a?
Sooietyof Pddwll a’fgirlec?rs
SPE 26668
Compressibility
Factors for Naturally Occurring Petroleum Gases
L.D. Piper, Texas A&M U.; W.D. McCain Jr., S,A, Holditch & Assocs. Inc.; and J.H, (lorredor,
Inters Petroleum Production Div.
SPE Members
COpyrighl 1993, Sc@efy of Petroleum Englneam Inc.
Thta paper was prepared for presentation at the 66fh Annual Technical Conferenw and Exhibition of the $ocie!y of Petroleum Engineers held In Houston, Texas, 3-6 October 1993.
Thle paper was selected for presentation by an SPE Program Committee following review of information contelnad In an abstrect submitted by the author(a). Contents ot the paper.
as praaantad, have not been ravlewad by the Soclafy of Petroleum En@eara and are eublect to C-Jrrecfionby the author(a). The material. as Preee~ted. doee not necessarily reflect
MY poaitlon of the SocIefy of Petroleum Engineere. IISoffiwra, or members. Pepara preeonled al SPE maatin?lsare eub]act to publication review by Editorial Commlftaos of the Soclaty
of Petroleum Enginaare. Permieelonto coPy lareetricfed to an abstract of not more than 3@ worde. Illuslratione may not be copied. The absfrdcf should contsln conspicuous acknowledgment
of where and by whom tha paper is praeantad. Write Librarian, SPE, P.O. Box S33836, Richardson, TX 76083-3S36. U.S.A. Talex, 1S3246 SPEUT.
The Sutton gas specific gravity correlation gives values of
pseudocritical properties which, when used with the Dranchuk
and Abou-Kassem (DAK) representation of the Standing and
Kak (SK) chtW currentiy provide the most accurate estimatesof
compressibility factors for naturally occurring petroleum gases.
However, other correlations must be used to account for the
presenceof acid gases. A new gas specific gravity correlation is
presented which takes into account the effects of the acid gases
and nitrogen. The new correlation provides more accurate
estimates of the compressibility factor than can be obtained by
current methods and also elimimtes the need for involving
additional correlations to comet for the presence of acid gases
and nitrogen. The new correlation was developed using a set of
1482data points, ranging in composition flom lean sweet to rich
acid gases.
correspondingstates, Kay’spseudocriticalpointi and the SK chart
are commonly used. If the composition of the gas is known, the
pseudocriticaltemperature and pressure may be calculated using
Kay’s rules--molar averages of the critical properties of the
mixture’scomponents. Otherwise,the pseudocriticaltemperature
and pressure may be estimated using correlations based on gas
;pecific gravity. Then, the reduced temperature and pressure
nay be calculated and the SK chart or its representation by the
MK equationof state maybe used to determinethe z factor.
3utton2 presented more accurate methods for both cases, His
nethod for calculating the pseudocritical temperature and
pressurewhen the composition of the gas is known is based on
theStewti Burkhard4and Voo (SBV) equationsgiven by
TP=+nd~=r
‘w
. . . . . . . . . . ..(la)
where,
Knowledgeof the pressure-volume-tempemture(PVT) behavior
of natural gases is necessary to solve many petroleum
engineeringproblems. Gas reserves, gas metering, gas pressure
gradients, pipeline flow and compression of gases are some of
the problems requiring the gas compressibtity factor, or z factor.
Typically,the z factor is determined by laboratorymeasurement.
Howevex,laboratory data is only applicable for the compositions
and conditions investigated. When conditions of interest are
different from those of the laboratory studies or data is not
available,correlationsmust be used.
The basic methods for esthnating the gas compressibility factor
are relatively simple and well known] The principle of
His gas specitic gravity correlation for estimating the pseudctcritkal temperatureand pressure when the compositionof the gas
is known, based on 634 compositions from 275 PVT reports, is
given by
TP = 169.2-t 349,5ys - 74.Oy;,
and
~,=756.8 - 131.0yg - 3.6y;.
Referencesand illustrations at end of ~aper.
661
. “ o “ o (z)
*
R
SPE 26668
2
COMPRESSIBILITYFACTORSFOR NATURALLYOCCURRINGPETROLEUMGASES
mrect
these
deficiencies.
For
this
study,
we
added
586 data
If the gas contains hydrogen suikde or carbon dioxid;, the
Wichert and &iz correlation:
mints from 37 PVT reports from the literature5-13 and other
)ources14-15.Table 1 shows the range of composition, physical
‘rpc = TP -e,
)roperties, and conditions of the resulting data base. Our
where,
;xpanded data basu contains signitkrmtly more gases with
.6
ipeciilc gravities ranging from 1.3 to 1.8. Additionally, it
& = 120”[(yms+ ymf
- (Yms+ Yc
:ontains significantly more gases with impurities than the data
15“(Msr
- (yIt?sf,
MM used by Sutton. While the maximum concentrations of
[
~y&ogen sulilde and carbon dioxide are quite large, only ten
and,
xment of the samples had an acid gas concentmtiongreaterthan
,welvepercent.
ppcl-’pc
. . . . . . . ...6....(3)
+
“PC = Tp + y~l
1
-
d]
)@’
Updated Coefficients for Eqs. 4. Our previous arnlysis was
repeated using the expanded data base to develop the new
should be used to adjust the pseudocritical constants.2-3 wefficients for Eqs. 4 shown in Table 2. We then evaluated the
However, Ref. 2 is unclear on how Eqs. 3 should be applied to WV rules, Sutton’smodilkation to the SBV rules (SSBV) and
Eqs. 2.
Eqs. la and 4 using the expandeddatabase. The averageabsolute
wrors of the calculated compressibility factors were 2.23, 1.53,
In an earlier pape~, we discussed Sutton’smodification to the md 1.07percentirespectively. These results were consistentwith
SW rules in detail and presented a new modification which hose in Ref. 4 and are shown in Table 3, for four different
takes into account the effects of the heprane plus fraction, acid wbsets of the data ranging from lean sweet gases to rich acid
gases and nitrogen. TM correlation, having a form simii to the Bases,and Figs. 1 through 4. Figs. 2 and 4 show the distribution
SBV equations, was based on 896 data points from 134 PVT ~f the errors with the experimental z factor. Higher emors
reports and is given by
mwrred at lower z factors. Even though the gases in Sutton’s
database containedno hydogen sultlde and only limited amounts
of carbon dioxide and nitrogen, Uwz factors calculated using his
modification fitted the expanded data base very well. This fact
gives a great deal of confidence in the theoretical basis of the
formof the SBV equations.
~v~
and,
To evaluate the current gas specific gravity correlations, we first
assumed that the amount of impurites in the mixture was known.
The technique given by Standing3 for applying the Wichert and
Aziz correlation, Eqs. 3, was used to correct for the presence of
acid gases. We evaluated !Mnding’sreservoir gas correlationand
P6Yc#f@
+’P~Y’#j
Sutton’s comelation, Eqs. 2. The results of these calculations
(4)
using
our data base are shown in Table 3 and Fig. 5. The
+ MYc@fc&
average absolute error was 1.99 and 1.42 percent respectively.
where yI G {~, yma YN2}J y] = {Ye],Yc2#o.*YDC6}s
ad *e a: We then assumed that the amount of impurites in the mixture was
unknown. As maybe seen in Fig. 6, the error was as large as 27
and pi were shown in Table 3 of Ref. 4. E@. 4, usti with Eqs percent and the maximum error varied linearly with the amount
la and the DAK representation of the SK chrul provided mor~ of impuritiesin the rjxture.
accurate estimates of the compressibtity factor, simplified tht
~
procedures,and included the effects of nitrogen.
‘=’o+$fi’’k%),+”wd
H)] +
.,,...
This paper reports on further studies using a larger database. Wt
present an update for the coefficients of Eqs. 4, based on UN
expanded data base, and anew gas spec~lc gravity correlation
Both Eqs. 4 and the new correlation elhnhm the need for E@
3 and include the effects of nitrogev and can be used with Eqs
la to calculate more accurate estimates of the compressibility
factor.
Our objective was a method for estimating the pseudocxitical
constants when composition is not known which, if used with the
DAK representationof the SK cM@ more accuratelyreproduces
the experimental compressibility factors. The data discussed
above was used with the DAK equation of state and a
minimization procedure to detexminethe inferred paeudocritkal
constants. TLis set of inferred pseudocritical values was then
used with multiple regression analysis to develop a new
correlation for J and K to be used with Eqs. lain calculating
values for the pseudocritical point, We later refer to the new
Our previous work on gas compressibdity cormdations used I method as the proposed gas specificgravity correlation.
data base with a limited number of high specific gravity gase
and gases with high impurities content. The data set has bee] Procedure. A muhidimensional conjugate gradient algorithm16
expanded by about 60 %, with emphasis on adding gases u
was used to find the point on the ~r-Tw
sW= giv~ by the
SPE 26668
L. D. PIPER, W. D. MCCAIN, JR. AND J. H. CORREDOR
DAK representation of the SK chart which minimized the
difference between experimental and calculated z factors. The
experimental compressibility factor, pressure and temperature,
and pseudocritical constants calculated using Sutton’s
modification to SBV rules were used as initial guesses. The
algorithm converged for all the data points and returned values
for the inferred pseudociitical temperature and pressure. Based
on our previous finding, that much of the scatter in compming
calculated to inferred values of pseudodtical temperamre and
pressure, ocurred at the last steps of a depletion study--a dtificult
laboratory procedure, 121 data points were not used in our
correlations. We attempted but were unable to correlate the
infersedpseudocritkal tempemttureand pressurewith gas specitic
gravity because of the large amount of impurities in the gases of
OLU data base.
Inferred Values of J and K. The 1482 remaining pairs of the
inferred pseudocritkal constants and Eqs. la were used to find
the inferred valuesfor the SBV parameters 1 and K, as shown
below:
3
lkulte. To evaluate Eqs. la and 6, we again assumed that the
unount of hnpurites in the mixture was known, Figs. 9 and 10
:ompare values of the pseudocritical constants calculated using
Zqs. la and 6 with the inferred values. The results of z factor
xdculations are shown in Table 3 and Fig. 11. The average
ibsolute error of the calculated z factor was 1.30 percent using
he proposed correlation. We then assumed that the amount of
mpurites in the mixture was unknown. As indkated in Fig. 12,
he error was again as large as 27 percent and the maximumerror
wied linearly with the amount of impurities in the mixture.
rable 5 shows a comparison of emors made in using the gas
;peciflc gravity correlations when the amount of impurities are
mknown. Notice that the errors am relatively small if the gas is
lean and sweet. However, the errors can be laxge if the gas
xxttainsmore than five percent acid gas and is at a high pressure.
I%eright half of Fjg, 12 shows results from several samples
wntaining a large amount of impurities. The large errors are
attributableto high concentrations of acid gas alone. The large
ange in error at a constant compositionis attributableto variation
[npressure, Generally, the larger errors occurred at the Wtgher
pressures.
n
1. A set of z factors, temperatures, pressures, and gas
compositions covering a very wide range of naturally
occurring petroleum gases and nonhydrocarbon impurities
After finding that the inferred values of J and K were strongly
has been used to develop two new pseudocritical property
correlations for use in calculating z factors. These
related to the specific gravity of the gas mixture as can be
correlations may be used with confidence for any naturally
observed in Flge. 7 and 8, we decided to use a regression model
occumingpetroleum gas with an acid gas content as high as
similar to Eqs. 4, which was originally developedby Corredor17.
50 percentand ni$rogencontent as high as ten percent.
Notice the data points in the lower right half of both figures,
These two samples, which contain very high concentrations 01
carbon dioxide, obviously are omliers with respect to the 2. One proposed correlation, based on gas composition, is a
modification of the SBV mixing rules, which does not
relationships between J and K and specific gravity. The
require the use of other correlations for the properties of the
correlationscan be improved by omitting them; however, they
heptanes plus fraction or the effect of acid gas and nitrogen.
were retained in the database because they were correlatable by
This
correlation resulted in z factors which fitted the data
the mcdel discussedbelow.
base with an average absolute error of 1.1 percent and a
maximum error of 5.8 percent.
Proposed Specific Gravity Correlation. Multiple regression
techniques were used with the 1482 pairs of inferred J and K as
dependent variables to empirically find a correlation 3. The other proposed correlation,based on gas speci!lcgravity
and the amounts of nonhydrocarbon impurities in the gas,
incorporating the fmt four terms of Eqs. 4 and the gas specific
also
does not require the use of other correlations for the
gravity. The new cordations are given by E+. 6.
effect of acid gas and nitrogen. This correlationresulted in z
factors which fitted the data base with an average absolute
emorof 1.3percent and a maximum error of 7.3 percent.
4. The presenceof nonhydrocarbonimpurities in a gas must be
accounted for when using a gas specific gravity~orrelation.
Errors in z factors as high as 27 percent occurred when high
concentrationsof acid gas were ignored.
‘~re YiE {ysf$,yc~ yN2}, ad the Ui axld pi are shown in
TabIc 4. Eqs. 6 directly account for the effects of hydrogem
sulfide, carbon dioxide, and nitrogen, eliuinatiug the need fol
Eqs. 3. The new method for calculating the z factor uses onl~
Eqs. 1a and 6 and the DAK representationof the SK chart. Nott
that the new method is simplier than current methods. Whik
Eqs. 6 contains terms similar to those in Eqs. lb, the introduction
of terms for nonhydmcarbongases is a departurefrom the currenl
melhod.
663
J
K
MC:
P
PG
= SBV parameter,OR/psia
= SBV parameter,OR/psiaO’S
= molar mass, lb-mole
= molar mass of heptane plus fraction,lb-mole
= pressure,psia
= aitical
pressure,psia
4
%
Ppr
1
Te
Tpc
TW
YC7+
Yi
z
ai
B,
7*
E
COMPRESSIBILITYFACTORS FOR NATI
= pseudocriticalpreSSIW,pSiZ
= pseudoredwed pressure
= correlationeoeffieierit
= tempemtum, ‘R
= critical temperature, ‘R
= psemkwrkicaltemwfi !ure, ‘R
= pseudoreducedtemperature
= mole fnwtion of heptane plus fraction
= mole fractionof the i-th component
= gas compressibilityfactor
= cuftieients of the chelations for J
= coefficientsof the correlationsfor K
= qwciftc gravity of the gas mixture
= Wichert and Aziupseudocriticaltemperature
adjustmentparameter, ‘R
We thank Core Laboratories Inc. and S. A. Holditch &
Associates,Inc. for providing data.
1. MeCain, William D., Jr; ThePropertiesofPetroleum
Fluids,2ndcd., PennWellBooks, Tulsa(1990) 104-22,
510-12.
2. Sutton, R. P; “CompressibdityFactors for High
MolecularWeight ReservoirGases,” paper SPE 14265
presentedat the SPE Annual TechnicalMeeting and
Exhibition,l-as Vegas,Sept. 22-25,1985.
3. Standing,M. B.: VolumetricandPhaseBehavwrof Oil
FieidH@rocarbonSystems,9thRiming, Society of
Petroleumengineersof AIME, Dallas(1977) 122.
4. Corredor, J.H., Piper, L.D., and McCain, W.D. Jr.:
“CompressibilityFactors for Naturally Oceuming
ALLYOCCURRINGPETROLEUMGASES
SPE 2666
PetroleumGases: paper SPE 24864 presentedat the SPB
AnnualTechnicalMeeting and Exhibition, Washingtm
D. C., Oct. 4-7,1992.
5. Wiche%E.: “CompressibilityFactor of Sour Natural
~7~” MEng Thesis, The Universityof Calgary, Alberta
6. Metcalfe,R. S. and Raby, W. J.: “PhaseEquilibriafw a
Rich Gas Condensate-NitrogenSystem,”FluidPhase
Equilibria29 (1986) 563-73.
7. Fimozabadi, A., Hem Y. and Katz, D. L.: “Resewoir
DepletionCalculationsfor Gas CondensatesUsing
ExtendedAnalyses in the Peng-RobmsonEquationof
State,”&M. Per.Tech, (Get.,1978)610-15.
8. Coats, K. H. and SmarLG. T.: “Applicationof a
Regression-BasedEOS PVT Program to LaboratoryData
SPERE(MZy,1986) 277-99.
9. KenyonD.E. and Behie, A.: ““lldrdSPE Comparative
Solution Projeec Gas Cycling of RetrogradeCondensate
Resxvoirs:
JPT (Aug., 1987)981-97.
10. Whiison,C. H. and Torp, S. B.: “EvaluatingConstant
VolumeDepletion Data: JPT (Ma@ 1983) 610-620.
11. Moses, P. L.: “EngineeringApplicationsof Phase
Behaviorof Cfude 011and CondensateSystems,”JPT
(July, 1986)715-23.
12. Coats, IL H; “Simulationof Gas CondensateReservoir
Performance: paper SPE 10512presentedat the Sixth
SPE Symposiumon ReservoirSimulation,New Orleans,
Jan. 31-Feb. 3,1982.
13. Kilgren, K. H..: “PhaseBehaviorof a High-i%essure
CondensateReservoirFluid; JPT (Aug, 1966) 1001-’7.
14. Vrla, F.: personal communication,May 29,1992.
15. Holditch,S. A,: personal communication,June 7,1993
16. Press, W. H., FJannery,B. P., Teukolsky, S. A. and
Vetterling,W. T.: NumericalRecipes,1st cd., Cambrklge
UniversityPress, New York (1986) 301-7.
17. Corredor, J. H.: “Compressibtity Factors for Retrograd
Gases: A New Correlation,” MS Thesis, Texas A&l
IJniversity,College Station (191).
TABLE 1--RANGE OF DATA
Variable
Hydrogen Sulfide
Carbon Dioxide
N~trogen
Methane
Ethane
Propane
iso-Butane
n-Butane
iso-Pentane
n-Pentane
Hmane
HeptanePlus
MC7+
7c3#+
z
T, ‘T
p, psia
7*(air= 1)
Mean
2.45
3.38
1.87
71.15
8.21
4.04
Minimum
0.00
0.OO
0,00
19.37
2.30
0.06
0.90
1.55
i%
0.00
0.00
0.64
0.88
0.65
4,28
w
98.0
135,2
0.779
0.710
0.989
243.8
3758.6
0.972
0.698
78.0
514.0
0.613
684
Maximum
51.37
67.16
15.68
94.73
18.40
12.74
2,60
6.04
2,24
:%
14.94
29;.0
0.884
2.099
326.0
12814.0
1.821
L. D. PIPER,W. D, MCCASN,JR, ANDJ. H, CORREDOR
TABLE 2-WPDATED COEFFICIENTS FOR EQS. 4
K
J
i
~
o
5.2073E-02
1.0160E@0
8,6961E-01
7.2646E-01
8.5101E-O1
1
:
4
~2
I
TABLE 3--ACCURACY
standard
Error
standard
Pi
8.8370E-03
2,3018E-02
2.1985E-02
4.1292E-02
1.5402E-02
I&or
I
0,981
2.2271E-01
1.5428E-02
1,6132E-02
4.2227E-02
1,S134E-02
-3.9741E-01
1,0503E+O0
9.6592E-01
7.8569E411
9.8211E-01
0,979
OF COMPRESSIBILITY
FACTOR
CALCULATIONS
Property
Correlation
Psmdocritlcal
SmdinL?
SEYSSBY
~
(0.61< ‘ygc 0.99)-628 data points
@C7,<4% & yH$+y~<5%)
AvemgeErru
-0.023
-:ol;
M@mum Absolute13m3r
0.065
1:577
AverageAbsoluteError,%
2,508
4,582
MaximumAbsoluteError,%
6,668
(0.63 c y~< 1,42)-369 data points
@c7+<4% & YH2S+Y~>5%)
Average13rm
-0,002
-:,;:
MaximumAbsoluteError
:04;
AverageAbsolute Error,%
1:627
6.467
6:518
Maximurn AbsoluteFaor, %
0.001
0.054
1.040
5.831
-:jloo
-Wlol
(/:();
-;:;;
1:293
5.882
0.001
0,079
1.304
6.371
~
-:.:;;
-g.::;
3:647
1:295
6.356
1:163
6.450
1:176
4.386
(0.84 c ‘ygc 1.82)-439 data points
(Yc7+Z4% ~ YIi2s+Yco2<5%)
AverageBra
-:.:;;
0.008
MaximumAlmoluteError
:05;
2:556
Awage AbsoluteError,%
MaximumAbsoluteWor, %
7.571
5:816
0,003
0,053
1,173
4,410
-0.034
0.162
3,070
9,795
0.009
p));
0.001
0.061
1.356
4.709
~
(0.84< Yge 1.82)-167 data points
ti~~+~4% & yn#+yC0225%)
AverageErnx
0,011
-:ol;
MaxirmunAbsoluteEmor
0.057
AverageAbsoluteWor, m
1.689
1:656
MaximumAbsoluteEmoL,m
7.719
5.789
0.001
0.048
1.069
3.674
-;.;;;
-:00;
3:307
9.829
1:715
6.786
0.001
(/.()):
-:.:::
0.002
::;;
BkkWWMM
~m~l~hta
7:856
-0,002
0.043
1.235
5.350
points
-::;:
MaximurnAbsoluteEaror
AverageAbsoluteEmor,%
MaximumAbsoluteError,%
2:230
7.5’..
665
-0.003
0,067
1.526
7.719
5:831
1:990
9.829
7:856
0.001
0.076
1.304
7.230
●
COMPRESSIBXLITY
FACIXIRSFORNATUW4LLYOCCURRINGPETROLEUMGASES
TABLE
4==PROPOSED
GAS SPECIFIC
GRAVITY
CORRELATION
Standard
Error
:
1.1582E-01
-4,582QE-01
-9.0348E-01
-6.6026E=-01
7.0729E-01
-9.9397E-02
o
1
4
5
Sta&rcd
\:\\,XE-O:
3.8216E+O0
-6.5340E-02
-4,21 13E-01
-9.1249E-01
1.7438E+-01
-3.2191E+O0
7.4SOE-03
1,3616E-02
1.5387E-02
3.9664E-02
1.3878E-02
6.055E-03
1.0812Ek2
4,I073E-02
3.1914E-01
1.3925E-01
0.975
0,979
TABLE 5--ACCURACY
OF GAS SPECIFIC GRAVITY
CORRELATIONS
WHEN IMPURITIES
ARE UNKNOWN
I
i
Is
YH*S
+ YcO~<$ %
utton
I
MS. 6
II
1
yH2S+ YC02~ 5 %
Sutton
I
YC7+<4 %
YC7+24%
—
1
I
1
666
1
1
~S. 6
SPE 26668
WE 26668
L. D. PIPER, IV. D. MCCAIN, JR AND J. H. CORREDOR
2.0-
2.0-
7
~
1
i
1.8-
...... ....
1.6-
I
kl
~
......... ...
1
t
...........*.....
...................+........
i:!
~
I
t
...........T..+
.......
1
1.4-
1*2
!:
1.....................+
.....................
!5 1.6--.............
j
g
......... .......
N 1.4- ......................+..
............................................+....
!
1.0
l.o--
0.13-.......
0.8=
.................................... ...
0.6
0.6
0.S
1.0
1.2
1.4
Eapsrimcntal z
1.6
1.8
2.0
0.6
0.8
Factor
Fig. I=-Calculated z Factor using Sutton’s
Modification to SBV Rules
1.0
1.2
1.4
Expcrimentsl z
1.6
1.8
2.0
Factor
Fig. 3-.Calculated z Factor using Proposed
Modification to SBV Rules
........................ ......................... ............ .........
i;;
+1
+j
1
l!
~
I
t
i
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..{
.....
+~+~~
1;
?*!
: : !
+l~i
-..*..I..
+1
,.
++:
I
1
1
+
........
+
... ...t
0:6
0:8
@
. .. .
1:0 1:2 1:4 1:6
Espcrimsntal z Factor
Fig. 2--Error ID Calculated
Modification to SBV Ruka
z Factor using Sutton’s
0:6
0:8
1:0
1:2
1:4
1:6
:
Expcdmental z Factor
Fig. 4-.Error in Calculated z Factor using Proposed
Modification to SBV RUISS
●
SPE266S8
COMPRESSIBIIII’Y FACTGRSFOR NATURALLYOCCURRINGPETROLEUMGASES
8
........
!%l-l~#i-i’
P ‘r-l ! I W(’
-
2.0 ................o
....o..\
...........i
..............""....."..
““”””””””””i””””””””*
;““”’
[$
. ..+..+.
I
1
........................
L............j............\......+..F ...........i.....i
la-t ...........i
I
.........../............................. ............ .......... .
...4..*......... ............!.....
4
:4*
}
++
;;...:! +
,+
I
Tj 1.2-
i
i
i
I
............ ....
~
i
}
~
~
...........*.....
~
!
i
.........
I
+
8
*1+
............ ...........
1.o- ...........
4+:
r
o.s- .......
0.6
0.6
0.8
S.0
1.2
1.4
1.6
1.s
:
!
1
I
--i-
3.4
11.6
(%s Specific Gravity
1.S
1.2
2.0
Experimental z Factor
Fig. 7--Variation of the Inferred Value of J with
the Specific Gravity of the Gas Mixture
Fig. S--Calculated z Factor using Sutton’s Specific
Gravity Correlation with Impurities Known
.-
i
:{;
i;
l~i
\...~
26
i
.....j.....\.....!.....j.....l.....i...~...~
...........~
.....l.....\.....j.....j.....i
24’
1
:?!
I ..............
i..............
I............1
...........~.....
,.............l*
24- ...............
i
1
I
h.$k
$ i
i
1
I
i
~1
1........ ‘+
‘“”””
""'""\
"."""~""""{"".""~".."""i""-"";"""""i""""'!"""4".".';"""[.*"~""'"j"""""!
..........................
22- .............!....
t
~
!~
,4
j
...!.....
20- .............
I..............!
........*4
..... .....+............j............y
...~..................
{~:
; ~.....f.....
;: j..:”+”j
R&.!...........+....
P#)
I
...........}::
....................
....................................
... .....
........
:+::
I.....:;+1
{1:::
j;:
I ::::............
@
.......
.
...............
.
........
.
..
.
.......
.
....
.
.......+.?.
...y
...t
:
I!!
i:;
.
i
i:
.....~...................
.... ........:. ..:
....................................’,
....;...
~*!*:
E 16!wi:
i!:\
fl
n
..l.~ ....y" . ...... ...f ....~...j.$ .. ....*...~
3
a12i
[~.:::;
.......
....................................+..
...........................................
[i:+::~;
..1...........+..... ......................... ...... ..... ............ ...... ...... ..;
...
31
4
20
M..i.. .......... ..........
-.’&””
q. ........t..~.-.;...:.. \.-...
..~..l~ ..
8
ILL:
‘ ‘
~iil;ilit~+~~:
. .... .... . ... .. ..
1
.... ,. . ....+.....
0:1
‘:-q4 ........j. ......$... +....
i
14.
..\ ......r .....~....J .....j .....f ....t ....\ ..........j ......
-r.. ...............
............
~Ji ...... ........................
‘i!’;
::
+~l~j:::
~:
.........!..... ...... .... ........... \...................
:+,:~~i
h
i;
i
,..’
..?.
......... ...........“............”.....
5...........1......
1
11 [ I B I
1
I
4..+F+;f
0:0
... ..... ................................. ..... ...... ....+.....
P ~:~i
.::.....+
...........................L
.............I.............~.....
9:2
0:3 0;4 0:S
YSM + Y- + YNJ
0:6
i
12
10
!
!.............i
.....
...2...
*.4
. ..........j
.............i
.............L............l
i~~
1
11
?.
I
i
““f”””””
““’”””;”””’”
i
?
i
1
1
I
!
I
I
0:7
Fig. 6--Error in Calculated z Factor using SUttds
Specific Gravity Correlation with Impurities Unknown
Gs8 Sedtlc Gravity
Fig. 8--Variation of the Inferred Value of K with
the SpecMic Gravity of the Gas Mixture
4
,,
L. D. PIPER,W, D,MCCAIN,JR, AND J, H. CORREDOR
SPE 2666J
E . . . . . . ..+
iyj
3oa
0.6
I
I
I
1
i
I
I
3io
4Q0
4s0
Soo
550
tfoo
I
0:6
I
0:8
Pseudocritical Temperature
Gravity Correlation
\........
1/
. . . . . . . . ..j
;
I
!:
I
1:0
I
1
1:2
. . . . . . . . . ..{ . . . . . . . . . ..+ . . . . . . . . ...*.....
:
;
~
!
I
j
I
~:
I
:
I
1:4
1.6
1.8
2.0
I
I
Experimental z Factor
Inferred Pscudocritlcal Temperature, ‘R
Fig. 9.=Calculated
I%opoeed Specific
. . . . . . . ..+
j
using
Fig. n--Calculated
z Factor using Proposed
Gravity Correlation with Impurities Known
Specific
...!
......".."""""~
.................
f
i
+*
““””””””
!
:
.................].........................................I*.4...........!.........
I\
;+* +
.................. .............
\
“ .. . . . . . . . . . . . . . . . .. . . . . . . . . . .. . . . . . . .. . . .. . . . . . . . . .
t
i
i
+
-.
..L..................................................
.............
..$
...........
j
i.
$
ti~
I;I!
.........&
.................i....
*; .....&
;
:-
Soo
900
800
7tio
Pressure, psla
InkrrcdPseodocrMcal
600
Fig. 10--Ctdcu1ated Pseudocriticai
Pressure
Proposed Specific Gravity Correlation
using
0:0
0:1
0:2
0:3
0:4
0:5
YIW + h: + yNa
Fig, 12--Error in Calculated
Specific Gravity Correlation
0.6
0.7
z Factor using Proposed
with Impurities Unknown
.
SPE266i8
.,,
......
~iH~:H~:=
of Gas Specific Gravity and Amount of Impurities
~ as a ~Unction
10
o
0
20
Mol % H2S
1.1
,
::
:
0
20
10
10
20
Mo1 % A’,
Mol % COa
;
1.o-
!
o.9-
9
g
:
1!
g
z
.
......f ....... ........}.......i............. :.......
~
-
006
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.S
1.6
1.7
1.8
l.~
Gas Specific Gravity
Burkharcit and Voo equations,
K2
T pC=~dkppC=
‘=to
J
estimate Tpc &
Ppc*
See Piper, McCain, & Corredor, “Compressibility Factors for Naturally
Occurring Petroleum Gases”, SPE 26668, presented at the 1993 WE Annual
Technical Conference and Exhibition in Houston, Texas, October 345, 1993.
670
,,W
SPE26668
K as a Function of Gas Specific G~avity and Amount of Impurities
.
.
.
.
.
.
.
.
,;H
,8=
10
0
0
20
10
0
20
10
Mo] % Na
Mol % C03
Mol % IIJ?
26
,:M,
i
i
24
I
9
I
&
I
I
12
0.6
0.7
0.8
0.9
1.0
l-l
~02
l-s
104
Gas Spcclfh! Gravity
I*5
1*6
1*7
108
1*9