114466
4.697202
4.848964
3.966619
4.425394
11
O.D7
0.07
0.54
0.51
ntage deviation of experimental
"AAPE = average absolute value of perce
ion
equat
fit
best
the
measurements from
ACK NOW LED GME NTS
Duarte·Garza for preparing the final
The authors are grateful to Dr. Horacio
provided by the Governor's Energy
was
copies of the figures. Financial support
y Research in Applications Program
Management Center - State of Texas Energ
(Contract No. 5217).
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•
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485
1.0
0.8 '-
R3 2
•
0.6
0.4
~
b
0.2
-
0.0
a..
•
••
• •
-0.2
'0
Ref eren ce 22
-
•• •
•
• •• •
•
••
•
•
• • •
•
•
.,
• •
•
-0.4
-0.6
-0.8
I
-1.0
150
250
200
400
350
300
T. K
ntal and calculated vapor pressures for R-32
Figure !.Differences between experime
1.0
0.8
,•
R1 34 a
,
0.6
!::..
0.4
~
!::..
!::..
0.2
0.0
b
Q_
-0.2
co
-0.4
Ref eren ce .24
Ref eren ce 25
lJ Ref eren ce 26
!::.. Ref eren ce 27
,,
, ,
!::..
!::..
!::..
!::..
!::..
!::..
!::..
lJ
!::..
lJ lJ
!::..
,,
,
-0.6
-0.8
-1.0
150
200
250
300
350
400
T, K
4a
tal and calculated vapor pressures for R-13
Figure 2.Differences between experimen
486
1.0
•
"'
R152a
0.8
Reference 32
Reference 33
0.6
0.4
~
b
a..
co
0.2
• -,.,.
.
0.0
•
....
-·······-....
•••
T
~
T T
-0.2
-0.4
-0.6
-0.8
.
~
-1.0
250
300
350
400
T, K
Figure 3.Differences between experimental and calculated vapor pressures for R·l52a
487