pvt correlations mccain_valko

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: [email protected] (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.


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.


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.


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


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.


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


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.


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.


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


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


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


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).


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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Table 4.2

The surface gas specific gravity estimates are consistent across the

data set

Data set Number

of points, N

ARE, % AARE, %

All data 618 � 0.7 2.2

PSPV 50 psig 274 � 0.6 1.9

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245 � 1.2 2.4

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300 scf/STB<RSPV700 scf/STB

205 � 0.5 2.1

RSP>700 scf/STB 243 � 0.3 1.3


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