Post on 30-Nov-2015
Reservoir oil bubblepoint pressures revisited; solution gas–oil
ratios and surface gas specific gravities
P.P. Valko, W.D. McCain Jr.*
Harold Vance Department of Petroleum Engineering, Texas A&M University, 721 Richardson Building, College Station, TX 77843-3116, USA
Received 14 May 2002; accepted 9 October 2002
Abstract
A large number of recently published bubblepoint pressure correlations have been checked against a large, diverse set of
service company fluid property data with worldwide origins. The accuracy of the correlations is dependent on the precision
with which the data are measured. In this work a bubblepoint pressure correlation is proposed which is as accurate as the
data permit.
Certain correlations, for bubblepoint pressure and other fluid properties, require use of stock-tank gas rate and specific
gravity. Since these data are seldom measured in the field, additional correlations are presented in this work, requiring only data
usually available in field operations. These correlations could also have usefulness in estimating stock-tank vent gas rate and
quality for compliance purposes.
D 2002 Elsevier Science B.V. All rights reserved.
Keywords: Oil property correlation; Bubblepoint pressure; Solution gas–oil ratio; Surface gas specific gravity; Non-parametric regression
1. Introduction
A large number of correlations for estimation of
bubblepoint pressures of reservoir oils have been
offered in the petroleum engineering literature over
the last few years to go with a handful of correla-
tions published earlier. Many of these new correla-
tions are based on data from a single geographical
area. Most of these correlations were derived using
petroleum service company laboratory fluid property
data.
The primary goal of this paper is to evaluate these
correlations. For this purpose a large set of service
company data has been assembled. The data set is
truly worldwide with samples from all major produc-
ing areas of the world; thus, it permits evaluation of
the necessity of geography-specific correlations. We
are indebted to the several authors listed in Table 2.3
who provided geographical data.
An even more exciting question is whether the
predictive power of such correlations can be signifi-
cantly improved or whether the known accuracy limit
is inherently determined by the quality of the available
data.
Related to the bubblepoint pressure prediction
from observable field data is the issue of estimating
stock-tank gas rate and specific gravity (shown as RST
0920-4105/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0920-4105(02)00319-4
* Corresponding author. Tel.: +1-979-845-8401; fax: +1-979-
862-1272.
E-mail address: mccain@spindletop.tamu.edu (W.D. McCain).
www.elsevier.com/locate/jpetscieng
Journal of Petroleum Science and Engineering 37 (2003) 153–169
and cgST in Fig. 1.1) Certain correlations, for bubble-
point pressure and other fluid properties, require
knowledge of these quantities. Since these data are
seldom measured in the field, additional correlations
are presented in this work, requiring only data usually
available in field operations.
An additional and potentially important application
of these new correlations could be in estimating stock-
tank vent gas rate and quality for compliance purpo-
ses.
This paper is organized as follows. The method-
ology is described in Section 1. Section 2 deals with
various aspects of bubblepoint correlations, evaluation
of published methods, improvement of existing meth-
Fig. 1.1. Notation for variables.
Table 2.1
The bubblepoint pressure data set has a wide range of values of the
independent variables
Laboratory measurement
(1745 records)
Minimum Mean Maximum
Solution gas–oil ratio at
bubblepoint, scf/STB
10 588 2216
Bubblepoint pressure, psia 82 2193 6700
Reservoir temperature, jF 60 185 342
Stock-tank oil gravity, jAPI 6.0 35.7 63.7
Separator gas specific gravity 0.555 0.838 1.685
Table 2.2
A comparison of published bubblepoint pressure correlations using
data described in Table 2.1 reveals the more reliable correlations
Predicted bubblepoint pressure
ARE, % AARE, %
McCain et al. (Eqs. 7–12) (1998) 3.5 12.4
Velarde et al. (1999) 1.2 12.5
Labeadi (1990) 0.0 12.6
Standing* (1947) � 2.1 12.7
Lasater** (1958) � 1.3 13.3
Levitan and Murtha (1999) 4.2 13.9
Al-Shammasi (1999) � 1.4 14.3
Vazquez and Beggs (1980) 7.1 14.6
Omar and Todd* (1993) 5.4 15.5
De Ghetto et al. (1994) 8.6 15.6
Kartoatmodjo and Schmidt (1994) 4.4 15.7
Dindoruk and Christman* (2001) 0.9 16.1
Glaso (1980) 4.8 16.8
Fashad et al.* (1996) � 5.6 17.8
Al-Marhoun* (1988) 8.8 17.8
Dokla and Osman* (1992) 0.3 21.8
Almehaideb* (1997) � 0.6 22.3
Khairy et al.* (1998) 4.9 23.1
Macary and El Batanoney* (1992) 12.6 23.1
Hanafy et al.* (1997) 10.6 28.8
Petrosky and Farshad* (1998) 17.7 37.7
Yi (2000) 42.4 45.2
*Author restricted the correlation to a specific geographical area.
**Not valid for jAPI < 18j.
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169154
ods, discussion of data quality, and investigation of
the geographical factor. Sections 3 and 4 present new
correlations for solution gas–oil ratio and weighted
average surface gas specific gravity.
2. Statistical methods
This work systematically uses a relatively novel
technique to reveal the underlying statistical relation-
ships among variables corrupted by random error. The
method of alternating conditional expectations (ACE)
developed by Breiman and Friedman (1985)—as
other similar non-parametric statistical regression
methods—is intended to alleviate the main drawback
of parametric regression, i.e., the mismatch of as-
sumed model structure and the actual data. In non-
parametric regression a-priori knowledge of the func-
tional relationship between the dependent variable y
and independent variables, x1, x2,. . .xm, is not re-
quired. In fact, one of the main results of non-para-
metric regression is determination of the actual form
of this relationship.
A model predicting the value of y from the values
of x1, x2,. . .xm is written in the generic form
y ¼ f �1ðzÞ where z ¼Xm
n¼1
zn and zn ¼ fnðxnÞ
ð1� 1Þ
The functions f1(�), f2(�),. . . fm(�) are called varia-
ble transformations yielding the transformed inde-
pendent variables z1, z2,. . . zm. The function f (�) is
the transformation for the dependent variable. In fact
the main interest is its inverse: f � 1(�), yielding the
dependent variable y from the transformed dependent
variable z.
Given N observation points, we wish to find the
‘‘best’’ transformation functions f1(�), f2(�),. . ., fm(�)and f � 1(�), but first not as algebraic expressions,
rather as relationships defined point-wise. The
method of alternating conditional expectations
(ACE) constructs and modifies the individual trans-
formations to achieve maximum correlation in the
0
2000
4000
6000
8000
0 2000 4000 6000 8000
Measured bubblepoint pressure, psia
Cal
cula
ted
bubb
lepo
int p
ress
ure,
psi
a
Fig. 2.1. Calculated bubblepoint pressures from Eq. (2-1) compare well with measured bubblepoint pressures (1745 data records).
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169 155
transformed space. Graphically this means that the
plot of z ¼Pm
n¼1 fnðxnÞ against zV = f( ymeasured)
should be as near to the 45j straight line as
possible. The resulting individual transformations
are given in the form of a point-by-point plot
and/or table, thus in any subsequent application
(graphical or algebraic) interpolation needed to
obtain the transformed variables and to apply the
inverse transformation to predict y. Obviously, the
smoother the transformation the more justified and
straightforward the interpolation is; therefore, some
kind of restriction on smoothness is built into the
ACE algorithm. In other words, based on the
concept of conditional expectation, the correlation
in transformed space is maximized by iteratively
adjusting the individual transformations subject to a
smoothness condition.
The particular realization of the algorithm, GRACE
(Xue et al., 1997), used here consists of two parts. The
first part provides the transformations in the form of
tables and the second part allows the user to construct
the final algebraic approximations using curve fitting
in a commercial spreadsheet program. Fortunately,
many physically sound problems have rather simple
shapes of the individual transformations, and can be
well approximated, for instance, by low order poly-
nomials.
Data reconciliation is a well-known statistical pro-
cedure, see for instance Liebman et al. (1992), Crowe
(1996), Weiss et al. (1996) and Vachhani et al. (2001).
GRACE also has an option to ‘‘reconcile’’ the
observed data set to the gleaned-out underlying stat-
istical dependency. The option provides reconciled
values for all the observations by ‘‘suggesting’’ slight
changes in the observed values. The adjustment is
done such that in transformed space the reconciled
observations follow the 45j straight line perfectly,
while the overall change in each observed value is
kept to a minimum (Xue et al., 1997). The plot of
adjusted versus observed variable offers a deeper
insight into the effect of measurement noise and/or
the possibility of a hidden variable.
Fig. 2.2. The bubblepoint pressure correlation, Eq. (2-1), is reliable (regarding unbiasedness ) across the spectrum of reservoir temperatures.
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169156
Statistical measures of correlations used through-
out the paper are:
Average relative error, ARE, % :
ARE ¼ 100
N
XN
i¼1
ycalculated � ymeasured
ymeasured
ð1� 2Þ
Average absolute relative error, AARE, % :
AARE ¼ 100
N
XN
i¼1
�����ycalculated � ymeasured
ymeasured
����� ð1� 3Þ
ARE characterizes the accuracy (bias) and AARE
describes the precision (scatter) of predicted values
obtained from a particular correlation. All correlations
are presented for the variables measured in the units
indicated in the Nomenclature. It is also possible (and
more correct) to consider any presented correlation as
a relationship between dimensionless quantities,
where the reference values are; for pressure 1 psi,
for solution gas–oil ratio 1 scf/STB, for temperature 1
jF (with offset at 0 jF), and for oil gravity 1j API.
With such interpretation in mind, even lnpb (the
natural logarithm of dimensionless bubblepoint pres-
sure) can be easily understood.
3. Bubblepoint pressures
A large number of correlations for estimating
bubblepoint pressures of reservoir oils have been
offered in the petroleum engineering literature over
the last few years to go with a handful of correla-
tions published earlier. Many of these new correla-
tions are based on data from a single geographical
area. Most of these correlations were derived using
laboratory fluid property data reported by service
companies.
0
5
10
15
20
25
50 100 150 200 250 300
Labedi
Reservoir Temperature, oF
Ave
rage
Abs
olut
e R
elat
ive
Err
or, A
AR
E, i
n ca
lcul
ated
Pb,
%
This workStandingGlasoLasater
Fig. 2.3. The bubblepoint pressure correlation, Eq. (2-1), is reliable (regarding scatter) across the spectrum of reservoir temperatures.
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169 157
3.1. Evaluation of published correlations
A large set of service company fluid property data
has been assembled. The data set is truly worldwide
with samples from all major producing areas of the
world. The wide range of values of the variables in
this data set, described in Table 2.1, span virtually all
the values to be expected in new discoveries/develop-
ments. Note that the fluid types vary from heavy oil to
volatile oil range.
Bubblepoint pressures calculated with many of the
published correlations using the measured values of
independent variables were compared with the labo-
ratory-measured bubblepoint pressures. The results of
this comparison are given in Table 2.2 arranged in the
order of increasing average absolute relative error
(AARE). None of the correlations shown in Table
2.2 was derived using the full data set of Table 2.1;
however, many were prepared using subsets of this
data set.
3.2. Improvement of existing correlations
With the thought that a correlation of improved
accuracy could be derived, the best four correlations
from Table 2.2 were refitted to the entire data set.
Standing (1947) deduced the form of his equation
using graphical methods. Velarde et al. (1999) used a
modification of the Standing (1947) equation origi-
nally proposed by Petrosky and Farshad (1998);
Labeadi (1990) used the Standing (1947) technique
and deduced new values for the slope and intercept.
The coefficients of the Standing (1947), Velarde et al.
(1999) and Labeadi (1990) equations were recalcu-
lated using nonlinear least-squares minimization. In
these cases the improvements in the predictions of
bubble point pressure were marginal.
There was some improvement in bubblepoint pres-
sure prediction using the GRACE technique (first
used for this purpose in McCain et al., 1998, Eq.
(7–12)) when the coefficients were determined using
-20
-10
0
10
20
0 500 1000 1500 2000
Labedi
Solution gas-oil ratio at Pb, scf/STB
Ave
rage
Rel
ativ
e E
rror
, AR
E, i
n ca
lcul
ated
Pb,
%
This workStandingGlasoLasater
Fig. 2.4. The bubblepoint pressure correlation, Eq. (2-1), is reliable (regarding unbiasedness) across the spectrum of solution gas–oil ratios at
the bubblepoint, Rsb.
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169158
the full data set. The new equations for estimating
bubblepoint pressure are given below.
lnpb ¼ 7:475þ 0:713 zþ 0:0075 z2 where
z ¼X4
n¼1
zn and zn ¼ C0n þ C1nVARn
þ C2nVAR2n þ C3nVAR
3n ð2� 1Þ
The average relative error (ARE) is 0.0 %, and the
average absolute relative error (AARE) is 10.9 %. Fig.
2.1 shows that there is no bias and the precision is
adequate.
The relative errors cited above and given in
Table 2.2 pertain to the entire data set. The reli-
ability of correlations across the spectrum of the
independent variables is also important. The data set
was sorted by reservoir temperature and partitioned
into 16 subsets of approximately equal size. The
accuracy of Eq. (2-1) as well as several of the more
popular correlations were tested with these subsets.
Figs. 2.2 and 2.3 show AREs and AAREs for five
of the correlations. The results obtained with Eq. (2-
1) stay constantly near zero ARE and consistently
have the lowest AARE. Figs. 2.4 and 2.5 show the
same results for the data set partitioned into 16
equal subsets by solution gas–oil ratio at the
bubblepoint. Figs. 2.6 and 2.7 show that the bub-
blepoint pressure correlation of this study is reliable
when the data set is partitioned by stock-tank oil
gravity, jAPI.
3.3. Universal versus geographical correlations
The petroleum industry has long debated whether
fluid property correlations should be universal or
Fig. 2.5. The bubblepoint pressure correlation, Eq. (2-1), is reliable (regarding scatter) across the spectrum of solution gas–oil ratios at the
bubblepoint, Rsb.
n VAR C0 C1 C2 C3
1 lnRsb � 5.48 � 0.0378 0.281 � 0.0206
2 API 1.27 � 0.0449 4.36� 10� 4 � 4.76� 10� 6
3 cgSP 4.51 � 10.84 8.39 � 2.34
4 TR � 0.7835 6.23� 10� 3 � 1.22� 10� 5 1.03� 10� 8
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169 159
based on data from a single geographical area. Several
of the geographically based correlations listed in Table
2.2 fit the full data set fairly well even though they
were developed with data sets limited in both size and
range. This implies that a well-done correlation does
not have to apply to a single geographical area.
The bubblepoint pressure correlation of this study
was tested against those subsets of the Table 2.1 data
set which could be identified by geographical area.
The results are in Table 2.3. The AAREs are approx-
imately the same for the correlation worldwide or by
geographical regions. Thus, it appears that geograph-
ical correlations are unnecessary and that a universal
correlation is adequate. Al-Shammasi (1999) arrived
at the same conclusion.
3.4. Evaluation of the data used for developing the
correlations
An AARE of almost 11% for a correlation to
predict values of such an important property as
bubblepoint pressure is disturbingly high. Can some
other correlating equation and/or technique produce
an improved correlation? The answer lies in exami-
nation of the data used to develop the correlations.
Virtually all the published bubblepoint pressure
correlations, including this study, used fluid property
data from oilfield service companies. The quality of
these data is not research grade. This is not meant to
denigrate the service companies. These companies
use laboratory equipment and procedures designed to
provide data with precision adequate for the engi-
neering calculations for which the data are gathered
and at a reasonable cost to the customer.
An interesting feature of the GRACE software is
the option to adjust the values of all the observed
independent and dependent variables simultaneously,
such that the adjusted set perfectly fits the correla-
tion, i.e., the ARE and AARE are both zero, while
each observed value is changed a minimum amount.
This process is called data reconciliation. The aver-
age relative adjustments, necessary to zero the rela-
Fig. 2.6. The bubblepoint pressure correlation, Eq. (2-1), is reliable (regarding unbiasedness) across the spectrum of stock-tank oil gravities.
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169160
tive errors for the full data set are given in Table 2.4.
The amount of adjustment indicated is an averaged
measure of the precision with which that variable
was measured/controlled during the laboratory pro-
cedure. The extremely low values of average neces-
sary adjustment (bias) show that the measurement
errors in the data are randomly distributed, i.e. there
is virtually no bias. The average absolute relative
adjustment for each variable is well within the
precision to be expected in the laboratory proce-
dures.
Figs. 2.8–2.12 show the relationships between
the laboratory measured values and the adjusted
values for each of the five variables. Those plots
do not have the usual meaning of calculated versus
Fig. 2.7. The bubblepoint pressure correlation, Eq. (2-1), is reliable (regarding scatter) across the spectrum of stock-tank oil gravities.
Table 2.3
The bubblepoint pressure correlation of this study can be used in
various geographical areas with adequate accuracy
Geographical area Predicted bubblepoint pressure
Number of
data records
AARE, %
Worldwide 1745 10.9
Middle-East, Al-Marhoun (1988) 157 9.8
North Sea, Glaso (1980) 17 11.1
Egypt, Hanafy (1999) 125 12.2
Malaysia, Omar and Todd (1993) 93 11.8
USA, Katz (1942) 53 12.2
Table 2.4
The extremely low values of the average relative adjustments (ARA)
indicate random scatter and the average absolute relative adjust-
ments, (AARA) are reasonable
Variable Adjustment in observed data required
to achieve ‘‘perfect’’ correlation
ARA, % ARAA, %
Temperature, jF � 0.1 4.0
Stock-tank oil gravity, jAPI 0.0 1.9
Separator gas specific gravity 0.0 1.4
Solution gas–oil ratio
at pb, scf/STB
0.3 2.5
Bubblepoint pressure, psia � 0.2 5.5
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169 161
measured, rather the distance of a data point from
the 45j line indicates the amount of adjustment
necessary for the data point to satisfy the correlation
exactly. The positions of the points on these five
plots show the randomness and minimal amount of
the adjustments.
0
100
200
300
400
0 100 200 300 400
Res
ervo
ir te
mpe
ratu
re, A
djus
ted,
o F
Reservoir temperature, Measured, oF
ARA: -0.1 % AARA: 4.0 %
Fig. 2.8. Reservoir temperatures adjusted to satisfy a ‘‘perfect’’ correlation compared with original measured reservoir temperatures.
Fig. 2.9. Stock-tank oil gravities adjusted to satisfy a ‘‘perfect’’ correlation compared with original measured stock-tank oil gravities.
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169162
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8Separator specific gas gravity, Measured
Sep
arat
or s
peci
fic g
as g
ravi
ty, A
djus
ted
ARA: 0.0 % AARA: 1.4 %
Fig. 2.10. Separator gas specific gravities adjusted to satisfy a ‘‘perfect’’ correlation compared with original measured separator gas specific
gravities.
10
100
1000
10000
10 100 1000 10000
Sol
utio
n ga
s-oi
l rat
io a
t Pb,
Adj
uste
d, s
cf/S
TB
Solution gas-oil ratio at Pb, Measured, scf/STB
ARA 0.0 % AARA 1.8 %
Fig. 2.11. Solution gas–oil ratios adjusted to satisfy a ‘‘perfect’’ correlation compared with original measured solution gas–oil ratios.
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169 163
The importance of the information displayed
in Table 2.4 and Figs. 2.8–2.12 is that the larger
than convenient AARE of the bubblepoint corre-
lation is not due to the special form of the equa-
tion or the technique of data fitting, but stems
from the quality of the data used to derive the
correlation. Further attempts to develop bubblepoint
pressure correlations would be futile unless a
comparable amount of research quality data is
collected.
4. Solution gas–oil ratios from field data
Many reservoir fluid property correlations require
a value of solution gas–oil ratio at the bubblepoint
as one of the input variables. Values of this property
can be obtained from field data as the sum of the
producing gas–oil ratios from the separator and
stock-tank as shown in Eq. (3-1). This is illustrated
in Fig. 1.1
Eq. (3-1) is valid only if RSP and RST are measured
while the reservoir pressure is above the bubblepoint
pressure of the reservoir oil.
The separator gas production rate and stock-tank
oil production rate are nearly always measured since
they are normally sales products. Thus, RSP is
usually known with some accuracy. Unfortunately
the gas rate from the stock-tank is seldom measured
as this gas is usually vented. The stock-tank vent
gas ratio, RST, can contribute as much as 20% of
10
100
1000
10000
10 100 1000 10000
Bub
blep
oint
pre
ssur
e, p
sia,
A
djus
ted
Bubblepoint pressure, psia, Measured
ARA -0.2 % AARA 5.5 %
Fig. 2.12. Bubblepoint pressures adjusted to satisfy a ‘‘perfect’’ correlation compared with original measured bubblepoint pressures.
Table 3.1
Separator/stock-tank data set has a wide range of values of the
independent variables
Laboratory measurement
(881 records)
Minimum Mean Maximum
Separator pressure, psig 12 130 950
Separator temperature, jF 35 92 194
Stock-tank oil gravity, jAPI 6.0 36.2 56.8
Separator gas–oil ratio, scf/STB 8 559 1817
Stock-tank gas–oil ratio, scf/STB 2 70 527
Surface gas specific gravity 0.566 0.879 1.292
Separator gas specific gravity 0.561 0.837 1.237
Stock-tank gas specific gravity 0.581 1.256 1.598Rsb ¼ RSP þ RST ð3� 1Þ
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169164
Rsb depending primarily on separator conditions.
Thus, a correlation for RST, based on readily avail-
able field data, is required to determine Rsb from
field data.
Eq. (3-2) was developed using the GRACE tech-
nique with a data set from 898 laboratory reservoir
fluid studies. Information about this data set may be
found in Table 3.1.
lnRST ¼ 3:955þ 0:83 z� 0:024 z2 þ 0:075 z3
where z ¼X3
n¼1
zn and
zn ¼ C0n þ C1nVARn þ C2nVAR2n ð3� 2Þ
Fig. 3.1 shows the solution gas–oil ratios at
bubblepoint pressure, Rsb, calculated with Eqs. (3-2)
and (3-1) compared with measured values from the
data set. The average error and average absolute error
for this correlation are given in Table 3.2 along with
the same measures for a previously published corre-
lation, Rollins et al. (1990).
The procedure of estimating the solution gas–oil
ratio at the bubblepoint, Rsb, using Eqs. (3-2) and
(3-1) retains its accuracy across the range of sepa-
rator conditions. The data set was partitioned into
three subsets according to separator pressure; less
than 50 psig, between 50 and 100 psig, and over 100
Fig. 3.1. Total surface gas–oil ratios, calculated with Eqs. (3-1) and (3-2) compare favorably with measured surface gas–oil ratios (881 data
points).
Table 3.2
Average errors in estimates of Rsb for this study are within expected
experimental error
Correlation ARE, % AARE, %
Eqs. (3-2) and (3-1) 0.0 5.2
Rollins et al. (1990) 9.9 11.8
Eq. (3-3) 0.0 9.9
Eq. (3-4) � 14.1 14.1
n VAR C0 C1 C2
1 lnpSP � 8.005 2.7 � 0.161
2 lnTSP 1.224 � 0.5 0
3 API � 1.587 0.0441 � 2.29� 10� 5
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169 165
psig. The data set was also partitioned into two
subsets according to separator temperature with 75
jF as the dividing line and three subsets on separa-
tor gas–oil ratio. Table 3.3 shows that the procedure
has approximately the same accuracy in these eight
subsets.
Eqs. (3-2) and (3-1) and also the Rollins et al.
(1990) correlation require knowledge of separator
temperature and pressure. The users of fluid property
correlations may not know the separator conditions. In
this instance, Eq. (3-3) can be used. Eq. (3-3) was
derived from the same data set, Table 3.1, using
simple statistical methods.
Rsb ¼ 1:1618 RSP ð3� 3Þ
Statistical measures for Eq. (3-3) with the data set
used in its development are given in Table 3.2.
Ignoring the stock-tank gas, RST is illustrated with
Eq. (3-4)
Rsb ¼ RSP ð3� 4Þ
This is not recommended; it is given here to
show the possible error caused by such a proce-
dure. As shown in Table 3.2, ignoring the stock-
tank gas causes an error of almost 14% with the
data set of Table 3.1. Notice that this error is
always biased negative, i.e. the estimate of Rsb is
always low.
5. Weighted average specific gravities of surface
gases
Most fluid property correlations are based on use
of the separator gas specific gravity. This property is
usually measured accurately since it is required in the
process of metering the separator gas production
rates. However, a few methods of estimating fluid
properties require values of the weighted average
specific gravity of the surface gases as defined in
Eq. (4-1).
cg ¼cgSPRSP þ cgSTRST
RSP þ RST
ð4� 1Þ
The McCain and Hill (1995) equation for oil
formation volume factors and the Glaso (1980) corre-
lations of bubblepoint pressure and oil formation
volume factor at the bubblepoint are two examples
of fluid property estimates that require this weighted
average property.
Unfortunately the specific gravity of the stock-tank
gas is seldom measured in the field. A correlation is
required if this property is to be used in other
calculations. The correlation, given as Eq. (4-2), was
developed using the GRACE procedure.
cST ¼ 1:219þ 0:198 zþ 0:0845 z2
þ 0:03 z3 þ 0:003 z4 where z ¼X5
n¼1
zn
and zn ¼ C0n þ C1nVARn þ C2nVAR2n
þ C3nVAR3n þ C4nVAR
4n ð4� 2Þ
Table 3.3
The Rsb prediction is consistent across the data set
Data set Number of
points, N
ARE, % AARE, %
All data 881 0.0 5.2
PSPV 50 psig 359 � 0.4 4.3
50 psig <PSPV100 psig
291 � 1.9 5.0
PSP > 100 psig 231 3.0 6.9
TSPV 80 jF 472 1.0 5.3
TSP > 80 jF 409 � 1.2 5.1
RSPV 300 scf/STB 294 1.3 9.6
300 scf/STB<RSPV700 scf/STB
287 � 0.8 3.8
RSP > 700 scf/STB 300 � 0.5 2.1
n VAR C0 C1 C2 C3 C4
1 lnpSP � 17.275 7.9597 � 1.1013 2.7735� 10� 2 3.2287� 10� 3
2 lnRSP � 0.3354 � 0.3346 0.1956 � 3.4374� 10� 2 2.08� 10� 3
3 API 3.705 � 0.4273 1.818� 10� 2 � 3.459� 10� 4 2.505� 10� 6
4 cgSP � 155.52 629.61 � 957.38 647.57 � 163.26
5 TSP 2.085 � 7.097� 10� 2 9.859� 10� 4 � 6.312� 10� 6 1.4� 10� 8
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169166
The data set described in Table 3.1 was used to
create this correlation, however, only 626 data points
could be used since the stock-tank gas specific gravity
was not measured in a number of the laboratory
studies.
Values cgST from Eq. (4-2) and values of RST
from correlation Eq. (3-2) are used in Eq. (4-1) to
estimate the weighted average specific gravity of the
surface gases. The errors in the calculated values of
weighted average surface gas specific gravities as
compared with measured values are given in Table
4.1. Fig. 4.1 shows the relationship between calcu-
lated and measured weighted average surface gas
specific gravities.
Eq. (4-2) require values of separator temperature
and separator pressure. Occasionally the users of fluid
property correlations will not have knowledge of
separator conditions. In this case, Eq. (4-3) can be
used to estimate the weighted average surface gas
specific gravity (Table 4.2).
cg ¼ 1:066cgSP ð4� 3Þ
This equation was developed with the data illus-
trated in Table 3.1 using a simple statistical method.
Average errors for the use of Eq. (4-3) along with
average errors associated with using the separator gas
specific gravity as a substitute for weighted average
surface gas specific gravity, Eq. (4-4), are given in
Table 4.1.
cg ¼ cgSP ð4� 4Þ
Table 4.1 shows that ignoring the stock-tank gas
specific gravity, i.e. Eq. (4-4), always results in
Table 4.1
Average errors in estimates of surface gas specific gravity are well
within expected experimental error
Correlation ARE, % AARE, %
Eqs. (4-2),
(3-2) and (4-1)
� 0.7 2.2
Eq. (4-3) 0.0 3.8
Eq. (4-4) � 6.2 6.2
Fig. 4.1. Weighted average surface gas specific gravities, calculated with Eqs. (4-2), (3-2), and (4-1) compare favorably with measured weighted
average surface gas specific gravities (618 data points).
P.P. Valko, W.D. McCain Jr. / Journal of Petroleum Science and Engineering 37 (2003) 153–169 167
negative error; the estimated value of cg is always
low.
6. Conclusions
(1) The use of Eq. (2-1) will result in reasonable
estimates of bubblepoint pressure.
(2) The 10% AARE of Eq. (2-1) cannot be improved
significantly. Given the precision with which the
input data are measured, an AARE of 10% or more
is to be expected. Further attempts at improving
the AARE of a bubblepoint correlation using data
of this quality will be futile.
(3) Generally, correlations based on data sets limited
to a specific geographical area are not necessary. A
carefully prepared universal correlation gives
adequate results.
(4) The use of Eqs. (3-2) and (3-1) to convert the field
measured separator gas–oil ratio, RSP, into sol-
ution gas–oil ratio at the bubblepoint, Rsb, results
in values of Rsb which are as accurate as routinely
measured in the laboratory.
(5) The use of Eq. (3-3) to estimate solution gas–oil
ratio at the bubblepoint from separator gas–oil
ratio data when separator conditions are not known
is adequate for engineering calculations and is
certainly preferred to ignoring the stock-tank gas–
oil ratio.
(6) The use of Eqs. (4-2), (3-2) and (4-1) to estimate
weighted average surface gas specific gravity re-
sults in an accuracy approaching laboratory mea-
surement.
(7) The use of Eq. (4-3) to estimate weighted average
surface gas specific gravity when separator con-
ditions are not known gives reasonable results and
is much preferred to ignoring the effect of stock-
tank gas specific gravity.
Nomenclature
ARA average relative adjustment, %
AARA average absolute relative adjustment, %
ARE average relative error, %
AARE average absolute relative error, %
pb bubblepont pressure, psia
pR reservoir pressure, psia
pSP separator pressure, psia
pST stock-tank pressure, psia
Rsb solution gas–oil ratio at bubblepoint, scf/
STB
RSP gas–oil ratio, separator, scf/STB
RST gas–oil ratio, stock-tank, scf/STB
API stock-tank oil gravity, jAPIcgSP separator gas specific gravity (air = 1)
cgST stock-tank gas specific gravity (air = 1)
cg weighted average surface gas specific gravity
(air = 1)
TR reservoir temperature, jFTSP separator temperature, jFTST stock-tank temperature, jFx independent variable
y dependent variable
z sum of transformed independent variables
zV transformed dependent variable
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