6S
DETERMINATION OF IDEAL GAS THERMODYNAMIC
PROPERTY RELATIONS BY MULTIPROPERTY ANALYSIS
Iraj Khajavi Noori and Kenneth E. Starling
School of Chemical Engineering and Materials Science, University of Oklahoma,
Norman, Oklahoma
Multipropeny analysis calculations were performed to corre1ate simulcaaeowl,
ideal ps heat capacilf, enthalpy, and entropy. The basis for the correlation is •
power series in temperature for the heat capacllf. It is shown that for any siqIe
propeny simultaneous correlation of three properties pves better rau1u than thOse
based 00 parameters obcaioed by corre1atins the other two. This deviatioa becomes
worse wilen only one propeny is used to obcaio parameters. Remlu are pven
for fifteen compounds of interest in the natural ps iodusuy.
The need for simple yet accurate relations needed for all the properties which an
for thermodynamic properties is well considered.
known. Although there are compilations
The object of this work was to find single
of ideal gas properties such as JANAF sets
of parameters in self-consistent relations
Thermodynamical Tables ( 1), API Reof
ideal gas enthalpy, entropy, and heat
search Project (2). and the works of Cancapacity.
jar (3) and Din (.{), most engineers prefer
to use equations which enable them to
calculate properties at any given state withMETHODS
out having to interpolate or extrapolate
The
method
of multiproperty analysis
between discrete values of tables. For this
purpose relations for properties have been was used for calculations whicb were apdeveloped which give excellent results in plied to fifteen compounds of interest in
prescribed ranges. These relations, al- the natural gas industry. These compounds
though very useful. to calculate the pro- are listed in Table 1.
perties for which they were developed, lose Thermodynamic relations
their significance when they are used to
To calculate the enthalpy. Ht. of any
calculate other properties. This is especially tcue when property relations are differ- component in the ideal gas state at tementiated in order to obtain relations for perature T, one can write
other properties. For example, Ellington
~ f~8. Cpd'r + ~1IJl + 8, Eq. 1
and Eakin (5) have shown that an uncertainty of the order of 1% in PVT data
causes uncertainty of the order of 10% in
In this relation C p is the ideal gas beat
the thermcdynamic properties obtained by capacity. The value of H is relati.e to
differentiation. For a second differentiation the enthalpy of elements Tat O°R, Hf it
the order of uncertainty rises to U)()9{,.
the enthalpy of formation of tbe compoUod
Owing to these faca, it is very desirable to from the elements at OOR and HTHll it the
assume a model for one property and. using enthalpy at the reference temperature 1HB.
the relationship among thermodynamic relative to the enthalpy of the compound
properties, develop depeodeot. rather than at absolute zero of temperature, O°R.
For entropy we have
independent, models lor ocher properties.
The remaining ~ the .most impor1aOt
'\t •
Cp,.? ) n + '\to Eq. 2
one. is to determine the parameters of these
relations. It can be shown that, wben a
model fOl' one property is taken 85 the where TO it the refeteO(le temperature
basis of developing
for other pr0- and STSIlis the entropy of the comPound at
perties, all or .IDQIt of the perameten of the referen" temperature relatift to the
the original model a.Iso appear in other entropy of the compound at abtoluce zero
models. Tberelore, for .U-<OOSisceot cal- temperature (assumed to be zero lICXOfdiog
culations, ooIy ooe set of peramecen is to the third law of thetlllOdyoamia).
•
/:0 (
mode..
Ptoe. 0IdL Aad. Sci. 54: 6~n (1974)
66
Choice of model
ODe muJd IIIIWDe a polynomial apen-
HP3
~l (IIp;r- cr
Eq.9
.ioa in temperatUre for entropy, for enthalpy, or for beat capacity from which the Npl, Np2, and Np3 are the number of
neceuary relatiOOl for the other two prop- data (or tabulated) points for entropy, heat
erda muld be developed. These possibili- capacity, and enthalpy, respectively; the
tiel were mmpared and the most appro- subscripts E and C indicate the experimenpria. model W8I fouad to be the oao in tal (or tabulated) and calculated values,
which we IUIUJDed a polynomial for C p respectively. The weighting factors u, v,
aod CODIidered it as the basil for calculat- and w were taken to be unity in the present
work.
in, entropy aod enthalpy.
Acmrding to the method of least squares,
Cp • a + a T + •• _ + a ~-l
1
2
n Eq. 3 we have
We obIerved that, by havin, ooIy a rela~ = 0, i = 1,2, ••• ,n
Eq.l0
tion for Cp as a function of temperature,
i
enthalpy aod entropy were readily found
from equations 1 and 2. Therefore, usin, This leads to a set of linear equations in
the value from equation 3 for C p in equa- the parameters, known as the normal
tion 1 for H." we have:
equations, to be solved for the parameter
2
values. Computations were carried out
.,. • a 1 [ 'I - Tn 1 + 11/2) a [ '12 - THR ) + ••• +
2
using the University of Oklahoma IBM
ClIn) an [ T" - 'taRn) + Ht + H.r
Eq. " ~/SO computer.
HR
Similarly, for entropy we obtain:
For purposes of discussion, the standard
IT • a 1 ln [ TIT. . ) + a 2 [ 'I - TSR 1+ ••• + .Eq. 5
error of estimate, S, and average absolute
per cent error, a, were calculated, where
11/ In - 1) ) an r T"-1 - 'tSRn-l ) + STSR
Oblervin, equations " and S, we notice
that the reference temperatures THR and
TSR can both be chosen arbitrarily for
enthalpy aod entropy, respectively. Herein
lies the major advantage of usin, Cp rather
than H or S as the buis polynomial. However, no matter which property is chosen
as the buil of calculations, we always end
up with one set of parameters alt a2, •••,an
for all three properties. The use of Cp is
merely the mOSt convenient basis.
Maltlpropeny 8IIalysis
To estimate the parameters alt aI, •.• Iln
we define an objective function Q by the
relation
°•
Eq, 6
uOl + v 02 + w 03
where u, v, and w are wei,htin, factors
for entropy, heat capacity, and enthalpy,
respectiftly, and 010 Qt, and Qa are the
sums of IqlW'es of errors defined by the
relations
01 -
°
2 •
NPI [
J:
SE - SC ) 2
1-1
1
1
NP2
E
. .1
(c -
J
C
p~. Pc
2
Eq. 7
Eq. 8
°3
H )2
NP
r
and
S =
.-f(T.)
1"1 YJ.
N -n
1
Ii
a=-r
NPi=l
NP
Y
J.
- f
Yi
2
1/2
Eq.11
I
Eq.12
(T i)
In th~ relations '\j is the tabulated property value at the temperature Ti and
f(Ti ) is the polynomial for the property,
n is the number of parameteR, and NP
the number of tabulated points.
800ftes of data
The data used in this work were extracted
from the following SOW'CleS.
With the exceptions of four materials
(ethylene, nitrogen, carbon dioxide and
hydroleD sulfide), the values of enthalpY,
heat capacity, and entropy of the remain....
mmpouods were obtained from the API« (2). The values of properties for the
above four materials were obtained from
JANAF Tables (1) because they CDftf a
lower temperature range than that ~
in API",", Table 1 shows the ranae of
temperatures used for enthalpy, heat capacity, and entropy of each mmpouad. Table 2
shows the values of reference temperatureS
and property values.
67
T_,.,.... ,....-,
TABU I.
~..~;", IIfItl ftIIroh.&
The heats of formation of ethylene, nitroand hydrosen sulfide
~ also obtained from JANAF. For itopentane, ••heCtane, and .-octane the values
were derived rom API-+( Tables. The heats
of formation of the remaining com~ds
were enraeted from the compilatlOO of
Caajar and Manning (3).
o/dlh6lh, IJuI
sen. carbon dioxide.
Compound
Mecbaae
&bane
Propene
.Batane
i-Butaoe
.PenlaOe
i-Pentane
.-Hexane
.·Hepaae
..ocuoe
Ethylene
Propylene
Niuosea
CO:
H:oS
180-1620
180-1620
180-1620
360-1620
360-1660
360-1660
360-1660
540-1800
540-1800
540-1660
180-1800
540-1980
180-1800
180-1800
180-1800
160-1660
210-1660
210-1660
460-1660
360-1660
160-1660
210-1660
210-1660
360-1660
360-1660
360-1660
360-1660
460-1660
460-1660
460-1660
180-1800
460-1860
180-1800
180-1800
180-1800
.f6o-166O
.f6o-166O
460-1660
.f6o-166O
460-1660
180-1800
460-1860
180-1800
180-1800
180-1800
The molecular weights of tbe compounds
are calculated from the following atomic
weights (6): hydrogen
1.008; carbon
12.011; nitrogen = 14.007; oxysen ==
16.000; sulfur = 32.064.
RESULTS AND DISCUSSION
a All temperatUres ate iD degrees RaokiDe.
The program written for calculation of
parameters has the flexibility of calculating
these parameters for any combination of
enthalpy, heat capacity, and entropy data,
i.e., it is possible to calculate
from the data supplied for only one property, for any of the twO properties, oe,
finally, from all three properties simultaneously. In order to determine the ennsistency among the data of the different
properties used in this study, all these combinations were tested.
The enthalpy data taken from API-+(
tables are modified foe each compound by
addition of the heat of formation of tbe
compound so that all enthalpies are relative to the enthalpies of the constituents at
the reference state (zero degree Rankine
and 1 psia). The values taken from JANAF
are also modified appropriately to maintain
consistency among the reference states and
units of all data.
TABU! 2.
Methane
Ethane
Propane
.-Butalle
i-Butaae
.·Pentane
i-PenlaOe
..HexaDe
..Heptane
..oaaae
Ethylene
Propylene
NitroAea
co,
H:oS
• T
HR
b h
T
HR
C T
'
SIt.
d S
T
• It
f
f
sa
M.".
.h ...,•
COIIJI'-JS 1ISe4 ;" ngr~llioIIJ ~sis.
a
T
Compound
=
=
HR
160.0
210.0
210.0
360.0
360.0
360.0
360.0
460.0
460.0
460.0
180.0
460.0
180.0
180.0
180.0
b
h
T
T
HR
79.08
c
SR
180.0
180.0
180.0
360.0
360.0
360.0
360.0
540.0
540.0
540.0
180.0
5-40.0
180.0
180.0
180.0
57.09
41.34
81.59
7I.43
78.56
72.13
110.os
105.52
107.42
51.01
112.00
«.53
28.42
41.99
= enthalpy refereoce temperature, oR.
=compouocl'l abeolute eadaalpy •
T
HR
= eattop)' refereoce ceaapencun, oK.
= compoaacfl
eauopy •
T
,Bcu/lb.,
SIt.
= hair of formaOoa, Bcullb.
, Baa/lb.
d
S
he
T
SR
f
2.559
1.639
1.267
1.227
1.167
1.091
1.079
1.139
1.074
1.023
1.728
1.645
1.553
1.093
1.342
-1793.83
-983.78
·795.29
·733.10
·783.04
-679.40
-718.68
-645.50
-620.67
-601.97
931.63
362.24
0.00
-3842.S3
-217.55
M.W.t
16.043
30.070
«.097
58.124
58.124
72.151
72.151
86.178
100.265
114.232
28.oS4
42.081
28.014
44.011
34.oeo
68
Table 3 iI • typical example of the resula
of mmputadou of different combinations
of data for ..baaoe. The fint mlwnn of
mil table iJldicaca the combination of the
properties used to obtain the puameten.
The IeCOOd mlwno Uta the nwnben of
parameterS used in mrrelatioD, and other
mlWllOl Jive the standard error of estimate
and -venae per cent deviacioD of enthalpy,
heat capacity, and entropy, respectively.
Examination of this table reveals that
.imultaneous cottelation of the three properties poerally gives _ better result for
each property than resula obtained for
the same property when calculated with
iDthalpy
~
1
2
3
40.895
.{.197
0.378
S
"
5
0.~1
H
aacl
1
2
3
40.895
aad
C
.{
5
S
aacl
H
C
aacl
S
H
1
2
3
S
.{.197
0.377
0.389
0.339
40.895
5
1
2
3
53.210
6,.{15
0.893
5
0939
1
2
3
40.89.f
"
"
C
G.390
"-320
0.238
0.07"
0.033
"
(%)
15.70
1.16
0.06
0.05
0.06
0.184
0.027
0.002
0.002
0.001
25.20
15.70
1.16
0.06
0.05
0.06
0.184
0.027
0.002
0.002
0.001
25.20
15.7.{
1.13
0.0.{
0.02
0.01
0.940
".325
0.233
error
Average
error
(%)
0.033
0.002
0.001
0.001
0.001
1.65
0.10
0.21
0.20
0.1.{
0.184
0.02.{
0.002
0.003
o.oo.f
25.20
3.19
0.23
0.31
0.41
0.033
0.003
0.001
0.001
0.001
1.65
0.12
122.78
3G.37
2.86
2.92
3.18
0.202
0.025
0.001
0.001
0.001
25.85
3.01
0.18
0.18
0.009
0.039
1.64
G.37
0.01
0.01
0.01
15.7.{
1.13
0.0.{
0.02
0.01
0.184
0.02.{
0.002
0.003
o.oo.f
25.20
3.19
0.23
0.30
1.65
0.12
o.o.f
G.36
0.033
0.003
0.001
0.001
0.001
12.{.70
31.-46
2.87
2.91
3.16
0.203
0.025
0.001
0.001
25.87
0.039
0.18
0.18
0.05
‫ס‬.‫ס‬oo
‫ס‬.‫ס‬oo
‫ס‬.‫ס‬oo
1.65
G.39
0.01
0.01
0.01
0.192
25,37
3.08
0.18
0.22
Q..{5
‫ס‬.‫ס‬oo
‫ס‬.‫ס‬oo
‫ס‬.‫ס‬oo
1
2
3
53.556
6.678
"
5
0938
0932
1
2
3
44307
023
67.95
5
0..51
0.767
2.22
"
(%)
1.65
0.10
0.0.{
0.0.{
0.05
0.080
G.038
0.856
error
SCaadanl
error
(Btullb)
0.033
0.002
0.001
0.001
0.001
5
0.8H
iDtropy
Heat capllCity
AYeJ'qe
Avenp
N
These observations indicate that although
a nearly perfect fit for a single property
might be obtained, it does not imply that
other properties can always be predicted
accurately on the basis of correlation ob-
Saadanl
error
(Btu/lb)
StaacIud
error
(lhu/lb)
Daca
parameten obtained from mrrelating the
other two. At the same time, mrrelatioD of
two properties Jives better resula for those
two properties than the results obtained
from .imultllOeOUS correlation of all three
properties. Finally, the parameters from the
data of only one property give the best
values for that property, and still poorer
raula for the other two.
l.38
2.87
1.33
o.ocn
0.028
0.001
0.002
0.004
3.09
0.21
0.20
0.14
3.09
O.os
3.02
0.000
0.000
0.000
0.009
0.033
G.OO2
o.O.f
0.0.{
0.05
o.o.f
0.03
0.02
G.03
0.G3
1.'"
0.10
0.01
0.01
0.00
69
taioed for that p~. Also, it appears
that the larger the number of properties
included. the better the results for those
which were not included originally. Similar
conclusions haft been reached by Passut
and Danner (1) in an independent stUdy
reported after completion of the present
work.
Examination of Table 3 also reveals that
the tabulated values for enthalpy, heat
capacity, and. possibly, entropy are not
quite consistent. The possibility of inconsistency exists in the data for all 15
compounds considered here, but to various
degrees. If the data of different properties
of one compound were perfectly consistent
and if equations 3, 4, and 5 for CPt H, and
S were correct, essentially the same results
would have been obtained no matter what
combination of properties was used. None
of the 15 compounds considered satisfies
TABU! 4.
Compound
.,
PtII"lIIIUlws
;ts
..
16,~"UruI;"g
this aiterioo and, as indicated previously,
the results obtained from different combinations of data are generally different.
As criteria for the level of accuracy of the
calculated values, a maximum standard
deviation of 0.3 Btu/lb for enthalpy and
0.003 Btu/lboR for entropy were ronsidered. Except for ,.-heptane, this left! was
satisfied for all compounds considered by
using polynomials with six or fewer parameters. For nine of these 15 materials the
criteria were satisfied with only three parameters. Space doe5 not permit the presentatidll of all of these results. Table "
reoords the values of the parameters in the
six-parameter polynomial for all compounds. Table 5 shows the standard error of
estimate and average per cent deviations
of enthaJpies, heat capacities, and entropies
of all compounds obtained by using the
parameters of Table 4.
aa
Med1aoe
0.552005Jl 00 -o.388922E-03 0.546747E-06
Edtane
0-354508Jl 00 -o.660753Jl-03 0.234779£-0'
Propane
0.305692E 00 -0.8061 87E-03 0.320346E-05
.-Butane
0.215054E 00 -o.192172E-03 0.174302£-05
i-Butane
0.268085E 00 -0.669140£-03 0.300679£-05
.·Pentane 0.2'1921£ 00 -0.451137£-03 O.238926E-05
i-Pentane
O.lS298IE 00 -0.902555£-03 0.152256E-oS
..Hexane -0. 11245 IE 00 O.131948E-02 -0.95 I 274E-06
..Hepune -o.925871EOI 0.118539£-02 -o.70473IE-06
..octane
-O.463255E-01 0.941057Jl-03 -0.12383 I E-06
Ethylene
0.404864£ 00 -o.115404E-02 O.343861Jl.05
Proplyene 0.196387E 00 -0.1 11278Jl.03 0.1 34306Jl-05
Nitro8eD
0.244689E 00 O.356575E-04 -0.115366£-06
0.142563Jl 00 0.10237811-04 0.381144E-06
u.s
0.245576E 00 -0.10412611-03 0.262S07E-06
Co.
TABU! 5.
SliMtlltl nrtH'S 01 .s,;",.,us _
Enthalpy
SUo·
Compound
Methane
Jidwae
Propane
..Butane
i-Ikataoe
..Pentane
i-PentaDe
..Heane
..Hepcaae
cIard
error
0.126
0.213
0.166
o.oso
0.086
0.088
0.110
0.025
0.034
..oaaae
0.029
co.
o.D39
Ethyleae
::=e
ILS
0.065
0.071
0.022
0.012
Averaae
error
SUo·
datd
0.01
Q.02
0.03
0.07
0.02
0.03
0.24
0.004
0.003
0.00
0.01
0.00
0.00
0.13
0.522 131 E-09
-o.2078781l-08
-o.333996E-08
-o.1745111l-08
-o.316424E-08
-o.250615E-08
-o.IS9462E-08
0.551223E-09
0.285173E-09
-o.331620E-09
-o.334607E-08
-o.131514Jl-08
0.152236E-09
-O.485579E-09
-o.207227E-09
-0.677861 Jl·12
0.M3175E·12
0.I'9272Jl·11
0.7631041l·12
0.148839E-l1
0.118260£·11
0.696393E·12
-0.182807£-12
-o.393949E-13
0.270474E-12
0.149325Jl·II
0.554482Ji·12
-0.75860611·13
0.24972I Jl.12
0.8SG292Jl.13
HeatcaJJlldty
error
0.06
..
e.~MiIy.
aa
0.188727£·15
-o.134132Jl·I5
-o.29-'042Jl·lS
-0.1281671l·I 5
-0.2676661·15
-o.215752Jl.15
-o.113578Jl.15
0.229476Jl.16
-o.710573E-17
-o.667791E-16
-o.255603Jl.15
-o.888333Jl.16
O.133867Jl.16
-o.472635E·16
-0.I 48408Jl.16
IIfItW166e fJn'enl tktNdioflt
(%)
CI.2O
0.02
..
1J01"",,,,;,," for nUJ.ln, nlron, MIll I"",
G..OO'
0.001
0.001
0.001
0.001
0.D05
Q.027
0.004
0.004
0.001
0Jl00
0.0D2
0.001
Aver·
qe
error
(%)
0.30
Q.33
0.62
0.10
0.19
0.13
0.09
0.41
3m
0,41
0.37
0.09
0.01
0.45
om
Bauopy
SCaa·
cIard
error
‫ס‬.‫ס‬oo
0.003
0.003
Q.OO2
0.001
0.001
0.001
0.001
0.023
0.001
0.001
0.001
‫ס‬.‫ס‬oo
0.000
‫ס‬.‫ס‬oo
Aver·
aae
error
(%)
0.01
o.os
0.15
om
0.04
0.06
0.02
0.02
0.66
Q.02
0.01
o.oz
0.00
0.01
0.00
70
ADaI,.... of el1'OlII In extrapolation
of polyaollltalB
It baa been shown that the parameters
obtained for approsimadng polynomials
give very ~ resula in the range of tem·
peratwe 01 the tabulated properties. It was
Of interest to determine whether these polynomials can be extended beyond their origi.
nal ranI' of temperature, and, if so, the
lowest and highest temperatures between
which the extrapolation can be made ac·
curately. Information on the accuracy of
extrapolations to low temperatures is par.
ticularly important because property tabulations are incomplete in regions of current
low-temperature processing of numerous
fluids.
To answer these questions, an error analysis was performed for methane. First a
temperature range of 460-1660 R was considered and polynomials with six parameters were used to fit the tabulated values
for enthalpy, heat capacity, and entropy
simultaneously. The polynomials thus obtained fit the data very closely for the temperature range considered. To see how well
the polynomials obtained for the three
properties can be extrapolated, the polynomials were evaluated for temperatures
DOt within the original range. The results
for enthalpy, as an example, are given in
Table 6. where the figures indicate that
the polynomial for enthalpy can be extrapolated up to 100 Rankine below the lowest
temperatwe originally considered without
iInoriog the criteria of accuracy set for
enthalpy (j.e., 0.3 Btu/lb).
(R.)
Figure 1 shows a plot of enthalpy deviations obtained from extrapolation of the
above three cases. as a function of temperatu.re. We observed that, for the polynomial fits between 460 to 1660 R, 360 to
1660 R, and 260 to 1660 R, the extrapolation can be accurately carried OUt for 110 R,
75 R, and 40 R below the lowest temperatures considered in each fit, respectively.
Extrapolation of these results for the case
of 160 to 1660 R (dashed line in Fig. I),
indicated that it is unsatisfactory to extrapolate the polynomial fit obtained for this
range for more than about 10 R below the
lowest temperature considered, i.e., 160 R.
These results showed that the range of
extrapolation for the low temperature
regions narrows very rapidly as the lower
limit of temperature used for polynomial
fit decreases. Therefore, for the lower temperature regions it is not possible to give
a range of extrapolation applicable to the
polynomials of all compounds because the
ranges start at different temperatures.
Similar calculation also was performed
for the higher temperature range and it
was observed that the extrapolation can be
carried out accurately up to 100 R beyond
the temperature range originally mnsidered.
/1", 01 ,.,~""'. . . r-8' .~. error I_s • •,
6. Til••
. .16-..
Temperacwe
TABU
The same procedure was repeated for
temperature ranges from 360 to 1660 Rankine and from 260 to 1660 Rankine, respectively. The resula of these extrapolations
also are recorded in Table 6.
H 1IzJJtL·
(Bcu!lb)
H. Calc.
(Btu/lb)
,xl"~~""W.
Deviatioa
(Btu/lb)
-1665.23
-1690.03
-17104.75
Tempehl1l1'e raoae
-1590.66
-1615.84
-IMI.05
-1666.63
-1692.96
-1720.049
209.69
-16ofO.043
-1665.23
-1690.03
-17Jot75
Temperature raqe 360 to
- 160f0.60
1665.79
-1691.504
-1718.21
209.69
-1690.03
-17104.75
Tempenmre raoae 260 to 1660 R.
-1690.042
0.39
-1716.204
1.049
_.69
359.69
309.69
259.69
209.69
159.69
309.69
259.69
159.69
159.69
-1590.63
-1615.63
-1640.-0
o4(j() to
1660 R.
0.03
0.21
0.62
1.040
2.93
5.64
1660 R.
0.17
0.56
1.51
3.046
of
~J.y.o.uls
Error
(%)
0.00
0.01
OM
0.08
o.l7
0.33
0.01
0.03
0.09
0.20
0.02
G.09
for
71
1.5
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I
\
1.0
\
.Q
r-f
':::s
+I
~
.
fJ)
ii"
~
H
~
H
:>
~
Q
~
~
E-.
Z
0
0
0
ID
ID
r-f
I
0
ID
0
ID
ID
0
ID
ID
~
)4
~
ii"
0
\
...
...
I
0
ID
I
0
ID
M
~
•
•
0.5
~
MAXIMUM
ALLOWED
LEVEL OF
~<;!R'.LAIl!TI..
0.3
o
o
\
100
110 0
200
300
400
500
TEMPERA'l'URE, oR
PlGuaB t. Comper&oa of allowable
tlIQIa
of esuapoJadoa eodlalpy polyaomiall for medwIe.
72
Jor GillS'S, Gulf Publishiq Co..
Houtaoa. Teas, 1967.
DIN, Tb".,oJ7"tJISI'" FIIII&Iw.s 01 GllUs,
Vol. I, 2, and 3, Butterworths, Loodoo
1961S. R. T. ELLINGTON and B. Eo EAKIN, Olem.
EoS. Pros. 59 80-88 (1963).
6. Ph,skJ. tJISUl. TbwfIIOd,lUIII" Pro,mus oJ
Ek",,,"s IIrIIl Co",polllllls, Olemeuon
Corporation, Catalysis Divisioo, New York,
IwflS
4. F.
1969.
7. Co A. PASSUT and R. P. DANNER, lad.
Olem. Process Desiso Develop. 11:
546 (1972).
Eos.
543-