COMPRESSIBILITY
FACTOR OF POLAR SUBSTANCES
BASED ON A FOUR-PARAMETER CORRESPONDING
STATES PRINCIPLE
HIDEO NISHIUMI
Chemical Engineering
Course, Department
Hosei University,
Tokyo 184
DONALDB. ROBINSON
of Mechanical
Department of Chemical Engineering, University
Edmonton, Alberta, Canada T6G 2G6
Engineering,
of Alberta,
A fourth parameter, ¥E, obtained from the second virial coefficients at low reduced temperatures, is proposed to correlate the compressibility
factor Z of polar substances. The value is
expressed in terms of WEand the acentric factor to as:
Z=Z<°>
+o>Z<1>
+VE(ZV
+<uZ<8>)
Tables of Z(0) through Z(3) are presented over the range of reduced temperatures from 0.4 to
4.0 and of reduced pressures from 0.03 to 40.0, using an approximate BWR equation of state.
For fifteen polar substances, the overall average absolute deviations in predicted compressibility
factor for the gaseous and liquid regions are 1.3 and 3.3 %, respectively.
The parameter can be
roughly related to dipole moments, whereas no strong correlations between WEand the Stockmayer potential model parameter is observed.
Introducti
on
1
The corresponding-state
principle
offers an effective means of predicting thermodynamic properties of
substances. Pitzer proposed an acentric factor <w
relating to the shape of a molecule as a third parameter18'.
The three-parameter
corresponding-state
principle has been very successful in correlating the
properties of nonpolar or slightly polar substances.
To extend the acentric factor corresponding-state
principle
to polar substances, an additional
fourth
parameter should be taken into account. Eubank
and Smith31 presented a parameter ^/TeVc relating to
a dipole moment for estimation of thermodynamic
properties
of dilute gases. Halm and Stiel*' defined
a fourth parameter i obtained from a reduced vapor
pressure at Tr=0.6. Based on this parameter, Stipp,
Bai and Stiel20' presented tables of the compressibility
factor for a reduced temperature range from 0.80 to
1.15 and reduced pressures from 0.2 to 6.0.
In a previous paper18', an improved BWRequation
of state for polar substances with three polar parameters was proposed. The objectives of this study
are to present a new fourth parameters, and to utilize
the equation of state to tabulate the compressibility
factor of polar substances over wide temperature and
pressure regions.
Received February 10, 1981
Correspondence
should be addressed to H. Nishiumi.
VOL.
14
NO.4
1981
concerning
this
article
. Fourth Parameter
It is well known
virial coefficients at
this work, a reduced
polarity is defined as:
for PVT Prediction
that polarity
affects the second
low reduced temperatures51.
In
fourth parameter ¥E concerning
v*
B._A.
Tr-BN
Ve
(1)
where
A*
C*
D* _ D*_j5°-___:±-(LJJff
£>0
rp
J,3
Ir
-/r
D*
4__rl°_
1
J.4
-Lr
(2)
B% is the reduced second virial coefficient
for a
normal fluid and the five coefficients with asterisks are
functions of o>19). The value of WE is determined
by
fitting experimental
data of the second virial coefficients B to Eq. (1).
The value, however, may be changeable
due to
scattering
or scarcity of data. To determine a reasonable value of WE, an improved BWR equation of
state10',
including
Eq. (1), was used. Three polar
parameters, WE, st and st, in the equation
of state
were adjusted to obtain the best fit of vapor pressures
and the second virial coefficients161.
Eventually,
the approximation
that sz=5.3 and st=
1.15 WE (approximate equation of state) leads to good
PVT predictions,
as shown in the 7th column of
Table 1. The average deviation of 2.4% is the same
as that for the original
parameters16'.
This means
259
T able 1
C om pressib ility factor predictions ob ta ined by using the approxim ate eq ua tion of state a nd T ables 2 th rough 5
R an ge o f v ariab les
1
/-C 3H 7O H
^
0 .7 3- 1 .16
0 .00- 2 .0 3
v
0 .6 8- 0 .8 5
5 .84- 32 .47
1
so
0 .64- 1 .2 1
0 .00- 3 .94
v
H 20
0 .57- 1 .7 7
0 .00- 1 .72
y
C H C 1F 2
C C 13F
89
* The same numbers as in the previous
** v oasenus nnase. i: nauia
of Compressibility
The compressibility
of written
work18)
Factor
of Polar
factor of a substance Z should
Z=Z*+ZP
(3)
Ztf and Zp represent the compressibility
factors of a
normal fluid and a correction for polar substances,
respectively.
The approximate equation of state without the
fourth parameter WEgives reduced density pr of a
normal fluid at a fixed Tr, Pr and a), and Z* can be
obtained from the definition Z=PrZc/prTr. A correlation for the compressibility
factor at the critical
point Zc of a normal fluid for 0<<o<l is expressed as
Zc=0.2923-0.093«
(4)
For various values of co between 0 and 1 at a fixed
TV, and Pr, the ZN values were found to be correlated
as
Z^=Z(0'+o>Z(1>
(5)
Z(0) and Z(1) are functions of Tr and Pr. Values of
Z(0) and Z(1) are shown in Tables 2 and 3, respectively.
The values around the critical
points are adjusted.
At a fixed TV, Pr, o> and Ws, the Zvalue of a polar
substance can be calculated
using the approximate
260
15
13 ,
8
9
10
1,7
7
7
6, 2 1
9
9
14
14
9
17
I, /
2
2
1
7
1
17, 22
pimsc
that a sinele oolar parameter WEis sufficient for PVT
prediction,
whereas three polar parameters, WSt slt
and sz, are needed for vapor pressure prediction due
to its greater sensitivity.
Values of ¥E for 39 polar
substances were presented in the previous work16'.
2. Correlation
Substances
D ata
sou rce
68
47
32
32
123
37
21
32
32
32
40
32
32
21
78
20
16
82
27
63
29
H CN
76
A v . dev. [% ]
A p pro xim ate
T ables
equ atio n ***
2-5
P oin ts
equation of state in this work. From these values,
Zp is obtained according to Eq. (3). Figure 1 shows
the relationship
between Zp and WEat Tr=Q.6 and
o>=0.2. It reveals that Zp is proportional
to WE up
to 0.3 in WE, where most polar substances are included
with the exception of acetone, hydrogen fluoride and
nitromethane.
As shown in Fig. 2, the relationship
between Zp and o>at Pr=1.60 and ^=0.175 shows
that Zp is linear with (a.
Based on the above results, Zp can be expressed as
Zp=?r£(Z<2'
+a>Z<3>)
(6)
Z(2) and Z(S) should be correlated
in terms of Tr and
Pr. They are shown in Tables 4 and 5. The values
of Z(2) and Z(3) in the region of Tr>\2and
Pr<3.0
can be treated as 0.0, and those around the critical
point are adjusted.
3.
Discussion
3. 1 Normal fluids
Comparison ofZ(0) and Z(1), shown in Tables 2 and
3 respectively,
for a normal fluid, were made with
Pitzer's18',
Lu's12' and Lee-Kesler's tablesll',
as shown
in Table 6. With regard to Z(0), each table shows
similar values of average deviation in comparison with
this work. Compared with Pitzer's18'
and Lu's12'
tables, values of Z(0) in Table 2 are greater over the
0.7<> Tr, 3.0<Pr region, and smaller elsewhere in the
range of Tr and Pr. In comparison with Lee-Kesler's
tablesll',
Z(0> in this work is greater over the region of
0.4<
5.0<Pr,
Tr<0.52,
0.01
<Pr<
and of l.l<^r,
JOURNAL
10.0,and
of0.54<
2.0<Pr,
and smaller
OF CHEMICAL
ENGINEERING
Tr<0.90,
in the
OF JAPAN
<
o
£
V a lu e s o f Z (0) fo r c o m p res sib ility fa c to r ca lc u la tio n
z
T a b le 2
^
p
P r
<o
CO
to.
o.
T r
0 .0 3 0
0 .1 0 0
0 .3 0 0
0 .6 00
0 .8 0 0
0
0
0
0
0
.9 4 3 9
.9 2 16
.9 0 0 8
.8 8 1 5
.8 6 3 5
1 .3 1 10
1 .2 7 9 1
1 .2 4 9 4
1 .2 2 1 7
1 . 19 5 8
1 .8 5 2 4
1 .8 0 5 9
1 .7 6 2 5
1 .7 2 1 9
1 .6 8 3 8
3
3
3
3
3
0
0
0
0
0
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.1 3 3 8
.1 2 4 5
.1 2 13
. 1 18 3
0
0
0
0
0
.1 9 3 9
.1 7 8 3
. 16 5 9
. 16 1 6
. 15 7 6
0
0
0
0
0
0
0
0
0
0
.5 6
.5 8
.60
.6 2
.64
0
0
0
0
0
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.0 0 5 7
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0
0
0
0
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.0
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19 3
18 9
18 5
18 2
17 9
0
0
0
0
0
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.0 5 5 5
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0
0
0
0
0
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0
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0 . 18 8 0
0 . 18 4 1
0 . 18 0 6
0 .2 2 54
0 .2 2 0 7
0 .2 16 4
0 .2 8 1 3
0 .2 7 5 4
0 .2 6 9 9
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0 .5 5 8 2
0
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0
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0
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0
0
0
0
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0
0
0
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0
0
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0
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0
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0
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0
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0
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1 . 10 80
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0
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0
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0
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0
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0
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0
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0
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0
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0
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.7 3 70
.7 17 6
1 .0 7 2 1
1 .0 5 5 9
1 .0 4 0 8
1 .0 0 74
0 .9 7 4 9
1 .4 9 9 3
1 .4 7 4 6
2 .8 4 8 6
2 .7 9 4 7
0 .9 5
1 .0 0
1 .0 5
1 .10
1 .1 5
0
0
0
0
0
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.9 9 10
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0
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0
0
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0
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0
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0
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0
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0
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0
0
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0
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0
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0
0
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0
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0
0
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0
0
0
0
0
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.9 34 9
.9 2 19
.9 13 3
.9 0 9 0
1 .3 0 7 9
2 .4 13 6
1 .2 4 82
1 .2 2 5 8
2 .2 6 0 8
2 . 19 6 8
1
1
1
1
1
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.30
.3 5
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0
0
0
0
0
.9 9 4 0
.9 9 4 7
.9 9 5 3
.9 9 5 8
.9 9 6 3
0
0
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0
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.9 8 4 3
.9 8 6 1
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0
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.9 4 6 1
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.8 9 0 0
.9 0 4 0
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0
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0
0
0
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.8 12 6
.8 3 8 6
.8 5 9 9
0
0
0
0
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.7 7 3 5
.8 0 6 2
.8 3 2 7
0
0
0
0
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.7 1 6 7
.7 5 9 9
.7 9 4 2
0
0
0
0
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.6 4 0 2
.6 9 60
.7 4 0 8
0
0
0
0
.5 5 5 8
.60 4 9
.6 5 30
.6 9 7 6
0
0
0
0
0
.7 17 2
.7 3 52
.7 57 2
.7 8 14
.8 0 6 3
0
0
0
0
0
.9 0 8 7
.9 1 2 3
.9 19 5
.9 2 9 6
.9 4 1 8
1 . 19 3 8
1 . 18 34
1 . 17 6 4
1 .1 7 2 3
1 .1 7 0 8
2 .0 8 8 5
2 .0 4 2 8
2 .0 0 2 0
1 .50
1 .6 0
1 .7 0
1 .8 0
1 .9 0
0
0
0
0
0
.9 9 7 0
.9 9 7 6
.9 9 8 1
.9 9 8 4
.9 9 8 7
0
0
0
0
0
.9 9 0 1
.9 9 2 0
.9 9 3 6
.9 9 4 8
.9 9 5 8
0
0
0
0
0
.9 7 0 5
.9 7 6 4
.9 8 1 1
.9 8 4 8
.9 8 7 7
0
0
0
0
0
.9 4 1 8
.9 54 0
.9 6 3 4
.9 7 0 8
.9 7 6 7
0
0
0
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0
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.9 3 9 7
.9 5 2 4
.9 6 2 2
.9 7 0 1
0
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0
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.9 32 3
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.9 8 5 8
0 .9 6 9 5
0 .9 9 7 5
1 .0 2 3 2
1 .0 4 5 8
1 .0 6 4 9
2
2
3
3
4
0
0
1
1
1
.9 9 9 0
.9 9 9 7
.0 0 0 0
.0 0 0 2
.0 0 0 3
0
0
1
1
1
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.9 9 9 0
.0 0 0 1
.0 0 0 6
.0 0 0 9
0 .9 9 0 2
0 .9 9 7 4
1 .0 0 0 5
1 .0 0 2 1
1 .0 0 2 8
0
0
1
1
1
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.9 9 5 6
.0 0 17
.0 0 4 6
.0 0 6 1
0
0
1
1
1
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.9 9 4 9
.0 0 2 8
.0 0 6 6
.0 0 8 4
0 .9 7 2 0
0 .9 9 4 7
0 .9 6 1 5
1
1
1
1
1
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.0 6 0 6
.0 8 0 4
.0 8 6 7
.0 8 7 3
1
1
1
1
1
1 .0 10 9
0 .9 6 8 1
0 .9 9 4 8
1 .0 1 3 5
0 .9 6 3 5
0 .9 9 5 7
1 .0 17 8
0 .9 5 8 9
0 .9 9 9 1
1 .0 2 5 6
.7 2 3 7
.6 64 7
.6 1 7 1
.60 0 6
.5 8 5 4
3 .9 2 7 6
3 .8 0 8 9
3 .6 9 8 2
.0 7 2 8
.0 6 7 0
.0 6 2 3
.0 6 0 7
.0 59 2
.8 3 3 3
.8 7 3 5
.9 0 3 6
.9 2 6 6
.9 4 4 6
0
0
0
0
0
2 .0 1 3 1
1 .9 5 5 6
1 .9 0 2 2
0
0
0
0
0
0
0
0
0
0
.4 8 3 4
.4 4 4 3
.4 1 2 9
.4 0 2 0
.3 9 1 9
1 .4 2 1 5
1 .3 8 1 9
1 .3 4 5 1
.0 2 4 3
.0 2 2 3
.0 2 0 8
.0 2 0 3
.0 19 8
.8 6 52
.8 9 6 4
.9 19 9
.9 3 7 9
.9 5 2 1
0
0
0
0
0
1 .6 7 5 1
0
0
0
0
0
0
0
0
0
0
.3 6 3 0
.3 3 3 7
.3 10 2
.3 0 2 1
.2 9 4 6
1 .2 0 12
1 .10 2 0
1 .0 2 1 7
0 .9 9 3 8
0 .9 67 9
.0 0 7 3
.0 0 6 7
.0 0 6 2
.0 0 6 1
.0 0 5 9
.8 8 8 6
.9 13 6
.9 3 2 5
.9 4 7 2
.9 5 8 8
0
0
0
0
0
2 0 .0 0 0
0
0
0
0
0
0
0
0
0
0
.2 9 0 6
.2 6 7 2
.2 4 84
.2 4 2 0
.2 3 6 0
10 .0 0 0
.4 0
.4 5
.50
.5 2
.54
.9 0 5 5
.9 2 6 2
.9 4 2 0
.9 5 4 4
.9 6 4 1
0
0
0
0
0
7 .00 0
0
0
0
0
0
.0 0
.5 0
.0 0
.50
.0 0
.2 4 2 2
.2 2 2 8
.2 0 7 2
.2 0 1 8
. 19 6 8
5 .0 0 0
0 .5 34 9
0
0
0
0
0
1 .0 4 3 6
.0 8 10
.1 2 6 5
.1 4 0 4
.1 4 17
.1 3 7 9
.5 9 4 9
.4 9 8 3
.4 0 7 6
.3 2 2 5
.2 4 2 5
1 .9 3 2 8
1 .1 8 1 5
1 .2 4 16
1 .2 3 2 8
1 .2 2 0 8
1 .5 9 8 2
1 .5 5 1 5
1 .5 1 0 2
4 0 .0 0 0
Table 3 Values of Z(1) for compressibility
TT
0.030
0. 100
0.300
0.600
0. 800
1.000
factor calculation
Pr
1. 500
1.200
2.000
3.000
5.000
7.000
10.000
20.000
40.000
0 .4 0
-
0 .0 0 3 3
-
0 .0 10 8
-
0 .0 3 2 5
-
0 .0 6 4 8
-
0 .0 8 6 3
-
0 . 10 78
-
0 .1 2 9 2
-
0 .1 6 1 2
-
0 .2 1 4 2
-
0 .3 1 9 4
-
0 .5 2 6 2
-
0 .7 2 8 5
-
1 .0 2 4 2
-
1 .9 5 3 8
0 .4 5
-
0 .0 0 3 0
0 .0 0 2 9
-
0 .0 10 1
0 .0 0 9 5
-
0 .0 3 0 4
0 .0 2 8 5
-
0 .0 6 0 6
0 .0 5 6 7
-
0 .0 8 0 6
0 .0 7 5 5
-
0 . 10 0 6
0 .0 9 4 1
-
0 .1 2 0 5
0 . 11 2 7
-
0 .1 5 0 3
0 .1 4 0 5
-
0 .1 9 9 6
0 .1 8 6 4
-
0 .2 9 7 1
0 .2 7 6 9
-
0 .4 8 7 9
0 .4 5 3 1
-
0 .6 7 3 6
0 .6 2 3 7
-
0 .9 4 3 7
0 .8 7 0 2
-
1 .7 8 3 7
1 .6 2 9 8
-
0 .52
-
0 .0 0 2 8
-
0 .0 0 9 3
-
0 .0 2 7 8
-
0 .0 5 5 3
-
0 .0 7 3 6
-
0 .0 0 9 18
-
0 .1 0 9 9
-
0 .1 3 6 9
-
0 .1 8 16
-
0 .2 6 9 5
-
0 .4 4 0 3
-
0 .6 0 5 2
-
0 .8 4 3 1
-
1 .5 7 3 0
-
2 .8 4 7 1
0 .5 4
-
0 .0 0 2 7
-
0 .0 0 9 1
-
0 .0 2 7 1
-
0 .0 5 4 0
-
0 .0 7 1 8
-
0 .0 8 9 6
-
0 .1 0 7 2
-
0 .1 3 3 5
-
0 .1 7 7 0
-
0 .2 6 2 4
-
0 .4 2 8 1
-
0 .5 8 7 6
-
0 .8 1 7 1
-
1 .5 1 8 9
-
2 .7 3 9 7
0 .5 6
-
0 .0 0 2 7
-
0 .0 0 8 9
-
0 .0 2 6 5
-
0 .0 5 2 8
-
0 .0 7 0 2
-
0 .0 8 7 5
-
0 .1 0 4 7
-
0 .1 3 0 3
-
0 .1 7 2 6
-
0 .2 5 5 7
-
0 .4 1 6 4
-
0 .5 70 7
-
0 .7 9 2 3
-
1 .4 6 7 5
0 .5 8
-
0 .0 0 2 6
-
0 .0 0 8 7
-
0 .0 2 5 9
-
0 .0 5 1 6
-
0 .0 6 8 6
-
0 .0 8 5 5
-
0 .10 2 3
-
0 .12 7 3
-
0 .16 8 5
-
0 .2 4 9 3
-
0 .4 0 5 3
-
0 .5 54 7
-
0 .7 6 8 7
-
1 .4 1 8 6
0 .6 0
-
0 .0 0 2 6
-
0 .0 0 8 5
-
0 .0 2 5 4
-
0 .0 5 0 5
-
0 .0 6 7 1
-
0 .0 8 3 6
-
0 .10 0 0
-
0 .1 24 4
-
0 .1 64 6
-
0 .2 4 3 3
-
0 . 39 4 7
-
0 .5 39 4
-
0 .74 6 1
-
1 .3 7 2 0
-
2 .4 5 1 3
0 .6 2
-
0 .0 0 2 5
-
0 .00 8 3
-
0 .0 2 4 9
-
0 .0 4 9 5
0 .6 4
-
0 .0 3 3 4
-
0 .0 0 8 2
-
0 .0 2 4 4
-
0 .0 4 8 5
-
0 .0 6 4 5
-
0 .0 8 0 3
-
0 .0 9 5 9
-
0 . 1 19 2
-
0 . 1 5 7 5
-
0 .2 3 2 2
-
0 .37 5 0
-
0 .5 10 8
-
0 .7 0 3 9
-
1 .2 8 5 3
0 .6 6
-
0 .50
0 .6 8
3 .2 7 2 3
2 .9 6 0 6
0 .0 2 8 1
-
0 .0 0 8 0
-
0 .0 2 4 0
-
0 .0 4 7 7
-
0 .0 6 3 3
-
0 .0 7 8 7
-
0 .0 9 4 1
-
0 .1 16 9
-
0 .1 5 4 3
-
0 .2 2 7 0
-
0 .3 6 5 9
-
0 .4 9 7 4
-
0 .6 8 4 2
-
1 .2 4 5 1
-
2 .2 0 7 4
- 0 .0 2 3 7
-
0 .0 0 7 9
-
0 .0 2 3 6
-
0 .0 4 69
-
0 .0 6 2 2
-
0 .0 7 7 3
-
0 .0 9 2 4
-
0 .1 14 6
-
0 .1 5 12
-
0 .2 2 2 1
-
0 .3 5 7 1
-
0 .4 8 4 6
-
0 .6 6 5 3
-
1 .2 0 6 6
-
2 .1 3 4 4
-
0 .0 9 0 7
-
0 .1 1 2 6
-
0 .1 4 8 3
-
0 .2 17 5
-
0 .3 4 8 7
-
0 .4 7 2 3
-
0 .6 4 7 1
-
1 .1 6 9 9
-
2 .0 6 5 3
0 .2 0 8 7
-
0 .3 3 2 7
-
0 .4 4 8 9
-
0 .6 1 2 7
-
1 .1 0 1 1
-
1 .9 3 7 0
0 .7 0
-
0 .0 2 0 0
-
0 .0 0 7 8
-
0 .0 2 3 3
-
0 .0 4 6 1
-
0 .0 6 1 1
-
0 .0 7 6 0
0 .7 2
-
0 .0 1 6 9
-
0 .0 0 7 7
-
0 .0 2 2 9
-
0 .0 4 5 4
-
0 .0 6 0 2
-
0 .0 7 4 8
0 .7 4
-
0 .0 14 3
-
0 .0 5 64
-
0 .0 2 2 6
-
0 .0 4 4 8
-
0 .0 5 9 3
-
0 .0 7 3 7
-
0 .0 8 7 8
-
0 .10 8 8
-
0 .1 4 2 9
-
-0 .0 12 0
-
0 .0 4 6 6
-
0 .0 2 2 4
-
0 .0 4 4 2
-
0 .0 5 8 5
-
0 .0 7 2 6
-
0 .0 8 6 5
-
0 .1 0 7 0
-
0 .1 4 0 4
-
0 .2 0 4 6
-
0 .3 2 5 1
-
0 .4 3 7 7
-
0 .5 9 6 3
-
1 .0 6 8 7
-
1 .8 7 7 4
0 .7 8
-
0 .0 10 1
-
0 .0 3 8 5
-
0 .0 2 2 2
-
0 .0 4 3 7
-
0 .0 5 7 8
-
0 .0 7 1 6
-
0 .0 8 5 3
-
0 .1 0 5 4
-
0 .1 3 8 0
-
0 .2 0 0 6
-
0 .3 1 7 6
-
0 .4 2 6 8
-
0 .5 8 0 4
-
1 .0 3 7 6
-
1 .8 2 0 6
0 .8 0
-
0 .0 0 8 5
-
0 .0 3 1 7
-
0 .0 2 2 0
-
0 .0 4 3 3
-
0 .0 5 7 1
-
0 .0 7 0 7
-
0 .0 8 4 1
-
0 .1 0 3 8
-
0 .1 3 5 6
-
0 .1 9 6 6
-
0 .3 1 0 3
-
0 .4 1 6 1
-
0 .5 6 4 9
-
1 .0 0 7 7
-
1 .7 6 6 5
-0 .0 0 5 3
-
0 .0 19 2
-
0 .0 8 6 3
-
0 .0 4 2 3
-
0 .0 5 5 6
-
0 .0 6 8 6
-
0 .0 8 1 3
-
0 .0 9 9 8
-
0 .1 2 9 7
-
0 .1 8 6 6
-
0 .2 9 1 9
-
0 .3 8 9 9
-
0 .5 2 7 4
-
0 .9 3 7 3
-
1 .6 4 1 2
-
0 .0 12 9
-
0 .0 4 9 1
-
0 .0 4 2 6
-
0 .0 5 4 9
-
0 .0 6 6 7
-
0 .0 7 8 1
-
0 .0 9 4 6
-
0 .1 20 8
-
0 .1 6 9 6
-
0 .2 5 8 4
-
0 .3 3 9 5
-
0 .4 5 1 9
-
0 .7 7 8 9
-
1 .3 2 2 3
0 .7 6
0 .8 5
0 .9 0
-
0 .0 0 3 6
0 .9 5
-
0 .0 0 18
-
0 .0 0 6 5
-
0 .0 2 3 0
-
0 .0 7 5 1
-
0 .0 4 7 9
-
0 .0 5 9 2
-
0 .0 6 9 8
-
0 .0 8 5 1
-
0 .10 9 3
-
0 .1 5 4 4
-
0 .2 3 6 6
-
0 .3 1 1 8
-
0 .4 1 6 2
-
0 .7 2 0 7
-
1 .2 2 8 0
1 .0 0
-
0 .0 0 0 6
-
0 .0 0 2 0
-
0 .0 0 6 7
-
0 .0 1 7 1
-
0 .0 3 0 8
-
0 .0 9 3 0
-
0 .0 3 2 0
-
0 .0 3 9 0
-
0 .0 7 9 2
-
0 .1 2 9 6
-
0 .2 1 0 3
-
0 .2 8 2 0
-
0 .3 80 5
-
0 .6 6 6 6
-
1 .14 3 0
-
-
0 .9 9 50
1 .0 5
0 .0 0 0 3
0 .0 0 1 1
0 .0 0 3 9
0 .0 1 0 7
0 .0 1 9 4
0 .0 3 8 2
0 .10 0 1
0 . 12 9 4
1 . 10
0 .0 0 10
0 .0 0 3 3
0 .0 1 1 0
0 .0 2 6 5
0 .0 4 1 4
0 .0 6 3 0
0 .0 9 6 0
0 . 15 6 1
0 . 1 19 6
0 .0 0 8 7
-
0 .1 3 3 2
-
0 .2 10 7
-
0 .3 0 6 1
-
0 .5 67 6
1 . 1 5
0 .0 0 14
0 .0 0 4 8
0 .0 1 5 7
0 .0 3 6 0
0 .0 5 3 2
0 .0 7 4 8
0 .10 1 6
0 . 14 7 8
0 . 1 6 5 5
0 .0 6 8 1
-
0 .0 8 0 3
-
0 .16 7 7
-
0 .2 6 6 4
-
0 .5 2 1 5
1 .2 0
0 .0 0 18
0 .0 0 5 9
0 .0 1 8 8
0 .0 4 1 7
0 .0 5 9 8
0 .0 8 0 7
0 .10 4 5
0 . 14 2 8
0 . 18 0 1
0 . 12 1 6
-
0 .0 2 4 0
-
0 . 12 12
-
0 .2 2 52
-
0 .4 7 7 3
-
0 .8 6 9 4
1 .2 5
0 .0 0 2 0
0 .0 0 6 6
0 .0 2 0 9
0 .0 4 5 1
0 .0 6 3 4
0 .0 8 3 5
0 .10 52
0 . 13 8 9
0 . 18 0 3
0 . 15 5 5
0 .0 2 7 6
-
0 .0 7 8 3
-
0 . 18 3 1
-
0 .4 3 4 6
-
0 .8 13 2
1 .3 0
0 .0 0 2 1
0 .0 0 7 1
0 .0 2 2 1
0 .0 4 6 9
0 .0 6 5 0
0 .0 8 4 3
0 . 10 4 5
0 .1 3 4 9
0 . 17 5 8
0 . 17 5 8
0 .0 6 9 7
-
0 .0 2 9 0
-
0 . 14 14
-
0 .3 9 3 4
-
0 .7 6 0 5
1 .3 5
0 .0 0 2 2
0 .0 0 7 4
0 .0 2 2 8
0 .0 4 7 7
0 .0 6 5 4
0 .0 8 3 9
0 .10 2 8
0 . 13 0 9
0 . 17 0 0
0 . 18 62
0 . 10 2 2
0 .0 10 7
-
0 . 10 14
- 0 .3 5 3 7
-
0 .7 1 1 1
1 .4 0
0 .0 0 2 2
1 .50
0 .0 0 2 2
0 .0 0 7 5
0 .0 2 2 8
0 .0 4 6 6
0 .0 6 2 7
0 .0 7 8 9
0 .0 9 4 9
0 .1 1 8 0
0 .1 5 1 5
0 .1 8 6 4
0 .1 5 6 5
0 .0 9 3 4
-
0 .0 0 1 5
-
0 .2 4 4 7
-
0
1 .60
0 .0 0 2 2
1 .7 0
0 .0 0 2 1
0 .0 0 7 0
0 .0 2 0 9
0 .0 4 19
0 .0 5 5 7
0 .0 6 9 3
0 .0 8 2 5
0 .1 0 1 3
0 .1 2 9 0
0 .1 6 5 9
0 .1 7 34
0 .14 1 2
0 .0 7 7 4
-
0 .1 2 7 6
-
0 .4 3 4 1
1 .8 0
1 .9 0
0 .0 0 2 0
0 .0 0 1 9
0 .0 0 6 2
0 .0 1 8 5
0 .0 3 6 7
0 .0 4 8 4
0 .0 5 9 9
0 .0 7 1 0
0 .0 8 6 7
0 .1 1 0 0
0 .14 4 0
0 . 16 5 9
0 . 1 5 3 1
0 .1 1 3 0
-
0 .0 4 5 6
-
0 .3 18 3
2 .0 0
2 .5 0
0 .0 0 1 8
0 .0 0 1 2
0 .0 0 4 1
0 .0 12 3
0 .0 2 4 0
0 .0 3 16
0 .0 3 8 9
0 .0 4 6 0
0 .0 5 5 9
0 .0 7 1 0
0 .0 9 5 1
0 . 12 2 2
0 .12 9 9
0 .1 2 3 5
0 .0 5 7 3
-
0 . 10 74
3 .0 0
0 .0 0 0 9
0 .0 0 3 0
0 .0 0 89
0 .0 17 4
0 .0 2 2 9
0 .0 2 8 2
0 .0 3 3 3
0 .0 4 0 5
0 .0 5 1 6
0 .0 70 0
0 .0 9 3 3
0 .10 3 8
0 .10 6 0
0 .0 7 3 4
-
0 .0 3 1 2
3 .5 0
0 .0 0 0 7
0 .0 0 2 3
0 .0 0 6 7
0 .0 13 0
0 .0 17 2
0 .0 2 1 1
0 .0 2 4 9
0 .0 3 0 4
0 .0 3 8 8
0 .0 5 3 1
0 .0 72 6
0 .0 8 30
0 .0 8 8 3
0 .0 7 19
4 .0 0
0 .0 0 0 5
5 7 9 1
T a b le
4
V a lu es o f Z (2) fo r c o m p re ss ib ility fa c to r c a lcu la tio n
P r
Tr
0 .0 3 0
0 .4 0
- 0 .0 10 3
- 0 .0 0 8 8
- 0 .0 3 4 1
- 0 . 10 2 6
- 0 .2 0 32
- 0 .2 70 7
- 0 .3 3 7 9
- 0 .4 0 4 7
- 0 .5 0 4 9
- 0 .6 7 10
-
0 .4 5
0 .5 0
- 0 .0 0 7 3
- 0 .0 2 3 7
- 0 .0 7 1 1
- 0 .14 1 1
- 0 .1 8 7 4
- 0 .2 3 3 6
- 0 .2 7 9 8
- 0 .3 4 8 6
- 0 .4 6 2 1
0 .52
- 0 .0 0 6 7
- 0 .0 2 2 4
- 0 .0 6 64
- 0 .1 3 20
- 0 .1 7 5 7
- 0 .2 1 8 9
- 0 .2 6 1 9
- 0 .3 2 6 0
- 0 .4 3 1 9
0 .54
- 0 .0 0 6 2
- 0 .0 2 0 8
- 0 .0 62 5
- 0 . 12 4 0
- 0 . 16 4 8
- 0 .2 0 5 5
- 0 .2 4 59
- 0 .3 0 5 7
0 .5 6
- 0 .0 0 5 8
- 0 .0 1 9 7
- 0 .0 5 8 8
- 0 .1 1 6 8
- 0 .1 5 5 3
- 0 .1 9 3 4
- 0 .2 3 1 2
0 .5 8
- 0 .0 0 5 5
- 0 .0 1 8 6
- 0 .0 5 5 4
- 0 .1 1 0 2
- 0 .14 6 4
- 0 .1 8 2 2
- 0 .2 17 9
0 .6 2
- 0 .0 0 5 2
- 0 .0 0 5 1
- 0 .0 1 7 6
- 0 .0 1 6 8
- 0 .0 5 2 4
- 0 .0 4 9 8
- 0 .10 4 2
- 0 .0 9 8 9
- 0 .1 3 8 5
- 0 .1 3 1 1
- 0 .17 2 1
- 0 .1 6 3 1
0 .64
- 0 . 1 12 1
- 0 .0 1 5 8
- 0 .0 4 74
- 0 .0 9 3 8
- 0 . 12 4 5
- 0 . 15 4 8
0 .6 6
- 0 .0 9 0 7
- 0 .0 1 5 1
- 0 .0 4 5 1
- 0 .0 8 9 5
- 0 .1 18 5
-
- 0 .0 7 3 8
- 0 .0 14 5
- 0 .0 4 3 1
- 0 .0 8 54
- 0 .1 13 1
-
0 .0 13 9
- 0 .0 4 14
- 0 .0 8 18
- 0 .1 0 8 2
- 0 .1 3 4 3
-
-
-
0 .6 0
0 .6 8
0 .7 0
0 .7 2
0 .7 4
0 .7 6
0 .7 8
0 .8 0
0 .8 5
0 .9 0
0 .9 5
1 .0 0
1 .0 5
1 .1 0
1 .1 5
1 .2 0
- 0 .0 6 0 5
- 1 .6 4 6 0
- 2 .2 7 7 3
- 3 .19 8 9
- 6 .0 8 1 3
- 0 .6 8 5 0
-
1.1159
-
1 . 5 30 3
- 2 .1 2 3 3
- 3 .9 0 9 0
- 6 .9 0 0 3
- 0 .6 3 9 4
-
1 .0 3 9 5
-
1 .4 22 4
-
1 .9 6 8 3
- 3 .6 0 0 4
- 6 .3 1 2 8
- 0 .4 0 4 7
- 0 .5 9 8 3
- 0 .9 7 0 4
-
1 . 32 50
-
1 .8 2 8 2
- 3 .3 2 3 4
- 5 .7 9 2 0
- 0 .2 8 7 3
- 0 .3 8 0 0
- 0 .5 6 1 0
- 0 .9 0 7 6
-
1 .2 3 6 2
-
1 .7 0 14
- 3 .0 7 4 5
- 5 .3 2 9 9
- 0 .2 7 0 8
- 0 .3 5 7 7
- 0 .5 2 7 2
- 0 .8 5 0 4
- 1 . 1 55 9
- 1 .5 8 6 3
- 2 .8 5 0 6
- 0 .2 0 5 8
- 0 . 19 4 8
- 0 .2 5 5 5
- 0 .2 4 1 8
- 0 .3 3 7 2
- 0 .4 9 6 3
-
0 .7 9 8 4
- 1 .0 8 2 7
- 1 .4 8 2 1
- 2 .6 4 9 1
- 4 .5 5 5 9
- 0 . 18 9 4
- 0 .2 2 9 3
- 0 .3 0 2 0
- 0 .4 4 2 9
-
0 .7 0 8 1
-
- 1 .3 0 14
-
- 3 .9 4 5 0
0 . 14 7 4
- 0 . 17 5 8
-
- 0 .2 8 6 6
-
0 .4 19 4
-
0 .6 6 8 7
- 0 .9 0 0 4
-
1 .2 2 3 2
- 2 .1 5 8 7
-
- 0 . 14 0 5
- 0 . 16 7 6
- 0 .2 0 7 6
-
0 .2 7 2 8
- 0 .3 9 8 2
-
0 .6 3 2 6
- 0 .8 5 0 0
-
1 .1 5 2 1
- 2 .0 2 6 6
- 3 .4 6 0 6
- 0 .1 6 0 1
- 0 .1 9 8 1
- 0 .2 6 0 0
- 0 .3 7 8 7
- 0 .5 9 9 7
- 0 .8 0 4 0
-
1 .0 8 7 5
-
1 .9 0 7 4
-
-
-
-
0 .2 17 9
1 .0 0 0 0
0 .9 5 5 7
-
l l . 1 80 0
2 .3 0 5 3
3 .6 8 9 1
3 .2 5 6 3
-0 .0 4 9 8
- 0 .0 4 1 1
0 .1 5 8 2
- 0 .0 3 8 3
-
0 . 12 3 6
- 0 . 14 7 1
-
0 .2 3 7 7
- 0 .3 4 4 5
-
0 .9 7 4 8
-
1 .7 0 2 7
- 2 .9 0 9 1
- 0 .0 3 4 1
- 0 .1 2 8 7
- 0 .0 3 7 0
- 0 .0 7 2 8
- 0 .0 9 6 2
- 0 .1 1 9 0
- 0 .14 1 5
- 0 .1 74 6
- 0 .2 2 8 0
- 0 .3 2 9 5
- 0 .5 1 6 6
- 0 .6 8 8 3
- 0 .92 5 8
-
1 .6 14 6
- 2 .7 6 1 0
- 0 .0 2 8 4
- 0 .10 5 4
- 0 .0 3 5 9
- 0 .0 70 5
- 0 .0 9 2 9
- 0 .1 1 4 9
- 0 .1 3 6 5
- 0 .1 6 8 1
- 0 .2 1 9 1
- 0 .3 1 5 8
- 0 .4 9 3 4
- 0 .6 5 6 0
- 0 .8 8 1 0
-
1 .5 34 8
- 2 .6 2 7 4
- 0 .0 2 3 7
- 0 .0 8 6 7
- 0 .0 3 4 9
- 0 .0 6 8 4
- 0 .0 9 0 1
- 0 .1 1 1 2
- 0 .1 3 2 0
- 0 .1 6 2 3
- 0 .2 1 11
- 0 .3 0 3 2
- 0 .4 7 2 0
- 0 .6 2 6 4
- 0 .8 4 0 0
-
1 .4 6 2 2
- 2 .5 0 6 3
- 0 .0 1 5 2
- 0 .0 5 4 2
- 0 .2 1 9 7
- 0 .0 6 5 4
- 0 .0 8 54
- 0 .10 4 7
- 0 .12 3 5
- 0 .1 50 8
- 0 .19 4 4
- 0 .2 7 6 3
- 0 .4 2 5 6
- 0 .5 6 2 3
- 0 .7 5 1 9
-
1 .30 7 5
- 2 .2 4 9 4
- 0 .0 0 9 8
- 0 .0 3 4 2
- 0 .12 3 5
- 0 .0 6 1 9
- 0 .0 79 7
- 0 .0 9 7 0
- 0 .1 1 3 9
- 0 .1 3 8 5
- 0 .1 7 7 7
- 0 .2 5 1 3
- 0 .3 8 5 2
- 0 .50 7 9
- 0 .6 7 8 1
-
1 .1 7 84
- 2 .0 30 6
- 0 .0 0 6 3
- 0 .0 2 1 8
- 0 .0 7 3 9
- 0 .2 10 5
- 0 .0 7 6 0
- 0 .0 9 2 7
- 0 . 10 8 5
-
0 .1 3 3 6
- 0 . 16 1 3
- 0 .2 2 6 7
- 0 .3 4 8 6
- 0 .4 6 0 4
- 0 .6 1 6 1
- 1 .0 7 5 2
- 1 .8 62 0
- 0 .0 0 4 0
- 0 .0 1 3 7
- 0 .0 4 4 8
- 0 . 10 7 3
- 0 . 17 5 4
- 0 .0 8 0 0
- 0 .0 9 1 5
-
0 .1 0 8 5
- 0 . 13 9 9
- 0 .2 0 19
- 0 .3 15 5
-
-
0 .5 6 3 9
- 0 .9 8 9 9
- 1 .7 2 2 6
- 0 .0 0 2 5
-
0 .0 0 8 5
- 0 .0 2 6 8
- 0 .0 5 8 8
- 0 .0 6 2 3
- 0 .0 6 3 5
- 0 .0 6 4 5
- 0 .0 6 50
- 0 .0 7 4 5
- 0 .1 6 1 6
- 0 .2 8 3 9
- 0 .3 8 3 3
- 0 .5 19 2
- 0 .9 18 3
- 1 .0 6 5 6
-0 .0 0 1 5
- 0 .0 0 5 0
- 0 .0 15 4
-
0 .0 3 18
- 0 .0 4 2 5
-
-
- 0 .0 3 6 0
- 0 .0 2 8 9
- 0 .0 8 3 3
- 0 .2 5 0 8
-
0 .3 5 0 1
-
0 .4 8 0 3
- 0 .8 5 7 4
- 1 .5 0 5 9
- 0 .0 0 0 8
- 0 .0 0 2 6
-
-
0 .0 15 7
- 0 .0 2 0 2
- 0 .0 2 2 8
-
- 0 .0 0 4 0
- 0 .0 2 4 6
- 0 .2 13 6
-
0 .3 18 5
-
0 .4 4 5 6
- 0 .8 0 4 8
- 1 .4 19 9
0 .4 14 2
-
- 1 .3 4 4 7
0 .0 0 8 0
0 .0 7 5 5
0 .0 9 9 8
0 .0 5 0 2
0 .0 4 4 4
- 0 .0 2 14
0 .1 8 17
0 .0 13 2
0 .5 4 19
0 .7 2 3 5
0 .4 19 6
ｰ -ｰ
0 -0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
- 0 .1 7 6 0
- 0 .2 8 7 9
-
0 .7 5 8 8
ｰ -ｰ
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
- 0 .0 9 3 2
- 0 .1 6 9 5
- 0 .2 7 7 1
- 0
5671
-
1 0 34 1
0 -0
0 .0
0 .0
0 .0
0 ,0
0 .0
0 .0
0 .0
0 .0
0 .0
- 0 .0 6 5 8
- 0 . 1 18 3
- 0 . 19 12
- 0 .4 0 2 0
-
0
1 .2 5
1 .3 0
1 .3 5
1 .4 0
1 .5 0
1 .6 0
1 .7 0
1 .8 0
1 .9 0
2 .0 0
2 .5 0
3 .0 0
3 .5 0
4 .0 0
758 9
COMPRESSIBILITY
FACTOR OF POLAR SUBSTANCES
BASED ON A FOUR-PARAMETER CORRESPONDING
STATES PRINCIPLE
HIDEO NISHIUMI
Chemical Engineering
Course, Department
Hosei University,
Tokyo 184
DONALDB. ROBINSON
of Mechanical
Department of Chemical Engineering, University
Edmonton, Alberta, Canada T6G 2G6
Engineering,
of Alberta,
A fourth parameter, ¥E, obtained from the second virial coefficients at low reduced temperatures, is proposed to correlate the compressibility
factor Z of polar substances. The value is
expressed in terms of WEand the acentric factor to as:
Z=Z<°>
+o>Z<1>
+VE(ZV
+<uZ<8>)
Tables of Z(0) through Z(3) are presented over the range of reduced temperatures from 0.4 to
4.0 and of reduced pressures from 0.03 to 40.0, using an approximate BWR equation of state.
For fifteen polar substances, the overall average absolute deviations in predicted compressibility
factor for the gaseous and liquid regions are 1.3 and 3.3 %, respectively.
The parameter can be
roughly related to dipole moments, whereas no strong correlations between WEand the Stockmayer potential model parameter is observed.
Introducti
on
1
The corresponding-state
principle
offers an effective means of predicting thermodynamic properties of
substances. Pitzer proposed an acentric factor <w
relating to the shape of a molecule as a third parameter18'.
The three-parameter
corresponding-state
principle has been very successful in correlating the
properties of nonpolar or slightly polar substances.
To extend the acentric factor corresponding-state
principle
to polar substances, an additional
fourth
parameter should be taken into account. Eubank
and Smith31 presented a parameter ^/TeVc relating to
a dipole moment for estimation of thermodynamic
properties
of dilute gases. Halm and Stiel*' defined
a fourth parameter i obtained from a reduced vapor
pressure at Tr=0.6. Based on this parameter, Stipp,
Bai and Stiel20' presented tables of the compressibility
factor for a reduced temperature range from 0.80 to
1.15 and reduced pressures from 0.2 to 6.0.
In a previous paper18', an improved BWRequation
of state for polar substances with three polar parameters was proposed. The objectives of this study
are to present a new fourth parameters, and to utilize
the equation of state to tabulate the compressibility
factor of polar substances over wide temperature and
pressure regions.
Received February 10, 1981
Correspondence
should be addressed to H. Nishiumi.
VOL.
14
NO.4
1981
concerning
this
article
. Fourth Parameter
It is well known
virial coefficients at
this work, a reduced
polarity is defined as:
for PVT Prediction
that polarity
affects the second
low reduced temperatures51.
In
fourth parameter ¥E concerning
v*
B._A.
Tr-BN
Ve
(1)
where
A*
C*
D* _ D*_j5°-___:±-(LJJff
£>0
rp
J,3
Ir
-/r
D*
4__rl°_
1
J.4
-Lr
(2)
B% is the reduced second virial coefficient
for a
normal fluid and the five coefficients with asterisks are
functions of o>19). The value of WE is determined
by
fitting experimental
data of the second virial coefficients B to Eq. (1).
The value, however, may be changeable
due to
scattering
or scarcity of data. To determine a reasonable value of WE, an improved BWR equation of
state10',
including
Eq. (1), was used. Three polar
parameters, WE, st and st, in the equation
of state
were adjusted to obtain the best fit of vapor pressures
and the second virial coefficients161.
Eventually,
the approximation
that sz=5.3 and st=
1.15 WE (approximate equation of state) leads to good
PVT predictions,
as shown in the 7th column of
Table 1. The average deviation of 2.4% is the same
as that for the original
parameters16'.
This means
259
T able 1
C om pressib ility factor predictions ob ta ined by using the approxim ate eq ua tion of state a nd T ables 2 th rough 5
R an ge o f v ariab les
1
/-C 3H 7O H
^
0 .7 3- 1 .16
0 .00- 2 .0 3
v
0 .6 8- 0 .8 5
5 .84- 32 .47
1
so
0 .64- 1 .2 1
0 .00- 3 .94
v
H 20
0 .57- 1 .7 7
0 .00- 1 .72
y
C H C 1F 2
C C 13F
89
* The same numbers as in the previous
** v oasenus nnase. i: nauia
of Compressibility
The compressibility
of written
work18)
Factor
of Polar
factor of a substance Z should
Z=Z*+ZP
(3)
Ztf and Zp represent the compressibility
factors of a
normal fluid and a correction for polar substances,
respectively.
The approximate equation of state without the
fourth parameter WEgives reduced density pr of a
normal fluid at a fixed Tr, Pr and a), and Z* can be
obtained from the definition Z=PrZc/prTr. A correlation for the compressibility
factor at the critical
point Zc of a normal fluid for 0<<o<l is expressed as
Zc=0.2923-0.093«
(4)
For various values of co between 0 and 1 at a fixed
TV, and Pr, the ZN values were found to be correlated
as
Z^=Z(0'+o>Z(1>
(5)
Z(0) and Z(1) are functions of Tr and Pr. Values of
Z(0) and Z(1) are shown in Tables 2 and 3, respectively.
The values around the critical
points are adjusted.
At a fixed TV, Pr, o> and Ws, the Zvalue of a polar
substance can be calculated
using the approximate
260
15
13 ,
8
9
10
1,7
7
7
6, 2 1
9
9
14
14
9
17
I, /
2
2
1
7
1
17, 22
pimsc
that a sinele oolar parameter WEis sufficient for PVT
prediction,
whereas three polar parameters, WSt slt
and sz, are needed for vapor pressure prediction due
to its greater sensitivity.
Values of ¥E for 39 polar
substances were presented in the previous work16'.
2. Correlation
Substances
D ata
sou rce
68
47
32
32
123
37
21
32
32
32
40
32
32
21
78
20
16
82
27
63
29
H CN
76
A v . dev. [% ]
A p pro xim ate
T ables
equ atio n ***
2-5
P oin ts
equation of state in this work. From these values,
Zp is obtained according to Eq. (3). Figure 1 shows
the relationship
between Zp and WEat Tr=Q.6 and
o>=0.2. It reveals that Zp is proportional
to WE up
to 0.3 in WE, where most polar substances are included
with the exception of acetone, hydrogen fluoride and
nitromethane.
As shown in Fig. 2, the relationship
between Zp and o>at Pr=1.60 and ^=0.175 shows
that Zp is linear with (a.
Based on the above results, Zp can be expressed as
Zp=?r£(Z<2'
+a>Z<3>)
(6)
Z(2) and Z(S) should be correlated
in terms of Tr and
Pr. They are shown in Tables 4 and 5. The values
of Z(2) and Z(3) in the region of Tr>\2and
Pr<3.0
can be treated as 0.0, and those around the critical
point are adjusted.
3.
Discussion
3. 1 Normal fluids
Comparison ofZ(0) and Z(1), shown in Tables 2 and
3 respectively,
for a normal fluid, were made with
Pitzer's18',
Lu's12' and Lee-Kesler's tablesll',
as shown
in Table 6. With regard to Z(0), each table shows
similar values of average deviation in comparison with
this work. Compared with Pitzer's18'
and Lu's12'
tables, values of Z(0) in Table 2 are greater over the
0.7<> Tr, 3.0<Pr region, and smaller elsewhere in the
range of Tr and Pr. In comparison with Lee-Kesler's
tablesll',
Z(0> in this work is greater over the region of
0.4<
5.0<Pr,
Tr<0.52,
0.01
<Pr<
and of l.l<^r,
JOURNAL
10.0,and
of0.54<
2.0<Pr,
and smaller
OF CHEMICAL
ENGINEERING
Tr<0.90,
in the
OF JAPAN
<
o
£
V a lu e s o f Z (0) fo r c o m p res sib ility fa c to r ca lc u la tio n
z
T a b le 2
^
p
P r
<o
CO
to.
o.
T r
0 .0 3 0
0 .1 0 0
0 .3 0 0
0 .6 00
0 .8 0 0
0
0
0
0
0
.9 4 3 9
.9 2 16
.9 0 0 8
.8 8 1 5
.8 6 3 5
1 .3 1 10
1 .2 7 9 1
1 .2 4 9 4
1 .2 2 1 7
1 . 19 5 8
1 .8 5 2 4
1 .8 0 5 9
1 .7 6 2 5
1 .7 2 1 9
1 .6 8 3 8
3
3
3
3
3
0
0
0
0
0
.1 4 5 5
.1 3 3 8
.1 2 4 5
.1 2 13
. 1 18 3
0
0
0
0
0
.1 9 3 9
.1 7 8 3
. 16 5 9
. 16 1 6
. 15 7 6
0
0
0
0
0
0
0
0
0
0
.5 6
.5 8
.60
.6 2
.64
0
0
0
0
0
.0 0 5 8
.0 0 5 7
.0 0 5 6
.0 0 5 5
.9 5 9 2
0
0
0
0
0
.0
.0
.0
.0
.0
19 3
18 9
18 5
18 2
17 9
0
0
0
0
0
.0 57 9
.0 5 6 6
.0 5 5 5
.0 5 4 4
.0 5 3 5
0
0
0
0
0
.1 15 6
.1 13 1
.1 10 8
.1 0 8 6
.1 0 6 7
0
0
0
0
0
. 15 4 0
. 15 0 6
. 14 7 5
. 14 4 6
. 14 2 0
0 . 18 8 0
0 . 18 4 1
0 . 18 0 6
0 .2 2 54
0 .2 2 0 7
0 .2 16 4
0 .2 8 1 3
0 .2 7 5 4
0 .2 6 9 9
0 .3 7 4 0
0 .3 6 6 1
0 .3 5 8 8
0 .5 5 8 2
0
0
0
0
0
.6 6
.6 8
.7 0
.7 2
.7 4
0
0
0
0
0
.9 6 30
.9 6 6 3
.9 6 9 2
.9 7 17
.9 7 4 0
0
0
0
0
0
.0 17 6
.0 17 3
.0 17 1
.0 16 9
.9 0 8 9
0
0
0
0
0
.0 5 2 6
.0 5 18
.0 5 1 1
.0 5 0 5
.0 4 9 9
0
0
0
0
0
.1 0 4 9
.1 0 3 3
.1 0 19
.1 0 0 6
.0 9 9 4
0
0
0
0
0
. 13 9 6
. 13 7 5
. 13 5 5
. 13 3 8
. 13 2 2
0
0
0
0
0
. 1 74 3
. 17 15
. 16 9 0
.1 6 6 8
. 16 4 8
0
0
0
0
.2 0 54
.2 0 2 4
.1 9 9 7
. 19 7 3
0
0
0
0
.2 5 6 1
.2 5 2 3
.2 4 8 8
.2 4 5 7
0
0
0
0
.3 4 0 0
.3 3 4 8
.3 3 0 0
.3 2 5 7
0
0
0
0
.50 5 9
.4 9 7 7
.4 9 0 2
.4 8 3 3
0
0
0
0
0
.8 4 6 8
.8 3 1 1
.8 16 6
.8 0 3 1
.7 9 0 6
1 . 17 16
1 . 14 9 0
1 . 12 7 8
1 . 10 80
1 .0 8 94
1 .6 4 8 1
1 .6 14 5
1 .5 8 30
3 . 16 7 1
3 .0 9 6 1
3 .0 2 9 0
0
0
0
0
0
.7 6
.7 8
.8 0
.8 5
.9 0
0
0
0
0
0
.9 7 6 1
.9 7 7 9
.9 7 9 5
.9 8 3 0
.9 8 5 8
0
0
0
0
0
.9 16 5
.9 2 3 2
.9 2 9 1
.9 4 15
.9 5 1 5
0
0
0
0
0
.0 4 9 5
.0 4 9 1
.0 4 8 9
.8 0 3 6
.8 4 1 1
0
0
0
0
0
.0 9 8 5
.0 9 7 7
.0 9 7 1
.0 9 6 6
.0 9 8 7
0
0
0
0
0
. 13 0 9
. 12 9 8
.1 2 8 9
. 12 8 0
. 12 9 9
0
0
0
0
0
.1631
. 16 17
. 16 0 5
. 15 9 1
.1 6 0 6
0
0
0
0
0
.19 52
. 19 34
. 19 19
.1 8 9 8
.1 9 0 8
0
O
0
0
0
.2 4 30
v2 4 0 6
.2 3 8 6
.2 3 5 4
.2 3 5 3
0
0
0
0
0
.3 2 1 8
.3 1 84
.3 1 5 5
.3 10 2
.3 0 8 0
0
0
0
0
0
.4 7 7 0
.4 7 1 3
.4 6 6 2
.4 5 6 1
.4 4 8 7
0
0
0
0
0
.7 7 8 9
.7 6 8 2
.7 5 8 3
.7 3 70
.7 17 6
1 .0 7 2 1
1 .0 5 5 9
1 .0 4 0 8
1 .0 0 74
0 .9 7 4 9
1 .4 9 9 3
1 .4 7 4 6
2 .8 4 8 6
2 .7 9 4 7
0 .9 5
1 .0 0
1 .0 5
1 .10
1 .1 5
0
0
0
0
0
.9 8 7 9
.9 8 9 6
.9 9 10
.9 9 2 2
.9 9 3 2
0
0
0
0
0
.9 5 8 9
.9 6 4 8
.9 6 9 7
.9 7 3 7
.9 7 7 0
0
0
0
0
0
.8 6 7 9
.8 8 87
.9 0 52
.9 18 5
.9 2 9 4
0
0
0
0
0
.6 9 16
.7 5 2 1
.7 9 5 0
.8 2 7 4
.8 5 2 8
0
0
0
0
0
. 13 7 9
.6 3 0 3
.7 0 7 4
.7 5 9 3
.7 9 7 7
0
0
0
0
0
. 1 67 7
.2 9 2 3
.5 9 9 0
.6 8 3 1
.7 3 9 0
0
0
0
0
0
. 19 7 0
.2 15 1
.4 4 9 2
.5 9 6 9
.6 7 6 8
0
0
0
0
0
.2 4 0 3
.2 5 4 5
.3 1 17
.4 6 5 3
.5 8 2 7
0
0
0
0
0
.3 10 8
.3 2 0 4
.3 4 2 4
.3 9 9 6
.4 8 6 1
0
0
0
0
0
.4 4 6 8
.4 50 0
.4 5 9 7
.4 7 8 6
.5 1 1 3
0
0
0
0
0
.7 0 5 5
.6 9 8 1
.6 9 53
.6 9 7 3
.7 0 4 5
0
0
0
0
0
.9 5 2 5
.9 34 9
.9 2 19
.9 13 3
.9 0 9 0
1 .3 0 7 9
2 .4 13 6
1 .2 4 82
1 .2 2 5 8
2 .2 6 0 8
2 . 19 6 8
1
1
1
1
1
.2 0
.2 5
.30
.3 5
.4 0
0
0
0
0
0
.9 9 4 0
.9 9 4 7
.9 9 5 3
.9 9 5 8
.9 9 6 3
0
0
0
0
0
.9 7 9 9
.9 8 2 3
.9 8 4 3
.9 8 6 1
.9 8 7 6
0
0
0
0
0
.9 3 8 4
.9 4 6 1
.9 5 2 5
.9 5 8 0
.9 6 2 8
0
0
0
0
0
.8 7 3 2
.8 9 0 0
.9 0 4 0
.9 1 5 8
.9 2 5 8
0
0
0
0
0
.8 2 7 6
.8 5 16
.8 7 1 3
.8 8 7 6
.9 0 15
0
0
0
0
.7 8 0 4
.8 12 6
.8 3 8 6
.8 5 9 9
0
0
0
0
.7 3 2 0
.7 7 3 5
.8 0 6 2
.8 3 2 7
0
0
0
0
.6 6 0 5
.7 1 6 7
.7 5 9 9
.7 9 4 2
0
0
0
0
.5 7 0 4
.6 4 0 2
.6 9 60
.7 4 0 8
0
0
0
0
.5 5 5 8
.60 4 9
.6 5 30
.6 9 7 6
0
0
0
0
0
.7 17 2
.7 3 52
.7 57 2
.7 8 14
.8 0 6 3
0
0
0
0
0
.9 0 8 7
.9 1 2 3
.9 19 5
.9 2 9 6
.9 4 1 8
1 . 19 3 8
1 . 18 34
1 . 17 6 4
1 .1 7 2 3
1 .1 7 0 8
2 .0 8 8 5
2 .0 4 2 8
2 .0 0 2 0
1 .50
1 .6 0
1 .7 0
1 .8 0
1 .9 0
0
0
0
0
0
.9 9 7 0
.9 9 7 6
.9 9 8 1
.9 9 8 4
.9 9 8 7
0
0
0
0
0
.9 9 0 1
.9 9 2 0
.9 9 3 6
.9 9 4 8
.9 9 5 8
0
0
0
0
0
.9 7 0 5
.9 7 6 4
.9 8 1 1
.9 8 4 8
.9 8 7 7
0
0
0
0
0
.9 4 1 8
.9 54 0
.9 6 3 4
.9 7 0 8
.9 7 6 7
0
0
0
0
0
.9 2 3 3
.9 3 9 7
.9 5 2 4
.9 6 2 2
.9 7 0 1
0
0
0
0
0
.8 0 2 9
.8 5 2 7
.8 9 0 7
.9 2 0 1
.9 4 3 1
0
0
0
0
0
.8 54 3
.8 9 6 6
.9 32 3
.9 6 1 8
.9 8 5 8
0 .9 6 9 5
0 .9 9 7 5
1 .0 2 3 2
1 .0 4 5 8
1 .0 6 4 9
2
2
3
3
4
0
0
1
1
1
.9 9 9 0
.9 9 9 7
.0 0 0 0
.0 0 0 2
.0 0 0 3
0
0
1
1
1
.9 9 6 6
.9 9 9 0
.0 0 0 1
.0 0 0 6
.0 0 0 9
0 .9 9 0 2
0 .9 9 7 4
1 .0 0 0 5
1 .0 0 2 1
1 .0 0 2 8
0
0
1
1
1
.9 8 1 5
.9 9 5 6
.0 0 17
.0 0 4 6
.0 0 6 1
0
0
1
1
1
.9 7 6 5
.9 9 4 9
.0 0 2 8
.0 0 6 6
.0 0 8 4
0 .9 7 2 0
0 .9 9 4 7
0 .9 6 1 5
1
1
1
1
1
.0 0 5 4
.0 6 0 6
.0 8 0 4
.0 8 6 7
.0 8 7 3
1
1
1
1
1
1 .0 10 9
0 .9 6 8 1
0 .9 9 4 8
1 .0 1 3 5
0 .9 6 3 5
0 .9 9 5 7
1 .0 17 8
0 .9 5 8 9
0 .9 9 9 1
1 .0 2 5 6
.7 2 3 7
.6 64 7
.6 1 7 1
.60 0 6
.5 8 5 4
3 .9 2 7 6
3 .8 0 8 9
3 .6 9 8 2
.0 7 2 8
.0 6 7 0
.0 6 2 3
.0 6 0 7
.0 59 2
.8 3 3 3
.8 7 3 5
.9 0 3 6
.9 2 6 6
.9 4 4 6
0
0
0
0
0
2 .0 1 3 1
1 .9 5 5 6
1 .9 0 2 2
0
0
0
0
0
0
0
0
0
0
.4 8 3 4
.4 4 4 3
.4 1 2 9
.4 0 2 0
.3 9 1 9
1 .4 2 1 5
1 .3 8 1 9
1 .3 4 5 1
.0 2 4 3
.0 2 2 3
.0 2 0 8
.0 2 0 3
.0 19 8
.8 6 52
.8 9 6 4
.9 19 9
.9 3 7 9
.9 5 2 1
0
0
0
0
0
1 .6 7 5 1
0
0
0
0
0
0
0
0
0
0
.3 6 3 0
.3 3 3 7
.3 10 2
.3 0 2 1
.2 9 4 6
1 .2 0 12
1 .10 2 0
1 .0 2 1 7
0 .9 9 3 8
0 .9 67 9
.0 0 7 3
.0 0 6 7
.0 0 6 2
.0 0 6 1
.0 0 5 9
.8 8 8 6
.9 13 6
.9 3 2 5
.9 4 7 2
.9 5 8 8
0
0
0
0
0
2 0 .0 0 0
0
0
0
0
0
0
0
0
0
0
.2 9 0 6
.2 6 7 2
.2 4 84
.2 4 2 0
.2 3 6 0
10 .0 0 0
.4 0
.4 5
.50
.5 2
.54
.9 0 5 5
.9 2 6 2
.9 4 2 0
.9 5 4 4
.9 6 4 1
0
0
0
0
0
7 .00 0
0
0
0
0
0
.0 0
.5 0
.0 0
.50
.0 0
.2 4 2 2
.2 2 2 8
.2 0 7 2
.2 0 1 8
. 19 6 8
5 .0 0 0
0 .5 34 9
0
0
0
0
0
1 .0 4 3 6
.0 8 10
.1 2 6 5
.1 4 0 4
.1 4 17
.1 3 7 9
.5 9 4 9
.4 9 8 3
.4 0 7 6
.3 2 2 5
.2 4 2 5
1 .9 3 2 8
1 .1 8 1 5
1 .2 4 16
1 .2 3 2 8
1 .2 2 0 8
1 .5 9 8 2
1 .5 5 1 5
1 .5 1 0 2
4 0 .0 0 0
Table 3 Values of Z(1) for compressibility
TT
0.030
0. 100
0.300
0.600
0. 800
1.000
factor calculation
Pr
1. 500
1.200
2.000
3.000
5.000
7.000
10.000
20.000
40.000
0 .4 0
-
0 .0 0 3 3
-
0 .0 10 8
-
0 .0 3 2 5
-
0 .0 6 4 8
-
0 .0 8 6 3
-
0 . 10 78
-
0 .1 2 9 2
-
0 .1 6 1 2
-
0 .2 1 4 2
-
0 .3 1 9 4
-
0 .5 2 6 2
-
0 .7 2 8 5
-
1 .0 2 4 2
-
1 .9 5 3 8
0 .4 5
-
0 .0 0 3 0
0 .0 0 2 9
-
0 .0 10 1
0 .0 0 9 5
-
0 .0 3 0 4
0 .0 2 8 5
-
0 .0 6 0 6
0 .0 5 6 7
-
0 .0 8 0 6
0 .0 7 5 5
-
0 . 10 0 6
0 .0 9 4 1
-
0 .1 2 0 5
0 . 11 2 7
-
0 .1 5 0 3
0 .1 4 0 5
-
0 .1 9 9 6
0 .1 8 6 4
-
0 .2 9 7 1
0 .2 7 6 9
-
0 .4 8 7 9
0 .4 5 3 1
-
0 .6 7 3 6
0 .6 2 3 7
-
0 .9 4 3 7
0 .8 7 0 2
-
1 .7 8 3 7
1 .6 2 9 8
-
0 .52
-
0 .0 0 2 8
-
0 .0 0 9 3
-
0 .0 2 7 8
-
0 .0 5 5 3
-
0 .0 7 3 6
-
0 .0 0 9 18
-
0 .1 0 9 9
-
0 .1 3 6 9
-
0 .1 8 16
-
0 .2 6 9 5
-
0 .4 4 0 3
-
0 .6 0 5 2
-
0 .8 4 3 1
-
1 .5 7 3 0
-
2 .8 4 7 1
0 .5 4
-
0 .0 0 2 7
-
0 .0 0 9 1
-
0 .0 2 7 1
-
0 .0 5 4 0
-
0 .0 7 1 8
-
0 .0 8 9 6
-
0 .1 0 7 2
-
0 .1 3 3 5
-
0 .1 7 7 0
-
0 .2 6 2 4
-
0 .4 2 8 1
-
0 .5 8 7 6
-
0 .8 1 7 1
-
1 .5 1 8 9
-
2 .7 3 9 7
0 .5 6
-
0 .0 0 2 7
-
0 .0 0 8 9
-
0 .0 2 6 5
-
0 .0 5 2 8
-
0 .0 7 0 2
-
0 .0 8 7 5
-
0 .1 0 4 7
-
0 .1 3 0 3
-
0 .1 7 2 6
-
0 .2 5 5 7
-
0 .4 1 6 4
-
0 .5 70 7
-
0 .7 9 2 3
-
1 .4 6 7 5
0 .5 8
-
0 .0 0 2 6
-
0 .0 0 8 7
-
0 .0 2 5 9
-
0 .0 5 1 6
-
0 .0 6 8 6
-
0 .0 8 5 5
-
0 .10 2 3
-
0 .12 7 3
-
0 .16 8 5
-
0 .2 4 9 3
-
0 .4 0 5 3
-
0 .5 54 7
-
0 .7 6 8 7
-
1 .4 1 8 6
0 .6 0
-
0 .0 0 2 6
-
0 .0 0 8 5
-
0 .0 2 5 4
-
0 .0 5 0 5
-
0 .0 6 7 1
-
0 .0 8 3 6
-
0 .10 0 0
-
0 .1 24 4
-
0 .1 64 6
-
0 .2 4 3 3
-
0 . 39 4 7
-
0 .5 39 4
-
0 .74 6 1
-
1 .3 7 2 0
-
2 .4 5 1 3
0 .6 2
-
0 .0 0 2 5
-
0 .00 8 3
-
0 .0 2 4 9
-
0 .0 4 9 5
0 .6 4
-
0 .0 3 3 4
-
0 .0 0 8 2
-
0 .0 2 4 4
-
0 .0 4 8 5
-
0 .0 6 4 5
-
0 .0 8 0 3
-
0 .0 9 5 9
-
0 . 1 19 2
-
0 . 1 5 7 5
-
0 .2 3 2 2
-
0 .37 5 0
-
0 .5 10 8
-
0 .7 0 3 9
-
1 .2 8 5 3
0 .6 6
-
0 .50
0 .6 8
3 .2 7 2 3
2 .9 6 0 6
0 .0 2 8 1
-
0 .0 0 8 0
-
0 .0 2 4 0
-
0 .0 4 7 7
-
0 .0 6 3 3
-
0 .0 7 8 7
-
0 .0 9 4 1
-
0 .1 16 9
-
0 .1 5 4 3
-
0 .2 2 7 0
-
0 .3 6 5 9
-
0 .4 9 7 4
-
0 .6 8 4 2
-
1 .2 4 5 1
-
2 .2 0 7 4
- 0 .0 2 3 7
-
0 .0 0 7 9
-
0 .0 2 3 6
-
0 .0 4 69
-
0 .0 6 2 2
-
0 .0 7 7 3
-
0 .0 9 2 4
-
0 .1 14 6
-
0 .1 5 12
-
0 .2 2 2 1
-
0 .3 5 7 1
-
0 .4 8 4 6
-
0 .6 6 5 3
-
1 .2 0 6 6
-
2 .1 3 4 4
-
0 .0 9 0 7
-
0 .1 1 2 6
-
0 .1 4 8 3
-
0 .2 17 5
-
0 .3 4 8 7
-
0 .4 7 2 3
-
0 .6 4 7 1
-
1 .1 6 9 9
-
2 .0 6 5 3
0 .2 0 8 7
-
0 .3 3 2 7
-
0 .4 4 8 9
-
0 .6 1 2 7
-
1 .1 0 1 1
-
1 .9 3 7 0
0 .7 0
-
0 .0 2 0 0
-
0 .0 0 7 8
-
0 .0 2 3 3
-
0 .0 4 6 1
-
0 .0 6 1 1
-
0 .0 7 6 0
0 .7 2
-
0 .0 1 6 9
-
0 .0 0 7 7
-
0 .0 2 2 9
-
0 .0 4 5 4
-
0 .0 6 0 2
-
0 .0 7 4 8
0 .7 4
-
0 .0 14 3
-
0 .0 5 64
-
0 .0 2 2 6
-
0 .0 4 4 8
-
0 .0 5 9 3
-
0 .0 7 3 7
-
0 .0 8 7 8
-
0 .10 8 8
-
0 .1 4 2 9
-
-0 .0 12 0
-
0 .0 4 6 6
-
0 .0 2 2 4
-
0 .0 4 4 2
-
0 .0 5 8 5
-
0 .0 7 2 6
-
0 .0 8 6 5
-
0 .1 0 7 0
-
0 .1 4 0 4
-
0 .2 0 4 6
-
0 .3 2 5 1
-
0 .4 3 7 7
-
0 .5 9 6 3
-
1 .0 6 8 7
-
1 .8 7 7 4
0 .7 8
-
0 .0 10 1
-
0 .0 3 8 5
-
0 .0 2 2 2
-
0 .0 4 3 7
-
0 .0 5 7 8
-
0 .0 7 1 6
-
0 .0 8 5 3
-
0 .1 0 5 4
-
0 .1 3 8 0
-
0 .2 0 0 6
-
0 .3 1 7 6
-
0 .4 2 6 8
-
0 .5 8 0 4
-
1 .0 3 7 6
-
1 .8 2 0 6
0 .8 0
-
0 .0 0 8 5
-
0 .0 3 1 7
-
0 .0 2 2 0
-
0 .0 4 3 3
-
0 .0 5 7 1
-
0 .0 7 0 7
-
0 .0 8 4 1
-
0 .1 0 3 8
-
0 .1 3 5 6
-
0 .1 9 6 6
-
0 .3 1 0 3
-
0 .4 1 6 1
-
0 .5 6 4 9
-
1 .0 0 7 7
-
1 .7 6 6 5
-0 .0 0 5 3
-
0 .0 19 2
-
0 .0 8 6 3
-
0 .0 4 2 3
-
0 .0 5 5 6
-
0 .0 6 8 6
-
0 .0 8 1 3
-
0 .0 9 9 8
-
0 .1 2 9 7
-
0 .1 8 6 6
-
0 .2 9 1 9
-
0 .3 8 9 9
-
0 .5 2 7 4
-
0 .9 3 7 3
-
1 .6 4 1 2
-
0 .0 12 9
-
0 .0 4 9 1
-
0 .0 4 2 6
-
0 .0 5 4 9
-
0 .0 6 6 7
-
0 .0 7 8 1
-
0 .0 9 4 6
-
0 .1 20 8
-
0 .1 6 9 6
-
0 .2 5 8 4
-
0 .3 3 9 5
-
0 .4 5 1 9
-
0 .7 7 8 9
-
1 .3 2 2 3
0 .7 6
0 .8 5
0 .9 0
-
0 .0 0 3 6
0 .9 5
-
0 .0 0 18
-
0 .0 0 6 5
-
0 .0 2 3 0
-
0 .0 7 5 1
-
0 .0 4 7 9
-
0 .0 5 9 2
-
0 .0 6 9 8
-
0 .0 8 5 1
-
0 .10 9 3
-
0 .1 5 4 4
-
0 .2 3 6 6
-
0 .3 1 1 8
-
0 .4 1 6 2
-
0 .7 2 0 7
-
1 .2 2 8 0
1 .0 0
-
0 .0 0 0 6
-
0 .0 0 2 0
-
0 .0 0 6 7
-
0 .0 1 7 1
-
0 .0 3 0 8
-
0 .0 9 3 0
-
0 .0 3 2 0
-
0 .0 3 9 0
-
0 .0 7 9 2
-
0 .1 2 9 6
-
0 .2 1 0 3
-
0 .2 8 2 0
-
0 .3 80 5
-
0 .6 6 6 6
-
1 .14 3 0
-
-
0 .9 9 50
1 .0 5
0 .0 0 0 3
0 .0 0 1 1
0 .0 0 3 9
0 .0 1 0 7
0 .0 1 9 4
0 .0 3 8 2
0 .10 0 1
0 . 12 9 4
1 . 10
0 .0 0 10
0 .0 0 3 3
0 .0 1 1 0
0 .0 2 6 5
0 .0 4 1 4
0 .0 6 3 0
0 .0 9 6 0
0 . 15 6 1
0 . 1 19 6
0 .0 0 8 7
-
0 .1 3 3 2
-
0 .2 10 7
-
0 .3 0 6 1
-
0 .5 67 6
1 . 1 5
0 .0 0 14
0 .0 0 4 8
0 .0 1 5 7
0 .0 3 6 0
0 .0 5 3 2
0 .0 7 4 8
0 .10 1 6
0 . 14 7 8
0 . 1 6 5 5
0 .0 6 8 1
-
0 .0 8 0 3
-
0 .16 7 7
-
0 .2 6 6 4
-
0 .5 2 1 5
1 .2 0
0 .0 0 18
0 .0 0 5 9
0 .0 1 8 8
0 .0 4 1 7
0 .0 5 9 8
0 .0 8 0 7
0 .10 4 5
0 . 14 2 8
0 . 18 0 1
0 . 12 1 6
-
0 .0 2 4 0
-
0 . 12 12
-
0 .2 2 52
-
0 .4 7 7 3
-
0 .8 6 9 4
1 .2 5
0 .0 0 2 0
0 .0 0 6 6
0 .0 2 0 9
0 .0 4 5 1
0 .0 6 3 4
0 .0 8 3 5
0 .10 52
0 . 13 8 9
0 . 18 0 3
0 . 15 5 5
0 .0 2 7 6
-
0 .0 7 8 3
-
0 . 18 3 1
-
0 .4 3 4 6
-
0 .8 13 2
1 .3 0
0 .0 0 2 1
0 .0 0 7 1
0 .0 2 2 1
0 .0 4 6 9
0 .0 6 5 0
0 .0 8 4 3
0 . 10 4 5
0 .1 3 4 9
0 . 17 5 8
0 . 17 5 8
0 .0 6 9 7
-
0 .0 2 9 0
-
0 . 14 14
-
0 .3 9 3 4
-
0 .7 6 0 5
1 .3 5
0 .0 0 2 2
0 .0 0 7 4
0 .0 2 2 8
0 .0 4 7 7
0 .0 6 5 4
0 .0 8 3 9
0 .10 2 8
0 . 13 0 9
0 . 17 0 0
0 . 18 62
0 . 10 2 2
0 .0 10 7
-
0 . 10 14
- 0 .3 5 3 7
-
0 .7 1 1 1
1 .4 0
0 .0 0 2 2
1 .50
0 .0 0 2 2
0 .0 0 7 5
0 .0 2 2 8
0 .0 4 6 6
0 .0 6 2 7
0 .0 7 8 9
0 .0 9 4 9
0 .1 1 8 0
0 .1 5 1 5
0 .1 8 6 4
0 .1 5 6 5
0 .0 9 3 4
-
0 .0 0 1 5
-
0 .2 4 4 7
-
0
1 .60
0 .0 0 2 2
1 .7 0
0 .0 0 2 1
0 .0 0 7 0
0 .0 2 0 9
0 .0 4 19
0 .0 5 5 7
0 .0 6 9 3
0 .0 8 2 5
0 .1 0 1 3
0 .1 2 9 0
0 .1 6 5 9
0 .1 7 34
0 .14 1 2
0 .0 7 7 4
-
0 .1 2 7 6
-
0 .4 3 4 1
1 .8 0
1 .9 0
0 .0 0 2 0
0 .0 0 1 9
0 .0 0 6 2
0 .0 1 8 5
0 .0 3 6 7
0 .0 4 8 4
0 .0 5 9 9
0 .0 7 1 0
0 .0 8 6 7
0 .1 1 0 0
0 .14 4 0
0 . 16 5 9
0 . 1 5 3 1
0 .1 1 3 0
-
0 .0 4 5 6
-
0 .3 18 3
2 .0 0
2 .5 0
0 .0 0 1 8
0 .0 0 1 2
0 .0 0 4 1
0 .0 12 3
0 .0 2 4 0
0 .0 3 16
0 .0 3 8 9
0 .0 4 6 0
0 .0 5 5 9
0 .0 7 1 0
0 .0 9 5 1
0 . 12 2 2
0 .12 9 9
0 .1 2 3 5
0 .0 5 7 3
-
0 . 10 74
3 .0 0
0 .0 0 0 9
0 .0 0 3 0
0 .0 0 89
0 .0 17 4
0 .0 2 2 9
0 .0 2 8 2
0 .0 3 3 3
0 .0 4 0 5
0 .0 5 1 6
0 .0 70 0
0 .0 9 3 3
0 .10 3 8
0 .10 6 0
0 .0 7 3 4
-
0 .0 3 1 2
3 .5 0
0 .0 0 0 7
0 .0 0 2 3
0 .0 0 6 7
0 .0 13 0
0 .0 17 2
0 .0 2 1 1
0 .0 2 4 9
0 .0 3 0 4
0 .0 3 8 8
0 .0 5 3 1
0 .0 72 6
0 .0 8 30
0 .0 8 8 3
0 .0 7 19
4 .0 0
0 .0 0 0 5
5 7 9 1
T a b le
4
V a lu es o f Z (2) fo r c o m p re ss ib ility fa c to r c a lcu la tio n
P r
Tr
0 .0 3 0
0 .4 0
- 0 .0 10 3
- 0 .0 0 8 8
- 0 .0 3 4 1
- 0 . 10 2 6
- 0 .2 0 32
- 0 .2 70 7
- 0 .3 3 7 9
- 0 .4 0 4 7
- 0 .5 0 4 9
- 0 .6 7 10
-
0 .4 5
0 .5 0
- 0 .0 0 7 3
- 0 .0 2 3 7
- 0 .0 7 1 1
- 0 .14 1 1
- 0 .1 8 7 4
- 0 .2 3 3 6
- 0 .2 7 9 8
- 0 .3 4 8 6
- 0 .4 6 2 1
0 .52
- 0 .0 0 6 7
- 0 .0 2 2 4
- 0 .0 6 64
- 0 .1 3 20
- 0 .1 7 5 7
- 0 .2 1 8 9
- 0 .2 6 1 9
- 0 .3 2 6 0
- 0 .4 3 1 9
0 .54
- 0 .0 0 6 2
- 0 .0 2 0 8
- 0 .0 62 5
- 0 . 12 4 0
- 0 . 16 4 8
- 0 .2 0 5 5
- 0 .2 4 59
- 0 .3 0 5 7
0 .5 6
- 0 .0 0 5 8
- 0 .0 1 9 7
- 0 .0 5 8 8
- 0 .1 1 6 8
- 0 .1 5 5 3
- 0 .1 9 3 4
- 0 .2 3 1 2
0 .5 8
- 0 .0 0 5 5
- 0 .0 1 8 6
- 0 .0 5 5 4
- 0 .1 1 0 2
- 0 .14 6 4
- 0 .1 8 2 2
- 0 .2 17 9
0 .6 2
- 0 .0 0 5 2
- 0 .0 0 5 1
- 0 .0 1 7 6
- 0 .0 1 6 8
- 0 .0 5 2 4
- 0 .0 4 9 8
- 0 .10 4 2
- 0 .0 9 8 9
- 0 .1 3 8 5
- 0 .1 3 1 1
- 0 .17 2 1
- 0 .1 6 3 1
0 .64
- 0 . 1 12 1
- 0 .0 1 5 8
- 0 .0 4 74
- 0 .0 9 3 8
- 0 . 12 4 5
- 0 . 15 4 8
0 .6 6
- 0 .0 9 0 7
- 0 .0 1 5 1
- 0 .0 4 5 1
- 0 .0 8 9 5
- 0 .1 18 5
-
- 0 .0 7 3 8
- 0 .0 14 5
- 0 .0 4 3 1
- 0 .0 8 54
- 0 .1 13 1
-
0 .0 13 9
- 0 .0 4 14
- 0 .0 8 18
- 0 .1 0 8 2
- 0 .1 3 4 3
-
-
-
0 .6 0
0 .6 8
0 .7 0
0 .7 2
0 .7 4
0 .7 6
0 .7 8
0 .8 0
0 .8 5
0 .9 0
0 .9 5
1 .0 0
1 .0 5
1 .1 0
1 .1 5
1 .2 0
- 0 .0 6 0 5
- 1 .6 4 6 0
- 2 .2 7 7 3
- 3 .19 8 9
- 6 .0 8 1 3
- 0 .6 8 5 0
-
1.1159
-
1 . 5 30 3
- 2 .1 2 3 3
- 3 .9 0 9 0
- 6 .9 0 0 3
- 0 .6 3 9 4
-
1 .0 3 9 5
-
1 .4 22 4
-
1 .9 6 8 3
- 3 .6 0 0 4
- 6 .3 1 2 8
- 0 .4 0 4 7
- 0 .5 9 8 3
- 0 .9 7 0 4
-
1 . 32 50
-
1 .8 2 8 2
- 3 .3 2 3 4
- 5 .7 9 2 0
- 0 .2 8 7 3
- 0 .3 8 0 0
- 0 .5 6 1 0
- 0 .9 0 7 6
-
1 .2 3 6 2
-
1 .7 0 14
- 3 .0 7 4 5
- 5 .3 2 9 9
- 0 .2 7 0 8
- 0 .3 5 7 7
- 0 .5 2 7 2
- 0 .8 5 0 4
- 1 . 1 55 9
- 1 .5 8 6 3
- 2 .8 5 0 6
- 0 .2 0 5 8
- 0 . 19 4 8
- 0 .2 5 5 5
- 0 .2 4 1 8
- 0 .3 3 7 2
- 0 .4 9 6 3
-
0 .7 9 8 4
- 1 .0 8 2 7
- 1 .4 8 2 1
- 2 .6 4 9 1
- 4 .5 5 5 9
- 0 . 18 9 4
- 0 .2 2 9 3
- 0 .3 0 2 0
- 0 .4 4 2 9
-
0 .7 0 8 1
-
- 1 .3 0 14
-
- 3 .9 4 5 0
0 . 14 7 4
- 0 . 17 5 8
-
- 0 .2 8 6 6
-
0 .4 19 4
-
0 .6 6 8 7
- 0 .9 0 0 4
-
1 .2 2 3 2
- 2 .1 5 8 7
-
- 0 . 14 0 5
- 0 . 16 7 6
- 0 .2 0 7 6
-
0 .2 7 2 8
- 0 .3 9 8 2
-
0 .6 3 2 6
- 0 .8 5 0 0
-
1 .1 5 2 1
- 2 .0 2 6 6
- 3 .4 6 0 6
- 0 .1 6 0 1
- 0 .1 9 8 1
- 0 .2 6 0 0
- 0 .3 7 8 7
- 0 .5 9 9 7
- 0 .8 0 4 0
-
1 .0 8 7 5
-
1 .9 0 7 4
-
-
-
-
0 .2 17 9
1 .0 0 0 0
0 .9 5 5 7
-
l l . 1 80 0
2 .3 0 5 3
3 .6 8 9 1
3 .2 5 6 3
-0 .0 4 9 8
- 0 .0 4 1 1
0 .1 5 8 2
- 0 .0 3 8 3
-
0 . 12 3 6
- 0 . 14 7 1
-
0 .2 3 7 7
- 0 .3 4 4 5
-
0 .9 7 4 8
-
1 .7 0 2 7
- 2 .9 0 9 1
- 0 .0 3 4 1
- 0 .1 2 8 7
- 0 .0 3 7 0
- 0 .0 7 2 8
- 0 .0 9 6 2
- 0 .1 1 9 0
- 0 .14 1 5
- 0 .1 74 6
- 0 .2 2 8 0
- 0 .3 2 9 5
- 0 .5 1 6 6
- 0 .6 8 8 3
- 0 .92 5 8
-
1 .6 14 6
- 2 .7 6 1 0
- 0 .0 2 8 4
- 0 .10 5 4
- 0 .0 3 5 9
- 0 .0 70 5
- 0 .0 9 2 9
- 0 .1 1 4 9
- 0 .1 3 6 5
- 0 .1 6 8 1
- 0 .2 1 9 1
- 0 .3 1 5 8
- 0 .4 9 3 4
- 0 .6 5 6 0
- 0 .8 8 1 0
-
1 .5 34 8
- 2 .6 2 7 4
- 0 .0 2 3 7
- 0 .0 8 6 7
- 0 .0 3 4 9
- 0 .0 6 8 4
- 0 .0 9 0 1
- 0 .1 1 1 2
- 0 .1 3 2 0
- 0 .1 6 2 3
- 0 .2 1 11
- 0 .3 0 3 2
- 0 .4 7 2 0
- 0 .6 2 6 4
- 0 .8 4 0 0
-
1 .4 6 2 2
- 2 .5 0 6 3
- 0 .0 1 5 2
- 0 .0 5 4 2
- 0 .2 1 9 7
- 0 .0 6 5 4
- 0 .0 8 54
- 0 .10 4 7
- 0 .12 3 5
- 0 .1 50 8
- 0 .19 4 4
- 0 .2 7 6 3
- 0 .4 2 5 6
- 0 .5 6 2 3
- 0 .7 5 1 9
-
1 .30 7 5
- 2 .2 4 9 4
- 0 .0 0 9 8
- 0 .0 3 4 2
- 0 .12 3 5
- 0 .0 6 1 9
- 0 .0 79 7
- 0 .0 9 7 0
- 0 .1 1 3 9
- 0 .1 3 8 5
- 0 .1 7 7 7
- 0 .2 5 1 3
- 0 .3 8 5 2
- 0 .50 7 9
- 0 .6 7 8 1
-
1 .1 7 84
- 2 .0 30 6
- 0 .0 0 6 3
- 0 .0 2 1 8
- 0 .0 7 3 9
- 0 .2 10 5
- 0 .0 7 6 0
- 0 .0 9 2 7
- 0 . 10 8 5
-
0 .1 3 3 6
- 0 . 16 1 3
- 0 .2 2 6 7
- 0 .3 4 8 6
- 0 .4 6 0 4
- 0 .6 1 6 1
- 1 .0 7 5 2
- 1 .8 62 0
- 0 .0 0 4 0
- 0 .0 1 3 7
- 0 .0 4 4 8
- 0 . 10 7 3
- 0 . 17 5 4
- 0 .0 8 0 0
- 0 .0 9 1 5
-
0 .1 0 8 5
- 0 . 13 9 9
- 0 .2 0 19
- 0 .3 15 5
-
-
0 .5 6 3 9
- 0 .9 8 9 9
- 1 .7 2 2 6
- 0 .0 0 2 5
-
0 .0 0 8 5
- 0 .0 2 6 8
- 0 .0 5 8 8
- 0 .0 6 2 3
- 0 .0 6 3 5
- 0 .0 6 4 5
- 0 .0 6 50
- 0 .0 7 4 5
- 0 .1 6 1 6
- 0 .2 8 3 9
- 0 .3 8 3 3
- 0 .5 19 2
- 0 .9 18 3
- 1 .0 6 5 6
-0 .0 0 1 5
- 0 .0 0 5 0
- 0 .0 15 4
-
0 .0 3 18
- 0 .0 4 2 5
-
-
- 0 .0 3 6 0
- 0 .0 2 8 9
- 0 .0 8 3 3
- 0 .2 5 0 8
-
0 .3 5 0 1
-
0 .4 8 0 3
- 0 .8 5 7 4
- 1 .5 0 5 9
- 0 .0 0 0 8
- 0 .0 0 2 6
-
-
0 .0 15 7
- 0 .0 2 0 2
- 0 .0 2 2 8
-
- 0 .0 0 4 0
- 0 .0 2 4 6
- 0 .2 13 6
-
0 .3 18 5
-
0 .4 4 5 6
- 0 .8 0 4 8
- 1 .4 19 9
0 .4 14 2
-
- 1 .3 4 4 7
0 .0 0 8 0
0 .0 7 5 5
0 .0 9 9 8
0 .0 5 0 2
0 .0 4 4 4
- 0 .0 2 14
0 .1 8 17
0 .0 13 2
0 .5 4 19
0 .7 2 3 5
0 .4 19 6
ｰ -ｰ
0 -0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
- 0 .1 7 6 0
- 0 .2 8 7 9
-
0 .7 5 8 8
ｰ -ｰ
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
- 0 .0 9 3 2
- 0 .1 6 9 5
- 0 .2 7 7 1
- 0
5671
-
1 0 34 1
0 -0
0 .0
0 .0
0 .0
0 ,0
0 .0
0 .0
0 .0
0 .0
0 .0
- 0 .0 6 5 8
- 0 . 1 18 3
- 0 . 19 12
- 0 .4 0 2 0
-
0
1 .2 5
1 .3 0
1 .3 5
1 .4 0
1 .5 0
1 .6 0
1 .7 0
1 .8 0
1 .9 0
2 .0 0
2 .5 0
3 .0 0
3 .5 0
4 .0 0
758 9
Table 5
T
r
0
.030
0
.100
0
.300
0
.600
0
Values of Z(3) for compressibility
1
.800
.000
1.200
Pr
1.500
factor calculation
2
.000
3.000
5
7
.000
10.000
.000
000
40.000
0 .4 0
0 .0 0 6 9
0 .0 2 3 9
0 .0 7 4 8
0 .1 4 6 6
1 .1 9 6 0
0 .2 4 4 4
0 .2 9 2 3
0 .3 6 3 9
0 .4 8 2 9
0 .7 1 5 7
1 . 16 54
0 .4 5
0 .0 0 6 3
0 .0 2 0 6
0 .0 6 1 6
0 .1 2 3 1
0 .1 6 2 9
0 .2 0 3 1
0 .2 4 2 8
0 .3 0 1 1
0 .3 9 8 6
0 . 5 8 8 5
0 .9 5 0 6
0 .5 0
0 .0 0 5 2
0 .0 1 7 1
0 .0 5 2 2
0 .1 0 3 0
0 .1 3 6 2
0 .0 0 4 5
0 .0 1 6 4
0 .0 4 8 4
0 .0 9 6 0
0 .1 2 7 8
0 .2 0 2 5
0 .1 8 9 9
0 .2 5 2 2
0 .2 3 5 1
0 .3 3 3 0
0 .30 9 7
0 .4 8 8 4
0 .5 2
0 .1 6 9 6
0 .1 5 8 9
0 .4 5 3 2
0 .7 7 8 7
0 .7 2 0 2
0 .9 6 5 4
1 .2 9 6 6
2 .1 7 6 1
3 .3 2 6 3
0 .5 4
0 .0 0 4 4
0 .0 1 5 2
0 .0 4 5 8
0 .0 9 0 1
0 .1 1 9 3
0 .1 4 8 6
0 .1 7 7 6
0 .2 1 9 4
0 .2 8 9 0
0 .4 2 1 9
0 .6 6 7 2
0 .8 8 9 9
1 .1 8 7 3
1 .9 6 2 4
2 .9 4 4 7
0 .5 6
0 .0 0 3 9
0 .0 1 4 5
0 .0 4 3 0
0 .0 8 4 9
0 .1 1 2 7
0 .1 3 9 6
0 .1 6 6 5
0 .2 0 5 6
0 .2 7 0 0
0 .3 9 2 7
0 .6 1 7 7
0 .8 1 9 5
1 .0 8 7 5
1 .7 7 0 1
2 .60 7 0
0 .5 8
0 .0 0 3 8
0 .0 13 6
0 .0 4 0 4
0 .0 7 9 7
0 .1 0 5 8
0 .1 3 1 0
0 .1 5 6 2
0 .19 32
0 .2 5 2 8
0 .3 6 6 3
0 .5 7 2 6
0 .7 5 5 8
0 .6 0
0 .0 0 3 7
0 .0 12 8
0 .0 3 8 0
0 .0 7 5 2
0 .0 9 9 6
0 .1 2 3 1
0 .1 4 6 9
0 .1 8 1 1
0 .2 3 6 7
0 .34 2 0
0 .5 3 1 2
0 .6 9 7 5
0 .9 1 3 3
1 .4 4 0 3
2 .0 4 7 0
0 .6 2
0 .0 0 3 8
0 .0 1 2 2
0 .0 3 6 2
0 .0 7 1 4
0 .0 9 3 8
0 .1 1 6 5
0 .1 3 8 3
0 .1 70 6
0 .2 2 2 2
0 .3 1 9 9
0 .4 9 3 6
0 .6 4 4 1
0 .8 3 7 5
1 .3 0 0 7
1 .8 1 6 5
0 .6 4
0 .0 6 3 6
0 .0 1 14
0 .0 3 4 4
0 .0 6 7 2
0 .0 8 8 9
0 .1 0 9 9
0 .1 3 0 8
0 .1 6 0 8
0 .2 0 9 3
0 .3 0 0 2
0 .4 5 9 3
0 .5 9 5 9
0 .7 6 8 8
1 .1 7 5 4
1 .6 1 3 4
0 .6 6
0 .0 5 38
0 .0 10 9
0 .0 3 2 6
0 .0 6 4 2
0 .0 8 4 6
0 .1 0 4 6
0 .1 2 4 0
0 .1 5 2 2
0 .1 9 7 4
0 .2 8 1 5
0 .4 2 8 0
0 .5 5 1 3
0 .70 6 2
1 .0 6 3 2
1 .4 3 5 4
0 .6 8
0 .0 4 56
0 .0 10 6
0 .0 3 12
0 .0 6 14
0 .0 8 0 6
0 .0 9 9 4
0 .1 1 7 9
0 .14 4 6
0 .1 8 7 0
0 .2 6 5 1
0 .39 9 1
0 .7 0
0 .0 3 8 9
0 .0 10 1
0 .0 3 0 1
0 .0 5 8 8
0 .0 7 7 2
0 .0 9 5 0
0 .1 1 2 4
0 .1 3 7 7
0 . 1 7 7 5
0 .2 5 0 2
0 .3 7 3 3
0 .4 7 4 8
0 .5 9 9 0
0 .8 7 2 8
0 .7 2
0 .0 3 3 2
0 .0 0 9 9
0 .0 2 9 1
0 .0 5 6 6
0 .0 7 4 2
0 .0 9 12
0 .1 0 7 8
0 .1 3 1 5
0 .1 6 9 2
0 .2 3 6 8
0 .3 5 0 0
0 .4 4 1 9
0 .5 5 2 8
0 .7 9 2 6
1 .0 1 8 3
0 .7 4
0 .0 2 8 5
0 .0 9 9 6
0 .0 2 8 3
0 .0 5 4 9
0 .0 7 2 0
0 .0 8 8 1
0 .1 0 3 9
0 .12 6 5
0 .1 6 1 8
0 .2 2 5 1
0 .3 2 9 0
0 .4 1 2 2
0 .5 1 1 2
0 .7 2 1 2
0 .9 1 1 1
0 .7 6
0 .0 2 4 5
0 .0 8 6 1
0 .0 2 7 7
0 .0 5 3 8
0 .0 7 0 2
0 .0 8 5 8
0 .1 0 1 0
0 .12 2 5
0 .1 5 6 0
0 .2 1 4 9
0 .3 1 0 4
0 . 3 8 5 5
0 .4 7 3 9
0 .6 5 7 2
0 .8 1 6 1
0 .7 8
0 .0 2 12
0 .0 7 4 4
0 .0 2 7 8
0 .0 5 3 3
0 .0 6 9 3
0 .0 8 4 5
0 .0 9 8 9
0 .1 19 6
0 .1 5 1 3
0 .2 0 6 5
0 .29 4 2
0 .3 6 2 0
0 .4 4 0 4
0 .60 0 0
0 .7 3 2 0
0 .8 0
0 .0 1 8 3
0 .0 6 4 3
0 .0 2 8 1
0 .0 5 2 3
0 .0 6 7 6
0 .0 8 4 2
0 .0 9 8 3
0 .1 1 8 1
0 . 14 8 4
0 .2 0 0 0
0 .2 8 0 2
0 .3 4 1 1
0 .4 1 0 6
0 .54 8 9
0 .6 5 7 8
0 .8 5
0 .0 12 9
0 .1 5 17
0 .0 5 1 3
0 .0 6 5 0
0 .0 8 2 0
0 .0 9 5 5
0 .1 1 3 2
0 . 1 39 0
0 .19 4 6
0 .2 5 5 9
0 .30 0 4
0 .34 9 9
0 .4 4 3 5
0 .5 0 6 2
0 .9 0
0 .0 0 9 0
0 .0 4 4 9
0 .0 3 0 7
0 .0 9 9 4
0 .0 4 8 2
0 .0 6 1 0
0 .0 7 8 0
0 .0 9 1 5
0 .10 8 3
0 . 13 1 5
0 . 1 8 90
0 .2 3 8 2
0 .2 6 74
0 .2 9 7 1
0 .3 4 0 1
0 .3 2 9 6
0 .9 5
0 .0 0 64
0 .0 2 1 8
0 .0 3 4 0
0 .1 5 0 2
0 .0 5 4 7
0 .0 7 15
0 .0 8 3 0
0 .10 20
0 .12 3 8
0 .1 84 0
0 .2 2 7 4
0 .2 3 8 9
0 .2 5 3 0
0 .2 6 9 3
0 .2 3 5 2
1 .0 0
0 .0 0 4 5
0 .0 2 5 5
0 .0 3 7 1
0 .0 7 2 0
0 .0 9 1 7
0 .1 1 2 0
0 .1 7 6 5
0 .2 1 7 6
0 .2 2 4 8
0 .2 2 1 9
0 .2 1 5 5
0 .1 6 64
0 .0 0 3 2
0 .0 18 5
0 .0 2 8 5
0 .0 4 5 3
0 .0 3 0 0
0 .0 6 0 0
1 .0 5
0 .0 1 5 5
0 .0 1 0 9
0 .0 4 10
0 .0 5 4 0
0 .0 7 5 5
0 .0 9 5 0
0 .1 6 7 5
0 .20 8 5
0 .2 2 3 4
0 .2 0 1 6
0 .1 74 8
0 . 1 14 7
1 .1 0
0 .0 0 2 3
0 .0 0 7 6
0 .0 1 1 5
0 .0 1 9 0
0 .0 2 15
0 .0 2 3 0
0 .0 2 8 5
0 .0 4 3 5
0 .0 7 1 0
0 .1 5 3 5
0 .19 8 5
0 .2 30 0
0 .1 8 9 4
0 .14 4 0
0 .0 7 5 3
1 .1 5
0 .0 0 1 6
0 .0 0 5 2
0 .0 0 65
0 .0 0 9 5
o .o n
0 .0 1 2 0
0 .0 1 3 0
0 .0 1 6 5
0 .0 2 1 0
0 .1 2 5 0
0 .1 8 7 0
0 .2 2 8 1
0 .1 8 1 9
0 .12 0 7
0 .0 4 54
1 .2 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .1 7 4 2
0 .2 2 6 2
0 .1 7 5 9
0 .10 3 3
0 .0 2 2 6
1 .2 5
1 .3 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .1 5 6 6
0 .2 0 0 1
0 .1 6 7 6
0 .0 9 0 1
0 .0 0 5 3
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0 9 1 6
0 .1 6 2 0
0 .1 5 4 8
0 .0 8 0 0
- 0 .0 0 7 7
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
1 .3 5
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0 5 0 0
-
0 .0 1 7 5
1 .4 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0 2 6 5
-
0 .0 2 4 6
1 .50
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0 0 5 7
0 .0 3 9 7
0 .0 7 5 7
0 .0 5 3 4
1 .6 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
-
0 .0 0 4 7
0 .0 1 5 0
0 .0 4 2 3
0 .0 4 1 1
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
1 .7 0
0 .0
0 .0
0 .0
-
0 .0 1 3 2
0 .0 0 0 6
0 .0 1 8 8
0 .0 2 8 0
1 .80
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0 2 0 4
-
0 .0 0 9 3
0 .0 0 2 7
0 .0 1 4 4
-
0 .0 4 2 6
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
-
0 .0
0 .0
0 .0
0 .0
1 .9 0
0 .0
0 .0
0 .0
-
0 .0 2 6 2
-
0 .0 1 7 1
-
0 .0 0 8 8
0 .0 0 1 5
-
0 .0 4 4 8
2 .0 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
-
0 .0 3 0 6
-
0 .0 2 3 3
-
0 .0 1 7 5
-
0 .0 1 0 4
-
0 .0 4 7 4
2 .5 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
-
0 .0 3 9 2
-
0 .0 3 9 3
-
0 .0 4 0 1
-
0 .0 4 8 2
-
0 .0 6 8 1
3 .0 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
-
0 .0 3 8 1
-
0 .0 4 2 2
-
0 .0 4 6 9
-
0 .0 6 2 8
- 0 .0 8 7 1
3 .5 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
-
0 .0 3 4 8
-
0 .0 4 0 7
-
0 .0 4 7 4
-
0 .0 6 7 3
-
0 .0 9 7 3
4 .0 0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
0 .0
-
0 .0 3 13
-
0 .0 3 7 9
-
0 .0 4 5 7
-
0 .0 6 7 5
-
0 .1 0 1 1
o
1 .5 9 6 0
20.
2 .2 0 8 3
6 .8 5 8 1
5 .0 8 9 4
3 .7 5 8 8
2 .3 0 8 8
1 .2 7 8 1
1 .1 3 9 9
-
0 .0 3 3 7
- 0 .0 3 8 3
- 0 .0 4 0 8
remainingregionofTrandPr.
WithregardtoZ(1),thevaluesinTable3aresmaller
thanthoseinPitzer's18'andLu's12'tablesinthe
regionsof0.7<rr<1.2,2.0<Pr,andof2.0<Tr,
0.01</V>andgreaterotherwise.Comparisonwith
Lee-Kesler'stablell'showsthatZ(1)valuesinTable3
aregreaterintheregionsof0.66<rr<0.9,Pr<0.2
and0.95<7;<1.20,Pr<3.0,andsmallerelsewhere
intheotherTrandPrrange.
TheabovecomparsionshowsthatTables2and3
inthisworkseemtohavecomparableprecisionwith
thatofothertablesll-12-18'foranormalfluid.
3.2Polarsubstances
AveragedeviationsofZvaluesobtainedfrom
Tables2through5for15polarsubstancesarelisted
inTable1.Thistableshowsthatdeviationsinthis
workarecomparabletothosefromtheimproved
equationofstate16'orapproximateequationofstate
inthiswork.Overallaveragedeviationsforgaseous
andliquidphaseare1.3and3.3%,respectively.
Table7forNH3at75°Cindicatesthatthecontributionofpolarityinliquidphaseisgreaterthanin
vaporphase,andthatnegativeZpseemstoresult
fromattractivecontributionduetoadipolemoment.
3.3CorrelationofWE
ThefourthparameterWErelatingpolaritywas
foundtoberoughlycorrelatedtoadipolemomentp
inapreviouspaper19',
0 .20
0.1
0.2
0.3
0.4
0.5
0.6
^E
Fig. 1 Relation
and o>=0.2
-0.02
N
between
Zp and WE at TV=0.6
between
Zp and to at Pr=1.60
h
-0.04h
WE=2.^f^lTcVc(7)
For53polarsubstances,whicharecheckedbyvapor
phaseprediction,arelisted16'.
ArelationshipbetweenW'
Eandthepolarparameter
/j,z/eazoftheStockmeyerpotentialmodel5'istobe
expected.Nostrongcorrelation,however,wasobserved.Themainreasonisthatthereisnoobvious
quantitativerelationbetweenTcand£andbetweenVc
andcr3forpolarsubstances.
-0.06
f-
-0.08
Fig. 2 Relation
and WE=0.175
Table 6 Comparison of PVT tables for a normal fluid
Conclusion
Thethreepolarparameterspreviouslyusedinan
improvedBWRequationofstate16'havebeensuccessfullyreplacedbyasinglenewparameter,WE
definedbyEq.(1)forPVTprediction.Thevalueis
obtainedfromthesecondvirialcoefficientdataatlow
reducedtemperatures,andcheckedbyvaporpressure
predictionsusingtheequationofstate16'.
ThecompressibilityfactorZforapolarsubstance
aswellasanormalfluidisexpressedas
Z=Z(0'+wZ(1'+F£(Z(2'+wZ(3>)(8)
ThevaluesofZ(0)throughZ(3)areshowninTables
2through5overtheregionof0.4<rr<4.0and
0.03<Pr<40.0.OveralldeviationsinPVTpredictionfor15polarsubstancesare1.3%inthegaseous
VOL.14
NO.4
1981
Tr
0 .8 - 4 .0
0 .5 - 0 .7
0 .4 - 4 .0
Pr
0 .2 - 5 .0
0 .2 - 5 .0
0 .2 - 5 .0
No. of
points
Av. dev.
Z<°> * Z<« **
[%]
References
36
1 .5
0 .0 5 0 0
P itze r e t a /.18>
15
56
1 .1
1 .1
0 .0 17 7
0 .0 3 8 7
L u et a W
L e e -K e sle rll'
* {(Z<°> in Table 2-Z<°> in reference)/(Z<°>
in Table 2)} x 100
at a fixed Tr and Pr
** (Z(1> in Table 3-Za> in reference) at a fixed Tr and Pr
phase and 3.3% in the liquid phase. These tables
provide a useful prediction method for PVT properties
for both normal fluids and polar substances over a
wide temperature and pressure region for engineering
calculations.
265
Table
7 Contribution
of polarity
for NH/> at 75°C (Tr=0.858)
Z from Tables 2 through
p
[a tm l
P r
10
20
0 .0 9
0 .1 8
30
50
10 0
200
400
z j z ^ p
7 (0)
7 (D
7 ( 2)
7 (3 )
- .0 4 4 1
.0 3 7 3
.9 4 6 0
-
0 .2 7
0 .4 4
0 .89
-
.0
.2
.0
.0
.0 7
.1 5
.0 5
.0 9
.8 8 6 5
.8 1 9 3
.0 6 4 2
- 3 .6
- 1 3 .4
1 .7 8
3 .5 6
- .1157
- .2 1 4 6
-
.1 7 3 5
.3 14 7
5
2
1
1
9 73
110
50 1
939
ular
Z(1),
Z(2>, Z(3)
= contribution
factor expressed
Z
Z
of compressibility
pointin t
y
in Eq. (8)
of compressibility
[- ]
factor of)f
v
= contribution
.,
=contribution of compressibility
factor of>f aa
polar substance expressed in Eq. (3)
a normal fluid expressed
]
in Eq. (3)
I
]
parameter of.Stockmayer potential
m
odel
[erg]
dipole moment
[Debye]
reduced molar density
[ ]
parameter of Stockmayer potential model [cm]
.fourth paramenter proposed by Halm and
Stiel
[_]
fourth parameter in this work defined
by Eq. (1)
[_]
Pitzer's acentric factor
f 1
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Cited
L. N. and F. S. Manning:
.0 5 7 4
.1 1 2 6
.2 1 8 4
.4 1 7 9
phase,
1: liquid
phase
5.
and Reduced Correlation
for Gases", Gulf Publish-
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factor at the critical
2 through
.9 4 2 0
.8 7 2 9
.7 9 2 5
- 1 3 .3
- 1 3 .2
b> v: vapor
erties
Nomen
clature
= compressibility
.
.1 2 6 6
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.4 8 0 0
O .i
7J
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Hirschfelder,
J. O., C. F. Curtiss
and R. B. Bird:
"Molec-
Munetake Motono, who assisted
in Eq. (2)
[-]
second virial coefficient
[cm3/mol]
reduced second virial coefficient for a
normal fluid
]
reduced pressure
]
critical temperautre
K ]
reduced temperature
I
critical molar volume
[cm r/m o ll
compressibility
factor
]
5
4
0
8
. 14 5 6
.2 14 2
atm, Fc=72.5 cm3/mol, (u=0.250,
2^=0.2116,
ofpolarityZp=ZK&l
ZN
factor calculated
from Eq. (8) using Tables
The authors acknowledge
with some of the calculations.
9
0
8
3
D ev.
7
2
2
7
1
3
8
3
6
Ackn owledgment
Z(0),
x 10 0
c>
- .0
- .0
- .0
- .0
Some polar substances, such as methanol or ethanol,
however, could not be fitted by a single polar parameter WE. These substances may be classified
as
another kind of polar substance.
c
7
- .0 1 5 4
a) rc=405.6
K, />c=112.5
c> Eq. (5),
d> Contribution
e) Zcal is the compressibility
Z
5
P h a se b>
24(2),
417
(1974).
Keller,
R. M., Jr. and L. I. Stiel:
241 (1977).
9
Kumagai,
A. and H. Iwasaki:
10
idem: ibid., 24, 261 (1979).
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C. Hsi and
13)
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15
/.
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19)
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at Nagoya,
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OF JAPAN