Title
Author(s)
Citation
Issue Date
URL
Thermodynamic properties of gaseous propane and propene
Watanabe, Koichi; Uematsu, Masahiko; Saegusa, Shogo
The Review of Physical Chemistry of Japan (1976), 46(1): 3953
1976-06-30
http://hdl.handle.net/2433/47027
Right
Type
Textversion
Departmental Bulletin Paper
publisher
Kyoto University
The
THE
REVIGw OF PHYSICAL CttEHlaraY
THERMODYNAMIC
PROPERTIES
By Kotcxt
Of
Review
of Physical
Chemistry
of Japan
Vol. 46 No.
OF JAPAN, VOL. 46, No. 1, 197fi
GASEOUS
PROPANE
39
AND PROPENE
W-ATANAHE. MAS.4HrK0 UEMATSU AND SHOGU SAEGVSA
Based upon the most probable and additional raommended values with respect to
the compressibility factor of propane and propene proposed by the High Pressure Data
Center of Japan (I3PDCJ), new thermodynamic formu]ations are devised for these substances in their gaseous phases covering the range of temperature from 273.15 K to 523,15
K and pressures up to 30 \IPa for propane and also [hat of temperature from 248.15 K to
498.ISK a¢d pressures up to 60 JfPa for propene, respativeh•.
Using the formulated
equations of state, the basic correlating iunctians for these hydrocarbons are derived and
then the essential thermodynamic properties such as molar volume, enthalpy, entropy
and isobaric specific heat capacity tan be calcu]ated.
Introduction
Accordingto the Criticalevaluation of the availableP-V-T property data, the most probable and
additional recommendedcompressibilityfactor values far propane and propene were proposed by Date
and hvasakit>after the discussionsat [he HPDCJ organizedin the Society of MaterialsScience, Japan,
under the sponsorshipof the Agency of Scienceand Technology. The covered range of the stale parameters of this previous work was 248.15-548.15Kand pressures up to 30MYa for propane, whereas
248.15-498.15K and pressures up to bObfPa for propene. As a next procedure of the programof the
HPDCJ, new equations of state [or both propane and propene are formulated based upon these most
probablecompressibilityfactor values for the purpose of calculatingthe P-V-T property values as well
as other thermodynamicproperty values at respective thermodynamic states. In the present paper,
these new equations of state which can cover the range of temperatures 273.15-523.15K and of pressures up [0 30MPa for propane. and also that of temperature 248.15-498.15Ii and of pressures up to
bOMPa for propene are described. Jforeover, the numerical tables of the important derived thermodynamic property values are also presented for these two difrerent hydrocarbons.
New
The so-called
skeleton
of Sfafe
table values of the compressibility
composed of the most probable
covering
Equations
and additional
recommended
ranges are shown in Figs. 1 and 2, respectively.
factor for propane
values proposed
and propene
are
by the HPDCJ and their
It is needless to say that these skeleton table
(Received Ayril 5, 1976)
f) K. Date and H. Iwasaki, TGfs lonrnal, 44, 1 (1974)
2) A. P. Kudchadker, G. H. Alani and B. J. Zwolinski, Chern. Rev., 68 , 659 (1968)
1
(1976)
The
40
F.
Review
\I. L'ematsu
watanabe,
of Physical
Chemistry
of Japan
Vol. 46 No.
1
and S. Saegusa
values are accompanied by the estimated uncertainties as in the previous skeleton tables for methaneal,
ethane and ethene•+l. In the present study, both of the most probable and additional recommended
values were used as the basic data sets in devising the new equations of state; in addition to using the
estimated uncertainties mentioned above as the criteria for judging the devised equations.
As shown in Fig. 1, the skeleton table of compressibility factor for propane includes those even in
the liquid phase and therefore those data below 373.15 K were excluded [o be covered by the present
formulation beforehand. ICis also noteworthy that the present equations of state have to be formulated
as a tunction of density and temperature, since they must cover suth wider ranges of [he state para-
- -
1.0~
c
,,,~b-tip
~5otiti5
~D?
~
_~
C
~.~--;•
a
'
y
~~
N
O
L_1.
0.5
N
a
C.P.
C3Hg
00
Fig.
O
r`I
5
N
N
J
10
p, mo4dm s
1 The most probable and additional recommended<ompressibility factor values for propane
~ most probable values
Q additional recommendedvalues
Q critical point (369.8211,4.250ibIPa,4.92mo1•dm3)~)
1.5
0=ea
ny
C3 H6
Fig.
.50
n
.44
a
c 1.0
r:
N
-ao
~1t
ooy _
y~~
~~
J~
1
as
2
The most probable and additional
recommended compressibility factor values for propene
~ most probable values
Q additional recommended values
0 critical point (36i.OK, 4.62 b1Fa,
5.54 mo]•dm-s) ~)
zo
•iowPa
i
!~.
0
5
10
P, mo4dm's
3) J. Osugi, P. Takewki and T. lfaki[a, Tiiit Journal, 41, 60 (1971)
4) R. Date, K 1Vatana6e and Nt. Uematsu, ibid., 43, 92 (1973)
(1976)
n
The
Review
of Physical
Chemistry
of Japan
Vol. 46 No.
Thermodynamic Properties of Gaseous Propane and Propene
41
meters as shown in Figs. 1 and 2. Although it is well known that the BenediU-W ebb-Robin (BR'R)
equation of state may correlate the P-V-T properties of simple hydrocarbons, it was experienced is
Table 1 Numerical constants in Eqs. (1) and (2) For propane and propene
Propane
61
-4
fia
fi3
fib
.090
9899 x 102
6.221
3928 x ]0=
-4
.269
6.987
~~
-6.741
2.527
Qb
Propene
1.770
6253 x 10+
Oli
0
.407
2709 x 106
ulB
0
5700 x 1010
419
-2
0632 x (016 -1.982
3817 x 1015
t!p
-
6069 x (021 -8.976
3010 x 1019
2012 x 1026
5.317
8693 x I D2a
0
9835 x 1011
fi3
-Z.18i
i 931 x (035
fiB
-1.294
8332 x 105
6g
3.186
fi10
0
-4
-1
2.815
-IS67
4256 x 106
Qal
8.302
6178
O22
0
aR3
0
4088 x I0~
Oat
3.341
9911 x 105
.064
7194 x 108
3220 x 106
QRS
.SOi
1735 x 1011
aas
-7
.422
0764 x 1011
azi
5824 x 108
Y
1.944
1961 x 1011
cl
3.6fi3 65
2383 x 1016
ca
2.547
file
1.i 28
3452 x 107
fi13
2.448
3052 x 101°
fil{
1.020
5948 x 1015
filb
3.160
9572
x L022
-4.218
4990 x 1072
~3
filfi
1.451
4779
x 1012
-4297
6459 x 1012
cq
2.321
-1.61
LIiO
i
Propene
-1
x lots
i349x
.458
LOtB
4748 x !0+
x 108
4l
x 10-a
-5.7i8
13
x 10-$
-3.047
05
x 10.8
[actor
values
1.138 5003
-].417 9285
0
0
1.0488404
0
2:4790640
3.20914
4.72483
2.714 90
-2 .328 43
for
\umber
of
data points
Compared
Average
deviatioa#
(q)
Skeleton table values[)
Sage et a7. (1934)m)
Beanie et al. (1937)trt
Deschner et al. (1940)%%~
Lv (I940)ta)
Reamer e/ al. (1949)s~)
Cherney et al. (1946ps1
178
0.092
i6
0.944
87
0.163
147
O.i00
164
0.133
15
0.359
Skeleton table valuestl
Farrivgton et ad. (1949)trt
1larchmaa et af, (1949)tr)
167
O.Oii
194
0.121
202
O.i1S
il4ichels e! al. (1953)tet
190
o.0ia
data
sources
_xa
Colculated by the expression given helow:
a(e)~31(Zr.y-Z~„l)/Zr,~l
x lOte
x IOts
9060 x IOu
~ 2.140
2.5602341
-2.976 8160
3929 x lOta
6.923
2 Average deviations of the-rompressibility
propane and propene from Eq. (I)
Available
Propane
x IOto
2512 x lOi+
3560 x 1013
Table
3613
LS48
.190
all
.782
-4
Propeoe
4.937 6880
-1 .821 7334
-1
7.109
i
Propane
x100
not
x lots
x lOte
x 10~r
x ]OTa
x lots
x la
x lOt
r. 10-~
x 30'+
x l0-%
1
(1976)
The
R. Natanabe,
42
Table
3-I
Calculated
their
values
wI. Uematsu
273.15
(O1
0.1
with the skeleton
323.15
(507
0.97948
0.5
the
373.15
(751
(1007
0.051/0.040
0 .028/0,040
0.006/0.040
east
1st
line
skeleton
2nd
line
calculated
3rd
line
deviation
deviation
348.15
0 .049/0.090
x0.9398
1
I•
and
0 .98392
-0 .265/0.35
----+
Z of gaseous propane
0.99204
.91433
probable
value,
.9987
0 .99851
10.082/0.25
0 .020/0.20
~0.8599
X0.85913
0.8927
.89262
10.069/0.25
_...1
0 .009/0.30
Z
Z
0.99198
-
0
values
(i)/uncertainty
(8)=[(ZST
0
10.93403
value, 28T
table
46 No. 1 (1976)
values
0 .99028
0 .99000
0
I
~____J
Vol.
0.98787
0.98737
0 .9119
r
of Japan
K (°C)
(251
0 .98440
-0.035/0.040
9
factor
table
298.15
0.97913
Chemistry
and 5. Saegusa
Temperature
MPa
3
of Physical
of compressibility
comparison
Pressure
2
Review
I
0
1
0 .75956
`0.
7565
903/0.50
.....y
_
0.9591
0.95911
-0.001/0.15
~
0.9140
I
0.91599
I
-0 .217/0.35
~
0.82069
1
-0.151/0.50
1
I
I 0.7057
I 0.70516
cal
(8)
ca1)/Zcal)X100
~
0 8194
I
I
I 0.077/0.30 I
I
I
~ 0.5380
I
10.53599
~
L 0.375/0 _30 ~
our precious works>that several additionalterms were required [o the originalBNR equationin order
to cover wider range of the present interest.
Hence; after several possibleadditional terms had been tested taking into considerationthe.possibility for obtaininga commonfunctional form for both substances,the followingfunctionalform which
was developed from the original BWRequation was adopted for the present purpose:
P=RT p+(a~Tt az+as/Tz+ a,/T°+a;/Ts+as/Ts+a; /Tsz)pz
+(aeT+ ay+aso/T+aaa/T")pa+(avT+aaa+aia/Tz+ais/ Ts)P'
+{azs+aia/T t a:slTz=assl Ta)Ps+(ass+as /T+ azs/Tz+azslTa)Ps
+(azaT+¢zs+¢ze/Tz+a.,/T')p°(1+7Pt)eXP (-TPz)~
(I)
where P=pressure is MPa. T=temperature in K, T=(+273.15, t=temperature in 'C on IPTS-bg,
p=molar density in mobcm ', R=molar gas constantin J•K'' mol'', and a,; az,•••,azr;T=numerical
constants.
The followingvalues were adapted as the atomic weights recommendedby Ili PACsIas well as
the molar gas constant recommended by CODATA7~:
C= 12.011 ±0.001 ,
i) AI.Uematsu,S Saegusa,R. R'atanabeandL Tanishita,ThisJournal,45, 53(I97i)
6) Pareanddppl.Chem.,37, i89(1914)
7) CODAT.9
Ball.,~\"o.
I t (1973)
The Review of Physical Chemistry of Japan Vol. 46
Tpermodynamic
Properties of Gaseous Propaae and Propeoe
Ta61e 3-2
TEI[~P2YdGUIE
Pressure
MPa
O.1
0.5
1
398.15
1125)
0,99339
0.99348
-0 .009/0
923.15
(150)
.040
_---
x0.9672
10.96699
10.022/0
10 .9328
.10
~0.93286
.10
2
3
4
~ 0.007/0
10:8623
10.86049
10.211/0 .10
I
10,7826
10.78069
10.244/0 .10
~0.6894
0.68956
5
6
498.15
0.99691
0.99688
0.003/0.040
0.99 620
0.99 629
-0 00 9/0.090
0.9727
~0.97300
-0.031/0.10
0.9773
0.97770
-0.041/0.10
0. 98 13
0 .98 144
-o .ol 4/0.10
0.9451
0.99549
-0.041/0.10
0.9550
0.95521
-0.022/0.10
0.8893
BB867
O.
0.071/0.10
0.9096
0.90965
-0 ,006/0.10
0.8299
o.ez9oz
0.106/0.10
0.8629
0.86327
-0.093/0.10
o. ss a9
0.96 288
0.00 2/D. 10
OL 92 57
0.92 582
-0 .01 3/0.15
0.88
0.88
0.02
91
891
2/0.15
(225)
523.15
(250)
0.99757
0.99737
0.020/0.040
-_~
0.9845
0.98445
0.005/0.10
I 0.9667
I 0.98692
I-0.022/0.15
0.9693
0.96903
~ 0.9713
1 0.97402
0.9389
0.93858
0.039/0.15
I 0,9484
I 0.94881
I-O.Oa_3/0,15
0.9097
0.90876
0.104/0.151
~ 0.9240
I 0.92447
L -0.051/0.15
______
0.9015
- ~
0.90111
i
0.028/0.10
i-0.279/0.15
.15
0.85 27
D. BS 227
O. DS 1/0.15
0.8611
0.87970
0.159/0 .ls
10 .5799
~ 0.57959
10 .054/0 I ,30
0.6973
0.69864
-0.192/0.10
0.7680
0.76817
-0 .022/0,10
0.81 60
0.81 611
-0 .01 4/D, 15
O.B521
0.05157
0.062/0 .ls
0.8784
0.87684
-0.050/0.151
10.4479
I D, 44589
10.338/0
.30
L . - - -
0.6258
0.62763
-0.292/0.20
0.7198
0.72010
-0 .042/0.15
0.6567
0.85780
-0.129/0.201
0.3726
i 0.37102
10.426/0
10 .3920
I o.zz2/o
10.4138
10 .41422
~-0.100/0
12
473.15
!2001
0.8161
0.81607
0.004/0.10
~0.39113
11
(°C)
0.99539
0.99555
-0.016/0.040
10.4372
10.43874
~-0.351/0
1
I
,05 0/0.15
67
690
7/0.15
0.7985
0.79909
-0,074/0
.15
0.6375
0.83817
-0.060/0.201
1
1
0.6284
0.63026
-0 .295/0.40
0.71
0.71
0.08
60
540
9/0.15
0.7753
0.77547
-0 .021/0 .15
0.6206
0.82015
1
I
0.5995
0.59557
-D.lao/o.zs
0.68
0.68
0.12
85
762
8/0.10
0.7542
0.75425
-0.007/0
.20
0.5740
o,s7z7s
0.213/0.15
0.66
0.66
0.14
61
513
5/0.10
0.7364
0.73607
0.044/0 .15
0.7903
0.78992
1
1
0.5646
0.5627.4
0.421/0.15
0.65
0.64
0.35
15
920
5/0.10
0.7211
0.72156
-0.063/0
.15
0.5632
0.56153
0.297/0.20
0.64
0.69
0.34
24
022
0/0.25
0.7107
0.71117
-0 .066/0 .15
0.63
0.63
0.01
78
769
8/0.35
0.7046
0.70511
-0 .072/0 .25
0.63 94
0.69 050
-0 .17 1/0.20
0.7023
0.70323
-0.133/0
.15
10.9635
10.46403
~-0 .113/0
0.5670
0.56775
-0 .131/0.20
14
10.4893
10.48972
0.5785
0.57861
-0 .020/0.15
L 0.086/0
1
1
0.79
0.74
-0.02
13
0.78 04
O,7B 079
0.049/0.15
0.8244
0.82960
-0.029/0
.15
8
10
K
0.99448
0.99464
-0.016/0.040
0.6726
0.67320
-0.089/0:20
9
(continued)
448.15
(1751
7
1 (1976)
33
0.7663
0.76589
0.054/0.10
-0 .026/0
No
-0
D.055/0.20
0.6048 i
0.60398
D.103/0.25
0.048/0.25
0.7783
1
0.77826
~
D. 005/0.151
1
0.7669
1
0.76926
1
-0 .045/0.151
0.7625
0.76308
-D. 077/0.20
r-----I 0.7596
1 0.75981
I
~
~ -0.027/0.20
The
Review
of Physical
Chemistry
of Japan
Vol. 46 No.
1
(1976)
K. Watanabe, bi. Uematsu and S. Saegusa
44
Table 3-3
398.15
lYe a
923.15
11251
-
~0 . 5157
~0
17
. 51563
0.64
]4B
O 5909
0.6265
0.6702
0.590]2
0.65.632
0.6]006
0.030/0.30
0.029/0.10
0.021/0.10
0.6131
0.6451
0.6449]
0.6846
0.68426
0. ]286
0.61366
10.5942
10.59376
1 D. 7]30
0.77917
-0.152/0.50
0.]1868
-0.094/0.
D.
I0
.76617
20~-0.700/0,20
I
1
]2903
0.020/0.25
0.078/0.
0.6992
o.7aos
I
o.7eza
0.6]642
0.6643]
0.69977
D. 73970
I
0.78134
0.6843
3s
0.7]678
0.106/0.401
tnc
1st
tine
skeleton
2nd
line
calculated
3rd
line
deviation
mst
0.78833
-0.067/0.25
probable
table
value,
o.emz
0.8309
D. BO]04
0.93@]
D.DZO/o.zo
Z
(4)/uncertainty
o.oe2/o.
_.._._~
0.084/0.20
ZST
0
1
0
zol
I
I
201
1 0.9179
10.91]28
valves
valve,
0.75277
0.142/0.
-0.039/0.20
1
0.7578
0.71626
-0.069/0.20
D.767e
/
i
0.121/0.201
D.715d
0.68431
-0.00?/0.30
r o.n72-~
r---"
L ____~
-0.081/0.20
-0.040/0.10
151
0_]]26
0.]7286
0.6641
0.65959
-0.150/o.
I
1
0.71]6
151 -0,0]9/0.20
1
I 0.7607
I 0.76157
20I -0.114/0.20
1 0 7654
0.021/0.10
0.6586
.69568
0.7102]
-0.193/0.
0.7588
0 .75936
0.6355
-0 .145/0.35
.6466
0.]069
0.69760
-0.096/0.30
-0.0.7/0.30
-0 .055/0.35
.20
:0.6205
0.65]3
0.608]2
0.138/0.25
1
0.70514
-0 .218/0.
10 .5680
10
.56]]0
10
0.6[85
0.56861
12501
0.7016
-0 .198/0.25
-0.039/0.10
i0.191/0.95
30
0.6962
0.59260
0:2]3/0.20
523.15
1225]
0.5692
10
25
_ _0.5924
0.54671
10.6197-0
10.123/0.30
20
_
498.15
(2001
1 0.5q 1]
10.54165
10.009/0.20
10:0]8/0
19
4]3.15
(1]51
0.5482
0.051/0.20
18
448.15
(150)
_
0.013/0.30
16
K 1°C1
Temperature
Pressure
15
(continued)
`0_068/0 _1J
.793]
.791331
o.zzn/D.zD
0.8558
0.8562]
-0.055/0.20
I
I
I
cal
(U:
deviation
143 =I/25T
Z
eal)/Zea11K100
H= 1.00790.0001 ,
R= 8.31441-r0.0002G
J•K-'mot-'.
In the procedureof determining the numericalconstants in Eq. (1), the skeletontable values were
introduced as a set of input daza into aleast-square processingand the characteristicbehavior of the
computed isobaricspecificheat capacity values were also carefully examined. Especially,the reported
experimental values by Biet ei a/.e>for propene in the range of temperature 298.11K-473.15K and
pressures up [0 12MPa were taken into considerationfor the present purpose. As a result of these
procedures,the numericalcon_~tan[s
for both propane and propene in Eq. Q) were fixed on as listed in
Table 1.
In caseqCcomputingthe isobaric specificheat capacity, the followingtorrelations for the isobaric
specificheat capacity at [he ideal gas state. C °; devised by Maki[asl were used:
Cp =c,+csTtcsT~+csTa.
(2 )
The numericalconstanu which appeared in Eq. (2) are also tabulated for both propane and propene
8) I{. Bier,G.Ernst, J, Kunzeand G.htaurer,!. Chem.TLermadynarnics,
6. 1039(19)4)
9) T. Makitn,privatecommunicationto the presentauthor
6
1
The
Review
of Physical
Chemistry
of Japan
Vol. 46 No.
1
(1976)
i
I
Thermodynamic
Properties
of Gauous-Propane
and P ropenc
45
I
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The
K. Watanabe,
4fi
hf. Uematsu
Table
4-]
398.15
15
3E
lJ
lP
19
26
Mk
30
35
49
(3501
r 0.4496 1 0:999]6
4)3.11
1200)
D.6J98
0. 5E252
-0.124/0.15
o. slez
0.51825
-0.009/0.16
o.se3o
0.583]6
-0.130/0.1$
0.6552
0.65511
0.019/0:10
0.]204
0.]2001
0.064/0.1
0.5301
0.534:]
-0.069/0.10
0.591
0.59132
-o. ozo/o.ls
0.6560
O.fi5591
D.ala/D.lo
0.]1]5
0.]1]66
-D.azs/41s1
D.svJ
0.5]]23
0.090/0.20
0.5523
O.6s229
0.003/0.15
0.6029
o: soma
0.063/0.16
O.E6Di
O.E6O39
0.031/0.30
O.Jll6
0.]Laz3
408)/0.1
0.5404
O. s4029
o.ozD/o. zo
D.ss33
0 .56394
-G.GZa/D.zG
O.Sr1J
O.5J116
a.osc/a.zo
0.6158
D.6li01
0.129/0.30
O.E5>0
D.[6]31
0.]205
0.]2133
-0.!15/0.15
0.59E
0.540)6
D.DSJ/o.za
0.6309
O.s2965
0.319/0.30
os]s]
D.6T6J0
0.000/0.10
0.]266
O.J266]
-0.009/O.ls1
I 0.s0G3
1 0.56662
1-o.osc/o.zG
1 o. s6s4
I 0.60990
I •o: ass/o,2o
I
~ G.]zs1
I O.J249J
I 0.010/0.15
I 0.8382
1 0.81829
1-0.013/0.15
I 0
.9999 1
0.99939
1
o.izsz_-1
O.J2s9s j
o. soaz
0.30410
1
I
1
I
1
I
1
1
'
Vol. 46 No.
)98.13
(3251
j-o.o3s/0.35-o. o5s/o.1o
1 0.4]18 '
0.9]1]9 I
1 0.002/0.20
' (1.9999
' OA993i
' u . uo/o.2s I
of Japan
1°cl
448.15
I1J51
423.15
11251
Chemistry
S. Saegusa
x
2aepetahre
MPa
la
and
of Physical
(continued)
4vazsu[a
13
Review
Dsua
0.61086
0.023/0.x0
o. s9ss
0.6;552
-0 .003/0.
0.6312
Os333D
-o_ols/0.20
0.6594
0.65645
-0.009/0.10
xc
o. GS2o
0.66230
-o. Ges/0.2s
r0
.]]59
1
0.]358]
0.000/0.151
0-B9L
0.8:113
I
0.009/0.101
0.9453
I
0.9454)
I
-o. ola/D.ld
O.68J2
0.68T90
-0 .102/0.10
onooG
0.]0053
_ o.0]s/a.la
D.1W/D.z01
I
s
I
I
.1
a
1
I
I
I
0.]394
1
O.J]392
I
0.063/0.301
D.]43a
0.]4281
1
1
0.13]/0.2)
~
-01020/0.15
' 1
3.o4J9 ~
.0588 1
1.0589]
-0.05]/0.15
j' -0.016/0.15
1
a5
3.
o4aso
.1665 '
1.16660
L1°-01
I
1.2]2]
1 .2]363
1.2501
I
1.2501)
1
0.011/0.201
1.1s013
-0.002/420
~-0.000/0.20
SO
'
'
~ 0.006/0.20
GO
1 1.4006
1.44]4
' 3 .48043 '
1.04]00
0 011/0 20 L
_.__.
1
1
0.025/0_2)
in Table 1.
Comparison
of the compressibility
values and also with the experimental
IO)
ll)
l2)
13)
14)
13)
16)
17)
l8)
factor
data
values
computed
of both propanelo-ls7
from Eq. (1) with the
and propenels-1s)were
skeleton
table
conducted.
B. H, Sage, J. G. Schaafsma and W. N. Lacey. /rtd. Eng. Chem., 26, 1218 (1934)
J. 4 Beanie, W.C. Kay and L Kaminsky, I. Am. Chem. Soc., 59, 1589 (1937)
N. lV. Deschner and G. G. Brown, Ind. Eng. CGeno.,32, 83fi (1940)
J. H. Burgoyne, Roc. Roy. Soc„ A176, 280 (1940)
H. H. Reamer, B. H. Sage and W. V. Lacey, Ind. Eng. Chem., 41, 482 (1949)
B.J. Cberney, H. Dlarchman and R. York, Jr., ibid., 41, 2613 (1949)
P. S. Farringma aad B. H. Sage, ibid., 41, 1734 (1949)
H. hiarchman, H. W, Prengle. Jr, aad R.L. DSotard, ibid., 41, 2638 (1949)
A. J4ichels, T. Wassenarr, P. Louwerse, R.J. Luabeck and G.J. R'olkers, Physics, 19, 287 (1953)
It
(1976)
The Review of Physical Chemistry of Japan Vol. 46 No. 1 (1976)
Thermodynamic
1'a61e 5
-L18a
ssz3xla
h
b.
b;
bs
b~
bB
by
bra
bar
-1 .273 70iix
Propane
-1
.360
6591 x I0/
2.6i 1 0580 x 102
and Propene
for propane
Propene
1.257 4194x102
dy
d.
d;
d;
b,
bz
of Gaseous
Kumerical cons[anls in Fq, (;
Propane
d.
Properties
and propcne
Propane
biz
baa
5.76t
-8.161
lso7
OIi2x
Propene
x loft
(00
10-~
-2.362
4147 x 10_z
ban
3.401 9827 x I01<
9.196 8764 x 10_s
-4.521
8282 x 10'5
bas
1.053 6324x
2,539 2081 x 10-9
4.650 7610x 30°
-4 .090 9899 x ]OZ
1022
bis
3.638 6947 x 101
-1.074
baa
0
1.234 4220 x 1016
-4Si4
3334x1016
1.770
6253 x 10°
bie
-1 .401
2709 x 108
bay
2.813
1700 x 101°
by
0
-6 .935 9033 x 1018
-3.696
1023 x 1013
6.987 083tx ]016
-6.741
6069 x 1O21
-1
.982
3811 x 1015
bar
1.660 5316 x 1018
-5 .976
3010 x 1019
baz
0
8697 x 10zt
bza
0
-2 .187 7931 X 1055
-6 .474 1658 x I0~
5.317
1.593 2143 x LOB
0
-1 .295 1780 x 1015
bza
0
-3
-7
.783
7044 x l05
bas
3.341 9911 x 105
-4 .064 7594 x l06
3.334
6610 x 108
bas
6.923 3929 x 1012
8673 x 101°
baa
-1 .456 5349 x 1016
0381 x 1011
r
.i1 i
-3.ill
3.834 1177 x ]015
-1.406
1663 x l Ozz
3623 x 10'8
6.211 3928 x 105
-4.269
9835 x 1011
2.827 2012 x IOzs
7.751 9414 x 107
-5 .390 6i36 x 1016
.3i i 7028 x 101
1.940
-2
ii
1.944 4748 x 104
4115 X ] 0°
5.332 2630x IOz0
1.120 4682 x 1016
->.953 6320x1012
2.277 OOOSx 1020
-2 .835 8570x102z
0
0
4.048 8404 x 1012
0
2.479 0640x 104
should be noted that the comparisonwith the at•ailahledata was performed only with those taken into
considerationfor the establishmentof the skeleton tables in the previous work by Date and Iwasaki».
The average deviation of these reported experimental data from Eq. (I) are shown in Table 2 and it
can be understoodthaz the computed compressibilityfactor values are in satisfactory agreement with
the skeleton table values and the experimental data which were evaluazedto be found more reliable
by the HPDCPI. The computed compressibility factor values as well as their comparisonwith the
skeleton [able values are tabulated for propane and propene in Tables 3 and 4, respectively.
I[ is confirmedthat Eq. (1) can reproduce satisfactorily the skeleton table values of propane and
propene for the whole temperature ranges assigned within the gaseous phases. But, simply becauseof
the fact that the derived values with respect to the isobaric specificheat capacity are lessreliable along
the two bounded isotherms of 298.15Ii and 548.15K for propane, the effective range of the present
equation of stazefor gaseouspropane is limited to somewhat narrow region as mentioned previously
and therefore those computedvalues in this limited range of temperature are only given in Table 3.
Oa the other hand, the derived values of the isobaricspecificheat capacity focpropene are not reasonable only along Cheisotherm of 373.15K for supercritical pressures and hence this region is excluded
from the effectiverange of the proposed equation as shown in Table 4, however the P-V-T hehavior
alongthis isothermis completely satisfactory. It may he understoodthat this kind of behavior is mainly
due to the difficultyof Httingthe P-V-T plane alone without consideringthe tendency of the derived
property values especially in such a vicinity of [be critical isotherm as 373.15K for gaseous propene.
The
A. R'atanabe,
48
Tahle
6-I
Calculated
values
of molar
hi. tiematsu
volume,
Pressure
Review
0.1
273.15
(0)
298.15
(25)
22245
-1903
-6.115
24391
-112 .6
0.1128
0.5
4533.1
-608.9
-14.38
1
323.15
(50)
348.15
175)
molar enthalpy
373.15
(100)
26529
1805
6.285
28657
3855
12.40
30776
6033
18.43
5019.1
1362
-8 .038
5491.2
3474
5951.3
5706
4.446
2308.3
723.7
-15.21
2567.8
2948
-8.581
2891.9
5269
-2.143
1099.3
1641
-17 .16
2
3
4
-1.745
K
398.15
(125)
32886
8332
24.40
6402.2
BO50
1
and molar
entropy
for
propane
Kase0u5
(°C)
923.15
(1501
34994
10750
30.29
498.15
(175]
37095
13290
36.11
473.15
(200)
498.15
(225)
923.15
(2501
39194
41289
18]00
47.55
43382
21570
53_17
e585.fi
21410
39.57
15940
41.
Bfi
10.52
22.39
28.19
8154.9
lesza
33.92
3088.1
7680
4.108
332fi.4
10180
10.20
3559.2
12]90
16.18
3787.9
15990
22.05
4013.5
18300
27.83
4236.7
21210
33.53
1273.0
4266
-9_879
1424.3
6866
-3.129
1567.7
9098
3.282
1694.7
12190
9.469
1821.1
14970
15.49
1943.7
17830
21.39
2063.5
20790
27.19
729.26
2976
-15 .92
861.96
5923
-8.278
972.24
8795
-1 _4x3
1072.2
11sfi0
5.066
1165.6
14430
11.28
1254:6
1]360
17.32
1340.4
415_73
893.9
-23.02
570.69
4774
-12 .93
673.64
7902
-5.306
760.19
B 38.20
].996
910.89
16870
14.20
979. BB
19940
20_21
383.73
3256
-17.93
491.60
6944
-8 _933
572.46
10160
-1.550
642.11
13260
5.192
]05.41
16360
11.58
764.53
1049
-29.26
368.03
5840
-12 .55
246.01
447.20
9375
-4 .426
511.93
12640
2.6]3
Sfi9.22
15850
9.2]4
621.86
19060
15.57
-1026
-29 .96
280.27
173.25
358.34
4597
8592
-16 _25
-7.179
419.76
lzooa
0.3410
972.81
15330
7.182
52D,
148.13
-2093
-32.95
221.17
3368
-19 .74
351.79
11350
-1 .851
401.48
19800
5.247
445.92
18180
11.87
185.81
2388
-22 .53
136.47
246.5]
300.56
-2612
-34.71
10]00
-3.914
347_11
1 C270
3.491
388.56
17740
10_23
-2970
-35 .94
165.19
1694
-24.58
129.48
213.92
fi101
-14.46
267.66
100]0
-5.829
304.87
13750
1.752
393.59
17300
8.705
lz4.ss
lsz
190.45
5485
-16.28
232.17
9496
-7.970
2]1.69
13260
0.1814
307.79
16880
7.279
7
B
9
10
11
ze
1st
1201
line a molarwlume
Vin em3.mo1
1 -36?B9
-26_12
2nd
line
molar
3rd
line
molaz entropy
H in J•mml 1
8 in J•X 1•mol 1
121
13o7a
10890
1.
6d9
293.55
7681
-9 .824
6845
-12
.29
7721,9
ls]4a
13860
20370
23.22
19500
17.7]
83
18620
13_69
.03
-7906
-37.67
143.50
837.7
-27 .33
174.36
4995
-17.78
209. BB
8985
-9.116
245.9fi
12800
-1.267
278.84
16480
5.948
-3548
-38.32
137.09
560.3
-28.32
118.16
162.73
192.97
esa7
-10.47
224.65
12370
-2. SBB
255.32
16100
a. na
-3659
-38 .90
132.16
342.5
-29.15
115.80
154.00
9299
-zo.97
179.98
8176
-11. sa
208.05
11990
-3; 78,2
236.07
15740
3.564
113.80
-]746
-39.40
128.23
168.1
-29.87
147.21
0041
-20 .97
169.81
7865
-12 .67
194.70
11660
-9 .857
220.20
lsa2o
z.so7
-3815
-39.86
124.99
26.34
-30.50
312.07
141.7s
3813
-21.]6
163.69
7603
-13.57
183.86
11370
-6.823
2ozoa
lslza
1.536
13
14
15
Vol. 46 No.
7286.0
6
enthalpy
of Japan
6806.5
10500
16.50
5
12
Chemistry
and S. Saegusa
Temperature
.rea
of Physical
16
4606
-19.03
(1976)
The
Thermodynamic
Review
Pressure
]98-15
123.15
!1251
l8
-4G.2fi
122.25
-89.94
-31.0]
109.19
119.90
310.55
-3865
20
10].98
31].85
-265 .2
-32
106.8]
$8
.05
116.01
-730 .8
-32 .44
-41.30
12001
13].28
3660
-22 .4fi
-14.
13]-SL
199.55
155.06
102.51
-3989
109.26
-512 .8
-C2 _]I
-]4.24
]301
IB
498.15
f 21st
Sz3.ls
1]4-95
11110
-6.694
196.01
0.6451
14620
-0 -1]19
-23.09
-15.10
lfi].52
1089e
-]-4fl3
130-29
3391
144.89
161.21
-23.66
-15
121.43
140.89
]2 B5
-24.11
G89]
-1G.34
11].58
?955
-36 .28
126.99
3519
-01.
-3966
25
Vol. 46 No.
39
rc1
4]3-15
11]51
-185.9
-40.66
-39¢3
-41 -ai
x
448.]5
1150)
-3911
19
of Japan
(continued)
Temperature
1]
Chemistry
Properties of Gaseous Propane and Propene
Table 6-2
Moa
of Physical
]193
]0]3
.]5
10]00
-8.19]
195.88
10530
-8.851
13]-55
6413
-18
.13
30
-1
995]
L G3
(2507
I d860
1fl6.]fi
1]e.fl]
14410
-0.9250
1]2.10
14220
-1 .618
198.98
13560
-C
Al]
126.64
9614
-13
15[
line
mler
2nd
line
e molar
3rd
11ne
Basic
molar
volume
u
on chalpv
entropy
Correlating
in
cn 3•rol
-40
-1
_1
ti
in
5 in
S•rol
J.x
l .roi
1
Function
When density and temperature are chosen as the independent vaziables,[he expressionsfor pressure and all other thermodynamicproperties can be derived directly by the partial differentiationof
a basic correlatingfunction A=.4(p, T), where A is the molar Helmholtzfunction. In the present study,
the molar Helmholtz function A in J•mol-' is derived from Eqs. (1) and (2) as follows:
i
A=d,tdxT+d,T'+dsT°+dsT`+dsT•1nT+RT•la
p
+(b,T +b~+b,/T °+b,/T ` +bs/T °+6s/T °+b,/T'E)p
+(LsTt bs+b,°/T +L„/T''-)p'+(b,aT+L,a+b„/T'+bs/T°)p°
+(b,s+b,r/T+b,e/T°+b,s/T„ip9
+(8P°+b„/T+bYS/7"+b„/T
°)ps
+(b„Ttb_s+ba/T'+b„/T`xll7-(P°12+1/r)exp(-rp')].
(3)
The numericalconstants in Eq. (3) are given in Table 5. The numerical values of d, and d=in Eq. (3)
are fixed due to the followingspecifiedconditions:
(i) Molar entropy, S=0 J•R''mol'' at 298.15Kand 0.301325MPa,
(ii) Molar enthalpy. A=0 pmol'' at 298.15K and 0 MPa.
Derived
Functions
1 (1976)
The
So
R. R'atanabe,
Table
7-t
Review
J4. Uematsu
T@a
298.15
(-25)
273.15
/0I
298.15
(251
0.1
20110
-3179
-11_13
22286
-1691
-5.423
24439
-110 .d
o.uzs
323.15
(50)
398.15
1]51
of Japan
enthalpy
t°ci
37].15
1100)
398_15
(125)
448.15
(1751
4]3.15
(2001
498.15
(225)
35019
9140
25.84
37118
31270
30.72
39215
13490
35.99
41310
15800
40.31
2x697
3315
10:T2
30810
5164
15.85
4586.6
-190.7
-14.40
SD67.9
1168
-9.73A
5532.1
2989
-3.305
5985.3
4884
1.950
6431.2
6860
7.073
6871.9
2071.9
-1312
-21.93
2362.7
615.6
-15 .72
262]_3
2595
-9 .969
2877.1
4512
-4 .512
3117.6
6540
0.7458
3352.0
8690
5.860
3582.0
959.67
-878.0
-25.02
1153_1
la7s
-17.99
1312.1
3673
-11.90
1455.2
SB47
-6.273
1589.1
8042
-0.9174
1717.2
623.07
-69.11
-29_90
776.45
2649
-37 .37
894.82
5053
-11.32
996.65
7393
-5.41]
1094.4
9740
-0 .0279
989.29
1258
-22.75
608.35
4129
-15.29
700.99
6880
-s.o7e
782.19
9152
-3.400
429.50 520.33
3009
5888
-19.41
-12.38
594.32
8528
-6.314
302.88 398.3]
1562
5003
-23.94
-15.54
968.93
3
n
5
6
7
32917
7105
20. BH
42].15
(1501
26574
1558
s.4as
2
8921
12.09
211.82 310.99
-227.4
4021
-29
-18.]0
.07
8
Vol. 46 No.
and 5. Saegusa
x
Temperature
1
Chemistry
Calculated values of molar volume. molar
and molar entropy for gaseous propeae
Pressure
0.5
of Physical
162.72
-1725
-33.30
7309.0
11070
17.0]
10820
10.86
10290
4.253
]743.2
13310
21:89
3800.9
13aea
I5.]]
81]5.3
15690
26.68
4033.4
15430
20.61
1841.3
12610
9.287
1962.5
1185.7
32130
S.15fi
1272.3
14570
10.19
e5fi. 89
11620
1.968
sn.al
660.0]
11100
-o.7zla
15010
14.21
14130
7.130
720.87
11680
4.588
7864
-8.973
529.1]
10560
-3.109
583.66
13220
2.369
379.74
7163
-ll.48
436.2?
10010
-5.29]
486.27
12760
0.3698
24].]0
313.93
767.40
413.97
2980
-21.81
6436
-13.87
9944
-7.337
12290
-Lass
9
141.27 203.88
-2587
1989
-35. B4 -26.fi9
26C.69
5]06
-16.16
315.02
88]8
-9.253
358.62
11830
-3.172
10
130.13
-3101
-37 .47
175.39
116fi
-27 .08
227.98
5008
-18.25
274.56
8322
-11 .05
315.33
11370
-4 .765
11
323.16
-3444
-38.65
ls7.la
537.7
-28.95
2on.s1
4377
:20.13
247.09
7]91
-12_]2
280,96
10930
-6.253
118.26 145.03
-3693
68.30
-39.58
-30.42
181.Ofi
3837
-21.77
218.53
7298
-14.25
253.40
10500
-7.639
13
ua.s3
-3882
-4o .3a
136.53
-ze7.2
-31 .59
166.39
3379
-23 .17
199.26
6852
-15 .63
231.13
loua
-s.s2a
}4
111.56
-<071
-al.oo
130.24
-562.9
-32.Sfi
155.37
3004
-24.37
189.08
6457
-16.87
213.01
9738
-10.11
15
los.lo 125.36
-a1s1
-781.8
-al.se
-33.38
146.89
2696
-25:39
172.02
6113
-17.9]
198.17
saoz
-11.20
is
107.20 121.44
-4249
-958.9
-39 .09
-42.10
140.20
2441
-26.28
162.32
5815
-18.95
185.92
9098
-12 .19
1?
1st
late
molar
volume
2nd
line
molar
enthalpy
3rd
line
mOlaY
enCYOpy
V in
m3•mol
H in
1
J•mol
5 3n J•K
1
1•mol
1
1
(1976)
The
Thermodynamic
7-2
xemperac~-e
Pzescura
of Physical
of Gaseous Propane and
Properties
Table
Review
Propene
49].15
Izaol
499.15
~zzv
109.]1
-4]31
110.21
-lla
-az.3i
-l4.]1
n;.ao
2230
-2).06
lsa.ax
9998
-19.83
1]s.]a
882]
-11.10
]e
301.63
-4399
-a 1.06
115. d]
-1x36
-]9. ]B
v9.3a
3093
-2].]9
la].90
9l3]
-20.62
18].21
8989
-11.9]
19
102.21
-dd55
-a].
as
111.11
-1321
-35.]9
136.59
1901
8.3]
1a2.4J
914)
-21.J2
199.99
Blil
-1469
39
100.93
-as93
-41 . ]e
311. os
-1411
-lc. xs
1]). )9
4984
-21.9]
193.8]
8181
-19. ]B
25
95.99]
-a619
-d5. ]5
301.56
-1681
-18.16
30
9].502
-asiB
-46.63
98.641
-1]95
-39.41
35
09.814
-rile
-4]sB
ss. aao
nel9
-a9s1
d0
ei.s4o
-:i6a
-a8.61
92.233
-1]0fi
-41.84
d5
es. 0x6
-La39
-a9.43
e9.9x6
-1]15
-4x.)5
50
8a. x58
-a]31
-50.18
Bi.9B2
-161fi
-41.5]
60
81.680
-a036
-51 _49
84. BS1
-1159
-45.
W
uzs
19
Vol. 46 No.
1
(1976)
57
K I•CI
9/d.15
395)
198.15
of Japan
(continued)
431.15
usm
NPe
Chemistry
1:3.39
1]]]
-38'.93
i
I6v
lim
Vin
3na 11ne
xLn
3cd iine
5Sn
mlaz wlwe
m •ml 1
~ mla en[Tilpy
3~m1 1
mlec mtre6+y
S•K1-ml 1
i
Accordingto the general thermodynamicrelations, the pressure P in MPa, the molar entropy S in
J•K'3mo1'r, the molazenthalpy H in J•mol-', the molarisobaric specificheat capacity C, in J•K'~mol'r
and the molar isochoric speci5c heat rapacity C, in J•K'' mol-' can be calculated by the following
expressions:
P=P=(aAlaP)r ,
(4 )
i
2(aA/aP)7+P(~~laP`)r
In addition, the compressibility factor Z and the molar volume V in cm'•mol'' can be calculated from
the followingexpressions,respectively:
X
The Review of Physical Chemistry of Japan Vol. 46 No. 1 (1976)
52
bi. Uematsu
K_ Watanahe
Calculated
and S, Saegusa
Thermodynamic
Properties
By differentiating the new equations of state expressed in the basic correlating functions for gaseous
propane and propene, Eq. (3), all of the thermodynamic properties may be calculated as shown in the
previous seRion. The calculated molar volume; the molar enthalpy and the molar entropy for both
gaseous propane and propene are tabulated in Tables 6 and 7, respectively.
With respect to the molar isobaric specific heat capacity for both propane and propene, the calculated results are shown on CP p diagrams in Figs. 3 and 4. It is also noteworthy that the calculated
Cp values for gaseous propene are in good agreement with the reported experimental data by Bier et
al.e>, wbere they overlap. The average deviation is found as 0.362% with respect to 96 data points
compazed.
300
250
i
i
2~
~`~~
1
isdc; r
1' j
usY~
200
E
~-3H8
200
O
X
~t
so
100
~-_
is~
0
2
~sY
4
6
8
50Q
70
Calculated
heal capacity
molar isobaric
\insc
III
2
4
p, mobdm _3
Fig. 3
3H
~
150
~~
,~o
ioo
~_ ~
I ,nt
6
8
o, mal•dm
specific
Fig. 4
for propane
Calculated
beat capacity
molar isobaric
I
10
12
s
specific
for propene
Conclusion
As a part of the activities of the High Pressure Data Center of Japan, new equationsof state, Eq.
(1), for both gaseouspropane and propene are formulatedbased upon the most probableand additional
recommendedcompressibilityfactor values proposed previously by the HPDCJ. The present formulations given as a function of the density and temperature can cover the range of temperature 273.15
K-523.15K and pressures up Co30MPa for propane, and also that of temperature 248.15K-498.15K
and pressures up to 60MPa for propene, respectively.
The
Thermodynamic
Based upon the established
Helmholtz
volume,
function are derived
molar entropy,
Review
of Physical
Chemistry
of Japan
Properties of Gaseous Propane and Propene
equations
of state, the basic correlating
and hence the additional
molar enthalpy
thermodynamic
functions
property
and molar isobaric specific heat capacity,
Vol. 46 No.
a3
given as the molar
values such as molar
are also calculated
and presented.
It was also confirmed that the so-called
wide range of the state parameters
e[hene. propane
and propene
extended
BR'R equations
in gaseous region especially
in the previous
are very effective to cover the
for the serial hydrocarbons
like ethane,
and present studies by the present authors.
Acknowledgment
The present work was discussed by the following members and the cooperator . of [be Working
Committee of the High Pressure Dafa Center of Japan:
J. Osagi, Y. Takezaki (Kyoto University);
H. Iwasaki, S. Takahashi. K. Date (Tohoku University);
T. Makita, Y. Tanaka (Kobe University);
I. Tanishita (Ikutoku Technical University;;
A. Nagashima (Keio University),
to whom the authors with to express their sincere appreciation for their valuable suggestions and dis•
cussions.
As for the financial support to the present work, the authors are partially indebted to fhe sponsorship of the Agency oCScience and Technology.
Deparlrnent of Mechmafc¢IEngineering
Aaadty of E>gineering
keno University
Yokohama 223
.lapan
1
(1976)