an empirical method of correlating compressibility factors
TRANSCRIPT
Scholars' Mine Scholars' Mine
Masters Theses Student Theses and Dissertations
1971
An empirical method of correlating compressibility factors of An empirical method of correlating compressibility factors of
nitrogen - helium - hydrocarbon systems nitrogen - helium - hydrocarbon systems
Terry Wayne Buck
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Recommended Citation Recommended Citation Buck, Terry Wayne, "An empirical method of correlating compressibility factors of nitrogen - helium - hydrocarbon systems" (1971). Masters Theses. 7232. https://scholarsmine.mst.edu/masters_theses/7232
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AN EMPIRICAL METHOD OF
CORRELATING COMPRESSIBILITY
FACTORS OF
NITROGEN - HELIUM - HYDROCARBON SYSTEMS
BY
TERRY WAYNE BUCK, 1948-
A THESIS
Presented to the Faculty of the Graduate School of the
UNIVERSITY OF MISSOURI-ROLLA
In Partial Fulfillment of the Requirements for the Degree
t4ASTER OF SCIENCE IN PETROLEUM ENGINEERING
1971
Approved by
. --';4.~t:-.;Mo..;;..;..;..~...;...::;..~--(Advisor) f·/ ~-
tQ¥
T2593 61 pages c.l
ABSTRACT
Compressibility factors have been taken from previous works by
Davis and Taneja for twelve different common oil-field hydrocarbon
mixtures which contain at least 2 mole % nitrogen.
i i
An effort has been made to show that by using the Benedict-Webb
Rubin Equation of State it is possible to predict compressibility
factors using a correlation of error in predicted compressibility
factor versus reduced pressure, at different mole % of nitrogen with
constant reduced temperatures. if the critical points of the mixtures
are known or can be calculated.
In the mixtures which contain helium. the only effect of helium
seems to be the raising of the critical pressure.
iii
ACKNOWLEDGEMENT
I would like to thank Dr. T. C. Wilson for the original idea, his
time, and his interest, not only in this study but also in me.
Also I would like to thank Dr. J. 0. Stoffer and Professor
J. P. Govier for the critical review of the study. Last, I would also
like to express mY appreciation to Mr. P. K. Taneja for his suggestions
and permission to use his experimental data and Mr. A. A. Merchant for
his suggestions from time to time.
iv
TABLE OF CONTENTS
Page
ABSTRACT • ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• i i
ACKNOWLEDGEMENT ••••••••••••.•••••••••••••••••••.•••••••••••••...••• ;;;
LIST OF ILLUSTRATIONS •••••••••••••••••••••••••••••••••••••••••••••••• v
LIST OF TABLES •••••••••••••••••••••••••••••••••••••••••••••••••••••• vi
I. INTRODUCTION • •••••••••••••••••••••••••••••••••••••••••••••••• • 1
II. LITERATURE REVIEW ••••••••••••••••••••••••••••••••••••••••••••• 2
III. DISCUSSION •••••••••••••••••••••••••••••••••••••••••••••••••••• 5
A. EQUATIONS ••••••••••••••••••••••••••••••••••••••••••••••••• 5
1. COMPRESSIBILITY ••••••••••••••••••••••••••••••••••••••• 5
2. CRITICAL POINTS ••••••••••••••••••••••••••••••••••••••• 6
B. MIXTURES USED IN CORRELATION •••••••••••••••••••••••••••••• 8
C. METHOD OF CORRELATION •••••••••••••••••••••••••••••••••••• 11
IV. RESULTS •••••••••••••••••••••••••••••••••••••••••••••••••••.•• l2
v. CONCLUSIONS AND RECOMMENDATIONS •••••••••••••••••••••••••••••• 41
VI. BIBLIOGRAPHY ••••••••••••••••••••••••••••••••••••••••••••••••• 42
VII. VITA ••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 43
VI II. APPENDICES ••••••••••••••••••••••••••••••••••••••••••••••••••• 44
A. SAMPLE CALCULATION FOR COMPRESSIBILITY FACTORS ••••••••••• 45
B. SAMPLE CALCULATION OF CRITICAL TEMPERATURES FOR
MIXTURES 1 THROUGH 4 ••••••••••••••••••••••••••••••••••••• 49
C. SAMPLE CALCULATION OF CRITICAL PRESSURES FOR
MIXTURES 1 THROUGH 4 ••••••••••••••••••••••••••••••••••••• 51
I X. NOMENCLATURE • •••••••••••••••••••••••••••••••••••••••••••••••• 53
v
LIST OF ILLUSTRATIONS
Figures Page
1. Correlation of Compressibility Factor T R = 1.10 ......•...•...... 36
2. Correlation of Compressibility Factor T R = 1.00 ......•.......... 37
3. Correlation of Compressibility Factor T R = 0.95 .••.•.•••.....•.. 38
4. Correlation of Compressibility Factor T R = 1.28 •.•...•...•...... 39
5. Correlation of Compressibility Factor TR = 1.40 •••••.•.•..•..••• 40
vi
LIST OF TABLES
Table Page
I. Composition of Mixtures by Davis ••••••••••••••••••••••••••••• 9
II. Composition of Mixtures by Taneja ••••••••••••••••••••••••••• lO
I II.
IV.
v. VI.
VII.
VIII.
IX.
x. XI.
XII.
XI II.
XIV.
XV.
XVI.
Experimental Compressibility Factors T = R 1.10 ..•.••..•.•.. 14
Experimental Compressibility Factors T = R 1.00 •••••..•••..• 15
Experimental Compressibility Factors TR = 0.95 ••••..••••••. 16
Experimental Compressibility Factors T = R 0.90 •••••••••.••. 17
Experimental Compressibility Factors TR = 0.85 ••........•.. 18
Experimental Compressibility Factors TR ~ 1.28 ••...•....... 19
Ex peri menta 1 Compressibility Factors TR ~ 1.40 .•••••.•••... 20
Computed Compressibility Factors T = R 1.10 .•.•..••.••...... 21
Computed Compressibility Factors T = R 1.00 .••.••..•••...... 22
Computed Compressibility Factors T = R 0.95 •••••••••••...••. 23
Computed Compressibility Factors T = R 0. 90 • .•• "' ..••••...... 24
Computed Compressibility Factors T = R 0.85 ......••••..... ~.25
Computed Compressibility Factors T -R - 1.28 •......•.....•.•. 26
Computed Compressibility Factors T -R - 1.40 ••.•.••••......•. 27
XVII. Experimental Minus Computed Compressibility Factors
TR = 1.10 ••••••••••••••••••••••••••••••••••••••••••••••••••• 28
XVIII. Experimental f4inus Computed Compressibility Factors
T R = 1. 00 ••••••••••••••••••••••••••••••••••••••••••••••••••• 29
XIX. Experimental Minus Computed Compressibility Factors
TR = 0.95 ••••••••••••••••••••••••••••••••••••••••••••••••••• 30
XX. Experimental Minus Computed Compressibility Factors
TR = 0.90 ••••••••••••••••••••••••••••••••••••••••••••••••••• 31
vii
List of Tables (continued) Page
XXI. Experimental Minus Computed Compressibility Factors
TR = 0.85 •••••.•••.•.••••••.•.••••.••••.•.••.•••••.....••.•. 32
XXII. Experimental Minus Computed Compressibility Factors
TR = 1.28 ••••••••••••••••••••••••••••••••••••••••••••••••••• 33
XXIII. Experimental Minus Computed Compressibility Factors
TR ~ 1.40 ••••••••••••••••••••••••••••••••••••••••••••••••••• 34
XXIV. Critical Temperatures and Pressures of the Mixtures ••••••••• 35
1
I. INTRODUCTION
As the range of operating conditions in the natural gas industry
become more and more varied. the need for prediction of compressibility
factors over a wide range of temperatures and pressures is becoming
more prominent.
The compressibility factors of natural gas mixtures have been
determined by various means. Ill However. certain limitations are
inherent to each of these procedures. 121 Because of these limitations
a more accurate method of predicting compressibility factors has been
sought.
The object of this study is to show that for a natural gas mix
ture. which contains from 2 to 25 mole % nitrogen. it is possible to
predict compressibility factors using the Benedict-Webb-Rubin Equation
of State 131 in conjunction with a correlation graph to correct for
the nitrogen which may be present in the mixture. Various graphs are
presented to correct for the presence of nitrogen. These graphs are
plots of the error in the compressibility factor calculated with the
Benedict-Webb-Rubin Equation of State versus reduced pressure at a
constant reduced temperature with different mole %of nitrogen for
each correction curve.
II. LITERATURE REVIEW
Several methods are available for computing compressibility
factors of hydrocarbon and natural gas mixtures. Ill In a method introduced by Kay Ill • which has the 11 La"' of
Corresponding States, .. as its theoretical basis, the pseudo-reduced
temperature and pressure are assumed to be adequate to predict com
pressibility factors of gaseous hydrocarbon mixtures. Kay introduced
the concept of pseudo-reduced temperature and pseudo-reduced pressure
which are defined mathematically as:
2
pPR = pI pPC
pTR = T I pTe
(1)
where: P and T are absolute pressure and temperature respectively.
and:
n pPC = L Y. p . ;
i=l 1 Cl
n pT = l Y. T .
C i=l 1 Cl
with: pPc =pseudo-critical pressure of the mixture;
( 2)
(3)
(4)
Pci =absolute critical pressure of the individual component;
Tci = absolute critical temperature of the individual component;
pTe = pseudo-critical temperature of the mixture;
Yi = mole fraction of the ith component in the mixture;
n = the number of components in the mixture
Once pPr and pTr are calculated, the compressibility factors may
be determined from graphs prepared by Brown, Katz, Oberfell and Alden.
121 These are standard graphs which the petroleum industry has
universally adopted to determine the compressibility factor for the
equation:
3
PV = ZnRT (5)
These graphs hold only if the mixture is a methane-rich natural gas.
Eilerts stated that the error resulting from nitrogen is less
than 1 % if nitrogen content is less than 10 mole %, less than 3 % if
nitrogen content is less than 20 mole %, and greater than 3 % if more
than 20 mole % nitrogen is present (assuming the Law of Corresponding
States). 121
To compensate for the presence of nitrogen in a hydrocarbon gas,
Eilerts proposed an additive compressibility factor defined as:
za = znyn + (1 - Yn)z9 where:
Zn =compressibility factor of the nitrogen;
Yn = mole fraction of the nitrogen;
Zg = compressibility factor of the hydrocarbon fraction
The true compressibility factor Z is then:
z = cz a
where: C = correction factor dependent of temperature, pressure, and
mo 1 e % nitrogen
Tables are presented l2lto determine the correction factor C.
Various other procedures of correcting for carbon dioxide,
hydrogen sulfide, and water vapor may be found in AmYX 1 Bass, and
Wh 1 t i ng "' 121
In 1940 Benedict, Webb, and Rubin proposed an empirical equation
of state for the phase and volumetric behavior of gases and liquids at
the bubble:.·• point. 131 This equation is a refinement of the Beattie-
Bridgeman Equation of State. The Benedict-Webb-Rubin Equation of
State contains eight empirical coefficients whereas the Beattie
Bridgeman contains only six. The equation developed by Benedict,
4
Webb, and Rubin was guided by several considerations. It is a com
promise between a simple equation and a reasonably accurate descrip
tion of the observed volumetric properties of gases. 131 The coeffi
cients of the equation were based mainly on three main properties; the
volumetric behavior of the gas phase, the prediction of critical pro
perties, and the determination of an accurate vapor pressure. 131
This equation of state does not accurately define the volumetric
behavior of the liquid except at points near the phase boundary of the
substance. This equation is explicit in compressibility factor ana
pressure and the effort to obtain, by reversion, an explicit expression
in molal volume yields an infinite series which is impossible to
develop into any expression of closed form. 131
In a paper presented by Opfell, Sage, and Pitzer 141 the Benedict
Webb-Rubin Equation was applied to the Theorem of Corresponding States.
In this paper, compressibility factors of pure hydrocarbons were com
puted to see if they were applicable to the Theorem of Corresponding
States. The predicted compre~sibility factors were within ± 0.01 of
the experimental values for the pure components. 141
In a paper by Davis, Bertuzzi, Gore, and Kurata a mathematical
technique for predicting critical points of mixtures is presented. 151 This technique for predicting critical points is the one used in this
study. This technique as well as Benedict's equation can be found in
Appendices A, B, and c.
5
III. DISCUSSION
!:.:_ EQUATIONS
.!:.. COMPRESSIBILITY
The equation used to compute compressibility in this study is the
Benedict-Webb-Rubin Equation of State which is:
Z = 1 + (Bo - ~- ~~3 )y-1 + (b - ~)y-2 + nT- y-5
+ ~ v-2 (1 + yV-2) exp (-yv-2) RT.,) • • •
(8)
In order to obtain molal volume for the above equation, another
form of the Benedict-Webb-Rubin Equation of State is used. This
equation is:
where:
-2 B2(T) = BoRT - Ao - CoT ;
Bj(T) = (bRT- a);
B6(T) = aa
(9)
(10)
( 11)
{12)
{13)
The coefficients Ao, Bo, co. a. b. c, a, and y are independent
of temperature and of molal volume.
The pressure equation was solved by a trial and error procedure
(Explained in Appendix A).
6
In order to obtain the coefficients Ao, Bo, Co, a, b, c, ~. and y
the mixing rules proposed by Benedict 161 were used. These rules are:
N Bo = l: n. Bo 1• ( 14)
. 1 1 1=
Ao = D "; (Ao;l~ 2 ( 15). 1
~ N ~ 2 (16) Co = l: n. (Co.) 2
i=1 1 1
~N (b; )1/3] 3 b = l: n. {17) i=1 1
a = l n. ~N i=1 1
(•;ll/~ 3 (18)
c = ~N l: n. =1 1
(c;ll/~ 3 (19)
~ = ~N l n. =1 1
(a;) 1/3] 3 (20)
y = r r n. (y1. )~l 2 G=1 1 J {21)
Where possible, the experimental critical pressure and tempera
ture were used in order to calculate reduced pressure (Pr) and
reduced temperature (Tr).
~ CRITICAL POINTS
When the critical pressure and temperature were not known, the
technique for predicting critical points presented by Davis, Bertuzzi,
Gore, and Kurata was used. 151 This method applies a set of corrections
to the weight average pseudo-critical temperature (mT~) and a set of
7
corrections to the molal average pseudo-critical pressure (P~). The
uncorrected equations are:
with:
n mT 1 = .I m. (Tci) .
c 1 ' 1=1
n p• = c l n.
i=1 1 (Pci)
n m1. = n1M1. I l n.M.
. 1 1 1 1=
where:
m. = weight fraction of the ith component 1
Tci = critical temperature of the ith component
Pci = critical pressure of the ith component
n1 = mole fraction of the ith component
Mi = molecular weight of the ith component
Davis says that: lSI
Tc - mT~ = A1,2 m1 m2 + A1,3 m1 m3 +
+ A2,3 m2 m3 + A2,4 m2 m4 +
+ •••
(22)
(23)
{24)
...
... (25)
where a term is included for each possible binary system. In order to
predict critical pressure a M* is calculated by:
n M* = l n. M.
i=l 1 1 (26)
Then the Tc (this is the predicted critical temperature of the
mixture) along with the P~ is determined and from a chart which is a
8
plot of Tc P~ I Pc with M* as a parameter, the critical pressure (Pc)
is then calculated.
~ MIXTURES USED IN CORRELATION
The mixtures used in this study were taken from the paper by
Davis. 151 The composition of these mixtures are shown in Table I.
The other mixtures were taken from a Masters Thesis by Mr. P. K.
Taneja. 171 The compositions of these mixtures are shown in Table II.
TABLE I
COMPOSITION OF MIXTURES BY DAVIS j5j
~ A-2 A-3 A-4 AB-2 AB-3 B c 0
Carbon Dioxide, t:1ol e % 1.09 1.00 0.91 0.30 0.20 0.13 0.20 0.25
Helium -- -- -- -- -- 1.00 0.60 0.31
Methane 82.86 76.25 68.70 85.80 73.64 76.65 75.15 85.32
Ethane 4.01 3.69 3.33 1.50 1.20 5.51 6.10 4.11
Propane 1.74 1.60 1.44 0.60 0,53 3.35 3.27 1.98
i-Butane 0.30 0,28 0.30 0.12 0.10 0.35 0,38 0.37
n-Butane 0.55 0.51 0.40 0.18 0.15 0.90 0.60 0.39
i-Pentane 0.19 0.18 0.16 0.06 0.05 0.17 0.20 0.22
n-Pentane 0.12 0.11 0.10 0.04 0.04 0.15 0,20 0.22
Hexanes 0.14 0.12 0.11 0.04 0,04 0.33 0.20 0.22
Heptanes + * 0.16 0.15 0.14 0,06 0.05 0.33 0,20 0.22
Nitrogen 8.84 16.11 24.41 11.30 24.00 11.46 13.50 7.05
*Heptane and higher hydrocarbon components
1.0
TABLE II
COMPOSITION OF MIXTURES BY TANEJA 171
Gas 1 2 3 -Methane, Mole Frac. 0.9707 0.94026 0.9110
Nitrogen 0.0270 0.05528 0.08453
Helium 0.0022 0.004559 0.0043179
4
0.90598
0.08405
0.009967
..... 0
~ METHOD OF CORRELATION
The method of correlation used in this study was to plot devia
tion in computed compressibility factors, using the Benedict-Webb
Rubin equation of state, versus reduced pressure at constant reduced
temperatures for different mole % of Nitrogen.
11
Tables 3 through 7 are taken directly from a paper by Davis. 151
Tables 8 through 9 are taken from a Master•s Thesis by Taneja. 171
Tables 10 through 19 are the result of this study. The -- in the
tables show that no information was available.
12
IV. RESULTS
The results of this study are shown in Figures 1-5. In Figures
1 through 3 the results of the deviation versus pressure at different
mole % Nitrogen at constant reduced temperature are shown for the
mixtures presented by Davis. In Figures 4 and 5 the results for the
mixtures presented by Taneja are shown. Because of the closeness of
the critical temperatures the mean was taken as Tc for all mixtures,
(± .85%). In both cases no effort was made to calculate compressi
bilities of any of the mixtures from the graphs, instead; the actual
results are plotted to show the relationship to each other.
Because there is no available data on Carbon Dioxide, as far as
Benedict-Webb-Rubin is concerned, the coefficients for Ethane were
used when Carbon Dioxide was present. IBI Also since there is no coefficient calculated for Helium it was
disregarded in the calculation of compressibility factors. This was
possible because of the small mole% of Helium present in the mixtures
and since the mixing rules for the Benedict-Webb-Rubin are based on a
mole % average.
As can be seen in Figure 3, the correlation is not good for low
values of PR and TR. This is to be expected, because the Benedict
Webb-Rubin equation is not applicable in the two phase region.
Therefore it is not possible to correlate compressibility factors in
that region with this technique.
Although Table XX and Table XXI were not plotted, each table was
prepared to show that the method of correlation used in this study
was not valid in the two phase region.
13
Correlation, in Figures 1 through 3, below values of the critical
temperature and pressure are coincidental and should not be used.
In Figures 4 and 5, Mixture 4 which contains 8.405 mole % of
Nitrogen seems to be out of line. This is probably caused by an
inaccurate prediction of critical pressure. The critical pressure
predicted for Mixture 4 is probably too high and should have been
lower. This would cause the curve to be shifted upwards and also
flattened out. As can be seen, if too high a predicted critical
pressure is actually the case then the two curves of ~1ixture 3 and
Mixture 4 should nearly coincide.
PR A-2
0.20 0.939
0.40 0.880
0.60 0.811
0.80 0.748
1.00 0.687
1.20 0.617
1.40 0.543
1.60 0.468
1.80 --
TABLE III
EXPERIMENTAL COMPRESSIBILITY FACTORS
TR = 1.10
A-3 A-4 AB-2 AB·3
0.940 0.937 -- 0.945
0.878 0.876 -- 0.896
0.807 0.807 -- 0.839
0.740 0.741 -- 0.774
0.667 0.677 -- 0.687
0.596 0.607 -- 0.598
0.524 0.546 -- 0.530
0.464 0.483 -- --0.403 0.421 -- --
B
0.930
0.870
0.804
0.774
0.690
0.630
0.572
0.504
0.450
c
0.937
0.880
0.806
0.736
0.673
0.610
0.555
0.494
0.434
.... •
TABLE IV
EXPERIMENTAL COMPRESSIBILITY FACTORS
T R = 1.00
PR A-2 A-3 A-4 AB-2 AB-3
0.20 0.920 0.912 0.905 0.924 0.911
0.40 0.837 0.825 0.810 0.845 0.829
0.60 o. 742 0.733 0.713 0.750 0.736
0.80 0.622 0.622 0.616 0.618 0.610
1.00 0.460 0.490 0.508 0.427 0.436
1.20 0.322 0.347 0.396 0.286 0.280
1.40 0.240 0.247 0.290 -- --1.60 -- -- -- -- --1.80 -- -- -- -- --
B c
0.910 0.910
0.828 0.820
0.740 0.720
0.646 0.617
0.550 0.509
0.452 0.411
0.370 0.337
0.302 0.302
0.262 0.222
D
0.917
0.830
0.735
0.621
0.485
0.340
0.250
~
0'1
TABLE V
EXPERIMENTAL COMPRESSIBILITY FACTORS
TR = 0.95
PR A-2 A-3 A-4 AB-2 AB-3
0.20 0.910 0.896 0.894 0.915 0.890
0.40 0.800 0.780 0.810 0.809 0.774
0.60 0.660 0.649 0.712 0,644 0.636
0.80 0.460 0.620 0.615 0.395 0.418
1.00 0.250 0.490 0.507 0.150 0.212
1.20 0.170 0.348 0.396 -- --1.40 0.205 0.248 0.290 -- --1.60 -- -- -- -- --1.80 -- -- -- -- --
B c
0.894 0.888
0.790 0.772
0.680 0.638
0.554 0.486
0.513 0.340
0.303 0.270
0.254 0.240
0.260 0.230
0.294
D
0.903
0.781
0.643
0.444
0.280
0.201
0.201
.... 0'1
TABLE VI
EXPERIMENTAL COMPRESSIBILITY FACTORS
TR = 0.90
PR A-2 A-3 A-4 AB-2 AB-3
0.20 0.880 0.877 0.855 0.899 0.860
0.40 0.720 0.694 0.699 0.715 0.690
0.60 0.479 0.470 0.511 0.389 0.421
0.80 0.190 0.245 0.311 -- --1.00 0.134 0.160 0.168 -- --1.20 -- -- -- -- --1.40 -- -- -- -- --1.60 -- -- -- -- --
B
0.855
0.702
0.538
0.390
0.284
0.235
----
c
0.850
0.688
0.505
0.329
0.211
0.180
0.188
0.204
D
0.873
0.706
0.490
0.248
0.162
0.185
0.221
.... ....,
TABLE VII
EXPERIMENTAL COMPRESSIBILITY FACTORS
TR = 0.85
PR A-2 A-3 A-4 AB-2 AB-3
0.20 0.802 0.786 0.780 0.828 0.821
0.40 0.580 0.501 0.551 0.537 0.502
0.60 0.182 0.230 0.320 -- 0.156
0.80 -- 0.110 0.127 -- --1.00 -- 0.150 -- -- --
B c
0.810 0.800
0.601 0.538
0.360 0.302
0.176 0.202
0.139 0.173
D
0.820
0.501
0.210
0.160
0.170
.... co
PR 1
1.184 0.796
1.775 0.706
2.367 0.698
2.959 0.738
3.551 0.806
4.143 0.878
4.734 0.958
5.326 1.058
5.918 1.142
TABLE VIII
EXPERIMENTAL COMPRESSIBILITY FACTORS
TR = 1.28
PR 2 PR 3
1.175 0.782 1.012 0.776
1.762 0.710 1.518 0.697
2.349 0.695 2.024 0.686
2.937 0.732 2.530 0.718
3.524 0.788 3.036 0.780
4.112 0.856 3.542 0.846
4.699 0.930 4.048 0.920
5.286 1.000 4.554 0.998
5.874 1.074 5.059 1.078
PR
1.109
1.664
2.218
2.773
3.327
3.882
4.437
4,991
5.546
4
0.762
0.701
0.694
0.736
0.800
0.871
0.946
1.028
1.104
..... 'Ci
TABLE IX
EXPERIMENTAL COMPRESSIBILITY FACTORS
TR = 1.40
PR 1 PR 2 PR 3
1.184 0.840 1.175 0.831 1.109 0.849
1. 775 0.786 1.762 0.778 1.664 0.802
2.367 0.773 2.349 0.758 2.218 0.790
2.959 o. 791 2.937 0.774 2.773 0.802
3.551 0.836 3.524 0.812 3.327 0.840
4.143 0.896 4.112 0.864 3.882 0.890
4.734 0.962 4.699 0.924 4.437 0.949
5.326 1.037 5.286 0.988 4.991 1,014
5.918 1.104 5.874 1.053 5.546 1.080
PR
1.004
1.506
2.007
2.509
3.011
3.513
4.015
4.517
5.018
4
0.842
0.800
0.788
0.806
0.848
0.908
0.962
1.022
1.094
N 0
TABLE X
C0~1PUTEO COMPRESSIBILITY FACTORS
TR = 1.10
PR A-2 A-3 A-4 AB-2 AB-3
0.20 0.931 0.936 0.949 -- 0.957
0.40 0.871 0.901 0.956 -- 0.957
0.60 0.825 0.899 1.015 -- 0.994
0.80 0.801 0.924 1.091 -- 1.050
1.00 0.798 0.966 1.171 -- 1.118
1.20 0.810 1.013 1.263 -- 1.189
1.40 0.830 1.065 1.345 -- 1.257
1.60 0.861 1.115 1.420 -- --1.80 -- 1.181 1.513 -- --
B
0.920
0.862
0.837
0.844
0.875
0.911
0.954
1.008
1.050
c
0.923
0.873
0.861
0.882
0.919
0.967
1.017
1.062
1.121
D
N .....
TABLE XI
COMPUTED COMPRESSIBILITY FACTORS
T R = 1.00
PR A-2 A-3 A-4 AB-2 AB-3
0.20 0.907 0.916 0.938 0.924 0.947
0.40 0.826 0.880 0.973 0.864 0.963
0.60 0.775 0.896 1.061 0.830 1.026
0.80 0.762 0.945 1.164 0.827 1.108
1.00 0.777 1.008 1.275 0.847 1.197
1.20 0.809 1.079 1.381 0.877 1.290
1.40 0.842 1.148 1.492 -- --1.60 -- -- -- -- --1.80 -- -- -- -- --
B c
0.891 0.896
0.821 0.841
0.810 0.848
0.841 0.891
0.890 0.953
0.946 1.015
1.006 1.092
1.070 1.143
1.131 1.228
D
0.909
0.823
0.756
0.720
o. 718
0.734
0.761
N N
TABLE XII
COMPUTED COMPRESSIBILITY FACTORS
TR = 0.95
PR A-2 A-3 A-4 AB-2 AB-3
0.20 0.890 0.903 0.933 0.911 0.942
0.40 0.796 0.871 0.987 0.843 0.971
0.60 o. 747 0.903 1.092 0.814 1.052
0.80 0.747 0.966 1.215 0.822 1.151
1.00 0.774 1.038 1.338 0.852 1.254
1.20 0.819 1.115 1.464 -- --1.40 0.865 1.196 1.574 -- --1.60 -- -- -- -- --1.80 -- -- -- -- --
B c
0.872 0.879
0.798 0.825
0.802 0.848
0.849 0.909
0.913 0.978
0.976 1.056
1.052 1.135
1.111 1.219
1.183
D
0.892
0.790
0.717
0.693
0.703
0.732
0.768
N w
TABLE XIII
COMPUTED COMPRESSIBILITY FACTORS
TR = 0.90
PR A-2 A-3 A-4 AB-2 AB-3 B c D
0.20 0.868 0.888 0.929 0.895 0.937 0.848 0.858 0.871
0.40 0.761 0.863 1.007 0.820 0.984 0.774 0.810 0.749
0.60 0.721 0.914 1.134 0.799 1.085 0.800 0,853 0.677
0.80 0.741 0.994 1.272 -- -- 0.868 0.932 0.670
1.00 0.783 1.080 1.420 -- -- 0.939 1.015 0.699
1.20 -- -- -- -- -- 1.021 1.098 0.738
1.40 -- -- -- -- -- -- 1.194 0.778
1.60 -- -- -- -- -- -- 1.266
~
TABLE XIV
COMPUTED COMPRESSIBILITY FACTORS
TR = 0.85
PR A-2 A-3 A-4 AB-2 AB-3
0.20 0.841 0.869 0.927 0.874 0.933
0.40 o. 720 0.860 1.033 0.794 1.004
0.60 0.700 0.935 1.192 -- 1.132
0.80 -- 1.037 1.346 -- --1.00 -- 1.139 -- -- --
B c
0.818 0.832
0.753 0.799
0.806 0.870
0.888 0.962
0.981 1.070
D
0.844
0.698
0.639
0.659
0.701
N CJl
TABLE XV
COMPUTED COMPRESSIBILITY FACTORS
TR = 1.28
PR 1 PR 2 PR 3
1.184 0.766 1.175 0.809 1.109 0.852
1.775 0.709 1.762 0.791 1.664 0.867
2.367 0.706 2.349 0.815 2.218 0.914
2.959 0.732 2.937 0.855 2.773 0.956
3.551 0.774 3.524 0.900 3.327 1.032
4.143 0.821 4.112 0.948 3.882 1.092
4.734 0.878 4.699 0.997 4.437 1.146
5.326 0.935 5.286 1.045 4.991 1.202
5.918 0.996 5.874 1.096 5.546 1.253
PR
1.004
1.506
2.007
2.509
3.011
3.513
4.015
4.517
5.018
4
0.854
0.868
0.914
0.971
1.031
1.091
1.147
1.199
1.250
N 0\
TABLE XVI
COMPUTED COMPRESSIBILITY FACTORS
TR ~ 1.40
PR 1 PR 2 PR
1.184 0.831 1.175 0.834 1.109
1.775 0.783 1.762 0.813 1.664
2.367 0.770 2.349 0.828 2.218
2.959 0.785 2.937 0.862 2.773
3.551 0.814 3.524 0.904 3.327
4.143 0.852 4.112 0.949 3.882
4.734 0.898 4.699 0.995 4.437
5.326 0.947 5.286 1.041 4.991
5.918 0.995 5.874 1.090 5.546
3 PR
0.883 1.004
0.884 1.506
0.913 2.007
0.957 2.509
1.007 3.011
1.057 3.513
1.108 4.015
1.157 4.517
1.205 5.018
4
0.884
0.885
0.914
0.957
1.007
1.056
1.106
1.155
1.203
1'\) ......
t."i.:' ~ :·, ...
PR
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
TABLE XVII
EXPERIMENTAL MINUS COMPUTED COMPRESSIBILITY FACTORS
T R = 1.10
A-2 A-3 A-4 AB-2 AB-3 B
+0.006 +0.004 -0.012 -- -0.012 +0.010
+0.009 -0.023 -0.080 -- -0.061 +0.008
-0.014 -0.092 -0.208 -- -0.155 -0.033
-0.053 -0.176 -0.350 -- -0.276 -0.100
-0.111 -0.299 -0.494 -- -0.431 -0.185
-0.193 -0.417 -0.656 -- -0.591 -0.281
-0.287 -0.541 -0.799 -- -o. 121 -0.382
-0.393 -0.651 -0.937 -- -- -0.500
-- -o. 778 -1.092 -- -- -0.600
c
+0.014
+0.007
-0.055
-0.146
-0.246
-0.357
-0.462
-0.568
-0.687
D
N ()0
TABLE XVIII
EXPERIMENTAL MINUS COMPUTED COMPRESSIBILITY FACTORS
TR = 1.00
PR A-2 A-3 A-4 AB-2 AB-3
0.20 +0.013 -0.004 -0.033 +0.000 -0.036 --0.40 +0.011 -0.055 -0.163 -0.019 -0.134 --0.60 -0.033 -0.163 -0.348 -0.080 -0.290 --0.80 -0.140 -0.323 -0.548 -0.209 -0.498 --1.00 -0.317 -0.518 -0.767 -0.420 -0.761 --1.20 -0.487 -0.732 -0.985 -0.591 -1.010 --1.40 -0.602 -0.901 -1.202 -- .... --1.60 -- -- -- -- -- --1.80 -- -- -- -- -- --
6 c
+0.014
-0.021
-0.128
-0.274
-0.444
-0.604
-0.755
-0.841
-1.006
D
+0.008
+0.007
-0.021
-0.099
-0.233
-0.394
-0.511
N
"'
TABLE XIX
EXPERIMENTAL MINUS COMPUTED COMPRESSIBILITY FACTORS
TR = 0.95
PR A-2 A-3 A-4 AB-2 AB-3 B
0.20 +0.020 -0.007 -0.039 +0.004 -0.052 +0.022
0.40 +0.004 -0.091 -0.177 -0.034 -0.197 -0.008
0.60 -0.087 -0.254 i. -0.380 -0.170 -0.416 -0.122
o.8o -0.287 -0.346 -0.600 -0.427 -0.733 -0.295
1.00 -0.524 -0.548 -0.831 -0.702 -1.042 -0.400
1.20 -0.649 -0.767 -1.068 -- -- -0.673
1.40 -0.660 -0.948 -1.284 -- -- -0.798
1.60 -- -- -- -- -- -0.851
1.80 -- -- -- -- -- -0.889
c
+0.009
-0.053
-0.210
-0.423
-0.638
-0.786
-0.895
-0.989
0
+0.011
-0.009
-0.074
-0.249
-0.423
-0.531
-0.567
w 0
TABLE XX
EXPERIMENTAL MINUS COMPUTED COMPRESSIBILITY FACTORS
TR = 0.90
PR A-2 A-3 A-4 AB-2 AB-3 B
0.20 +0.012 -0.011 -0.074 +0.004 -0.077 +0.007
0.40 -0.041 -0.169 -0.308 -0.105 -0.294 -0.072
0.60 -0.242 -0.444 -0.623 -0.410 -0.664 -0.262
0.80 -0.551 -o. 749 -0.961 -- -- -0.478
1.00 -0.649 -0.920 -1.252 -- -- -0.655
1.20 -- -- -- -- -- -0.786
1.40 -- -- -- -- -- --1.60 -- -- -- -- -- --
c
-0.008
-0.122
-0.348
-0.603
-0.804
-0.918
-1.006
-1.062
D
+0.002
-0.043
-0.187
-0.422
-0.537
-0.553
-0.557
w ....
TABLE XXI
EXPERIMENTAL MINUS COMPUTED COMPRESSIBILITY FACTORS
T R = 0.85
PR A-2 A-3 A-4 AB-2 AB-3 B
0.20 -0.039 -0.083 -0.147 -0.046 -0.112 -0.008
0.40 -0.140 -0.359 -0.482 -0.257 -0.502 -0.152
0.60 -0.518 -0.705 -0.872 -- -0.976 -0.446
0.80 -- -0.927 -1.219 -- -- -0.712
1.00 -- -0.989 -- -- -- -0.842
c
-0.032
-0.261
-0.568
-0.760
-0.897
D
-0.024
-0.197
-0.429
-0.499
-0.531
w 1\l
TABLE XXII
EXPERIMENTAL MINUS COMPUTED COMPRESSIBILITY FACTORS
TR :: 1.28
PR 1 PR 2 PR 3
1.184 +0.03 1.175 -0.027 1.109 -0.076
1.775 -0.003 1.762 -0.081 1.664 -0.170
2.367 -0.008 2.349 -0.120 2.218 -0.228
2.959 +0.006 2.937 -0.123 2.773 -0.258
3.551 +0.032 3.524 -0.112 3.327 -0.252
4.143 +0.057 4.112 -0.092 3.882 -0.246
4.734 +0.080 4.699 -0.067 4.437 -0.226
5.326 +0.1233 5.286 -0.045 4.991 -0.204
5.918 +0.1461 5.874 -0.022 5,546 -0.175
PR
1.004
1.506
2.007
2.509
3.011
3.513
4.015
4.517
5.018
4
-0.092
-0.167
-0.220
-0.235
-0.231
-0.220
-0.201
-0.171
-0.146
w w
TABLE XXIII
EXPERIMENTAL MINUS COMPUTED COMPRESSIBILITY FACTORS
TR = 1.40
PR 1 PR 2 PR 3 PR 4
1.184 +0.009 1.175 +0.022 1.109 -0.034 1.004 -0.042
1.775 +0.003 1.762 -0.014 1.664 -0.082 1.506 -0.085
2.367 +0.003 2.349 -0.057 2.218 -0.123 2.007 -0.126
2.959 +0.006 2.937 -0.081 2.773 -0.155 2.509 -0.151
3.551 +0.022 3.524 -0.088 3.327 -0.167 3.011 -0.159
4.143 +0.044 4.112 -0.084 3.882 -0.167 3.513 -0.148
4.734 +0.064 4.699 -0.073 4.437 -0.159 4.015 -0.144
5.326 +0.090 5.286 -0.054 4.991 -0.143 4.517 -0.133
5.918 +0.109 5.874 -0.043 5.546 ·0.125 5.018 -0.109
~
TABLE XXIV
CRITICAL TEMPERATURES AND PRESSURES OF THE MIXTURES
Mixture T p c c
1 339.6* 884.9*
2 336.0* 851.27*
3 332.6* 901.6*
4 332.3* 996.3*
A-2 368. 955.
A-3 356. 968.
A-4 340. 973.
AB-2 343. 790.
AB-3 329. 815.
B 376. 1143.
c 370. 1107.
D 364. 918.
*These values are calculated, all others are experimental values. (see Appendices B and C)
35
36
Mole % N2 .-40 - 0 1.0 ~ q-O -Lt) q-. . . • • . ~~ 1.0 M .-4 00 ---1.80
1.60
1.40 <IJ s.. :::::1 1.20 en en <IJ s..
Q..
"C 1.00 <IJ u :::::1
"C <IJ 0.80 ex II
ex Q..
0.60
0.40
0.20
o.o -1.8 -1.6 -1.4 -1.2 -1.0 -.8 -.6 -.4 -.2 0
Correction Factor For z
Fig. 1: CORRELATION OF Z TR = 1.10
o.o
LO 0 . "'
-1.8 -1.6 -1.4 -1.2 -1.0 -.8 -.6 -.4 -.2 0 Correction Factor For Z
Fig. 2: CORRELATION OF Z TR = 1.00
37
38
Mole % N2 ..... 0 \0 tS ..... Ln od" . . . . \0 M ..... co ..... ..... .....
1.80
1.60
1.40
cv 1.20 s-:s Ill Ill
~ 1.00 Q.
'"0 cv (,J :s 0.80 '"0 cv ex: II
ex: 0.60 Q.
0.40
0.20
o.o -1.8 -1.6 -1.4 -1.2 -1.0 -.8 -.6 -.4 -.2 0
Correction Factor For Z
Fig. 3: CORRELATION OF Z TR = 0.95
39
Mole% N2 M In co In 0 N 0 .q .q In ....... . . . . co co In N
6.0
5.0
4.0
f :::J lit lit 3.0 (lJ
'-c.. ~ (lJ u :::J
"'tJ Ql
c:z::: II 2.0
c:z::: c..
1.0
0.0~--~--~~--~--~----~--_. ____ ._ __ _. __ ~ -.30 -.25 -.20 -.15 -.10 -.05 0 0.05 0.10 0.15
Correction Factor For Z
Fig. 4: CORRELATION OF Z TR = 1.28
cu s.. :::1
"' en QJ s..
c... "'0 cu u :::1
"'0 QJ
0:::
II
0::: c...
6.0
5.0
4.0
3.0
2.0
1.0
o.o
M 1.0 "d" . 00
00 N L.O
-.30 -.25 -.20 -.15 -.10 -.05 0 0.05 0.10 0.15
Correction Factor For Z
Fig. 5: CORRELATION OF Z TR ~ 1.40
40
41
V. CONCLUSIONS AND RECOMMENDATIONS
The investigation of the varying hydrocarbon systems presented in
this study would tend to indicate that Helium's effect on the compress
ibility factors of these mixtures is to raise the critical point and
that should the critical points of a mixture be known it would then be
possible to predict compressibility factors of mixtures which contain
nitrogen by use of the Benedict-Webb-Rubin equation and a correction
graph for nitrogen. This study seems to indicate that as soon as it
is possible to predict critical points more accurately than is now
possible that charts may be drawn to correlate compressibility factors
over a wide range o~ temperatures and pressures.
It would be interesting to tabulate and study a wide variety of
binary systems to see if a mixing rule as proposed by Lorentz 131 could be used to correct the Benedict-Webb-Rubin equation directly.
If this were possible then most compressibility factors could be cal
culated with one basic equation.
Also a refinement of the method of predicting critical points
used in this study might be found to predict critical points more
accurately.
VI. BIBLIOGRAPHY
1. Kay, W. B. 11 Density of Hydrocarbon Gases and Vapors at High Temperatures and Pressure," Ind. Eng. Chern., vol. 28, 1014, (1936).
2. Amyx, J. W., Bass, M. B., Jr., and Whiting, R. L. Petroleum Reservoir Engineering, McGraw Hill Book Co., New York, (196o}.
3. Opfell, J. B., Pings, c. J., and Sage, B. H. 11 Equations of State for Hydrocarbons, .. API Research Project 37, (1952).
4. Opfell, J. B., Sage, B. H., and Pitzer, K. s. 11Application of Benedict Equation to Theorum of Corresponding States, .. Ind. Eng. Chern., vol. 48, 2069-2076, (Nov. 1956). ----
5. Davis, P. c., et al. "The Phase and Volumetric Behavior of Natural Gases at Low Temperatures and High Pressures, .. Petroleum Transactions. A.I.M.E., vol. 201, 245-251, (1954).
42
6. Benedict, M., Webb, G. B., and Rubin, L. C. "An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures, Constants for Twelve Hydrocarbons," Chemical Engineering Progress, vol. 47, 419-422, (August, 1951).
7. Taneja, P. K., "A Comparative Study of Experimental and Computed Compressibility Factors of Methane-Nitrogen-Helium System, .. Master's Thesis at the University of Missouri at Rolla, (July, 1971}.
B. Wilson, T. c., and Park, E. Personal interview, July 1, 1971.
9. Muckleroy, J. A. Bibliography on Hydrocarbons, 1946-1960, Natural Gas Producers Association, Tulsa, Oklahoma, {1962).
43
VII. VITA
Terry Wayne Buck was born May 23, 1948 in Kennett. Missouri. He
received his primary and secondary education in Hornersville, Missouri
and in Senath, Missouri. He enrolled in the University of Missouri at
Rolla in September 1966. He received a Bachelor of Science degree in
Petroleum Engineering in August of 1970.
He has been enrolled in the Graduate School of the University of
Missouri at Rolla since September of 1970.
APPENDIX A
SAMPLE CALCULATION FOR C0~1PRESSIBILITY FACTORS
First the coefficients of the Benedict-Webb-Rubin Equation of
State must be calculated.
Bo was calculated in the following way with the other seven
coefficients calculated similarly:
n
45
Bo= l n.Bo. i=1 1 1
(A-1)
with:
n = number of components
ni = mole fraction of the nth component
Boi = individual coefficient for that particular component
CALCULATION OF Bo FOR MIXTURE 1
n = 3
"1 = .9707 (Hethane)
n = 2 .0270 (Nitrogen)
n3 = .0022 (Hel i urn)
Since Helium was disregarded in Calculation of Compressibility
factor Bo 3 = 0.0 (Helium)
Bo 1 = 0.682401 (Methane)
Bo2 = 0.733661 (Nitrogen)
Bo = (0.682401) {0.9707) + 0.733661 (0.0270) + o.o (0.0022)
Bo = .682215
46
Next a molal volume must be calculated to use in the calculation
of compressibility factor. The equation in P was used with a trial
and error procedure on V: •
P = B1(T)/y + B2(T)ty 2 + Bj(T}ty3 + a6(T)/y 6
+ c/V3T2 (1 + yV-2) exp (-yv-2) . . . where:
a1 (T) = RT;
B2(T) = BaRT -Ao -CoT-2;
B3{T) = {bRT -a);
a6(T) = aa
and:
(A-2)
(A-3)
(A-4)
(A-5)
(A-6)
Ao, Bo, Co, b, c, a, and y = Benedict-Webb-Rubin coefficients
For a set P and T, a V is assumed to be 0.5 then P is calculated •
from the above equation. If the Pcalc.<calculated) is greater than
the Pset an increment of 0.005 is added to y and a new P is calculated
and so on until Peale. is less than Pset and that volume is used for
the compressibility equation. The computer was used to calculate this
pressure.
~XAMPLE CALCULATION OF MOLAL VOLUME OF MIXTURE 1 WITH P = 1000. psig
AND T = 470° R
Ao = 6888.60
Bo = 0.682215
Co = 267,276,000.
c = 723,527,000.
b = 0.849957
a = 2885.03
a. = 1. 54237
y = 0.521307
An example of computer output for different values of V is: . Assume V = 0.5
•
From Equation (A-2)
81(470) = 5044.70
82(470) = -4656.94
83(470) = 1402.79
86(470) = 4449.78
p = 299.517
Because Peale. is greater than Pset• a new value is selected by the
computer.
v = 0.505 . Peale. = 280.928.
and •••
Until V ,., 4.130 •
Peale. = 1015.75 psia
Peale. is greater than Pset
So V = 4.135 •
P = 1014.68 psia
p 1 is less than P ca c. set
Use V = 4.135 for compressibility factor calculation .
47
48
CALCULATION OF COt4PRESSIBILITY FACTOR \HTH P = 1000. psig AND T = 470° R
Z = 1 + (Bo - Ao/RT - Co/RT3) v- 1 + {b - a/RT) v-2 • •
With coefficients as previously mentioned and T = 470° Randy = 4.135
z = 0.831
APPENDIX B
SAMPLE CALCULATION OF CRITICAL TEMPERATURES
FOR MIXTURES 1 THROUGH 4
For calculation of critical temperature the weight average
critical temperature (mT~) was first calculated:
n
49
mT 1 = I m. T . C i= 1 1 Cl
(B-1)
where:
n = number of components.
m = mass fraction of individual component
Tci = critical temperature of individual component
with mi defined as:
where:
n = number of components
x1 = mole fraction of individual component
M1 = molecular weight of individual component
CALCULATION OF WEIGHT AVERAGE CRITICAL TEMPERATURE FOR MIXTURE
Component X M xM m T 0 R c
c1 0.9707 16.04 15.57 0.9529 343.4
N2 0.0270 28.02 0.76 0.0465 227.0
He 0.0022 4.00 0.01 0.0006 9.45
(B-2)
1
mT c 327.2
10.6
16.34 1.0000 mT • = 337.8 c
Next a correction factor was applied to the weight average
critical temperature according to:
Tc - mT~ = A1,2 m1 m2 + A1,3 m1 m2 + ... + A2,3 m2 m3 + A2,4 m2 m4 + •••
... + •••
where:
Tc = corrected critical temperature
A1, 2• A1,3• A2, 3• ••• = correction factor read from the
literature lSI CALCULATION OF CRITICAL TEMPERATURE FOR MIXTURE
m
c1 0.9529
r~2 He 0.0006
(N2)
c1 He 0.0006
(Cl)
T = mT 1 + 1 8 c c •
T = 337.8 + 1.8 = 339.6° R c
A
41.0
Not Given
0.0465 X
Not Given
0.9529 X
1
rnA
39.1
... 39.1 = + 1.8
...
... = ... + 1.8
50
(B-3)
APPENDIX C
SAMPLE CALCULATION OF CRITICAL PRESSURES
FOR MIXTURES 1 THROUGH 4
51
The correlation of critical pressures was made through a method
presented by Davis. lSI The correlation is a plot of TcP~ I Pc versus T~ with Mas a
parameter.
where:
with:
Tc = calculated critical temperature
T' = molal average critical temperature c
P' = molal average critical pressure c
PC = corrected critical pressure
M = arbitrary correlation variable for nitrogen
n T' = I n. T .
C i=l 1 C1
n = number of components
ni = mole fraction of individual component
Tci = critical temperature of individual component
n P' = I c i=l
n. P • 1 C1
where:
Pci =critical pressure of the individual component
(C-1)
(C-2)
52
n M* = l n. Mi
i=1 1 {C-3)
where:
Mi = molecular weight of the individual component
Once Tc• Pc• M, and T~ are calculated TcP~ I Pc is read off of
the graph and Pc is calculated by:
Pc = (Value off of graph) (Tc P~)
In order to account for helium 100 psi is added to the calculated
critical pressure for each mole %of helium present.
CALCULATION OF CRITICAL PRESSURE FOR MIXTURE 1
T = 339.6° R c
P' = 0.9707 (673) + 0.0270 {491) + 0.006 (33.2) c
P' = 666.7 c
T' = 0.9707 (343.4) + 0.0270 (227) + 0.006 (9.45) c
T' = 339.49 c
M = 16.34
T P' I P = 339.49 (666.7) I Pc = 275 c c c
p = 822.9 + 22 (correction for Helium) c
P = 844.9 psia c
53
IX. NOMENCLATURE
Ao,Bo,Co,a,b,c,a, and y = Benedict-Webb-Rubin coefficients
c
M*
mT' c
= Correction factor dependent on temperature,
pressure, and mole %nitrogen
= Arbitrary correlating number
= Weight average pseudo-critical temperature
=Molecular weight of ith component
= Absolute pressure, psia
= Mole average pseudo-critical pressure
= Absolute critical pressure of the ith campo-
nent
= Pseudo-reduced pressure
= Universal Gas Law constant
= Absolute temperature, oR
= Corrected critical temperature
= Mole average pseudo-critical temperature
= Absolute critical temperature of the ith
component
= Pseudo-reduced temperature
= Volume
= Specific volume
= t-1ol e fraction of i th component
= ~Dle fraction of nitrogen component
= Compressibility factor
=Additive compressibility factor