spe-71302-pa

SummaryThis paper evaluates published correlations and neural-networkmodels for bubblepoint pressure (pb) and oil formation volumefactor (Bo) for their accuracy and flexibility in representing hydro-carbon mixtures from different locations worldwide. The studypresents a new, improved correlation for pb based on global data.It also presents new neural-network models and compares theirperformances to numerical correlations.

The evaluation examines the performance of correlations withtheir original published coefficients and with new coefficients calculated based on global data, data from specific geographicallocations, and data for a limited oil-gravity range. The evaluationof each coefficient class includes geographical and oil-gravitygrouping analysis. The results show that the classification ofcorrelation models as most accurate for a specific geographicalarea is not valid for use with these two fluid properties. Statisticaland trend performance analysis shows that some published corre-lations violate the physical behavior of hydrocarbon fluid proper-ties. Published neural-network models need more details to bereproduced. New developed models perform better but sufferfrom stability and trend problems.

IntroductionSolutions to reservoir performance problems at various stages ofreservoir life require knowledge of the physical properties of reser-voir fluids at elevated pressures and temperatures. Thepressure/volume/temperature (PVT) properties for reservoir hydro-carbon mixtures are usually obtained from laboratory analysis ofpreserved or recombined reservoir fluid samples. Because experi-mental facilities are not always available, other means for estimatingPVT properties have been developed; during the last 50 years,many correlations have been developed for this purpose.

PVT properties are a function of temperature, pressure, compo-sition of the hydrocarbon mixture, and the presence of paraffinsand impurities. The performance of an empirical model dependsmainly on how accurately a correlation model represents this mix-ture under specific conditions. The purpose of this paper is to studythe performance of models available in the literature, based onpublished experimental data.

The study was carried out to model the pb and the Bo at and belowthe pb. Both empirical correlations and neural-network models wereconsidered to reach a clearer understanding about what model to useand what to expect. A large global database gathered for this studywas used to develop correlation models that predict oil propertiesbetter than existing models.

Literature Review Since the 1940s, engineers in the United States have realized theimportance of developing empirical correlations for PVT properties.Studies carried out in this field resulted in the development ofnew correlations. Several studies of this kind were published byKatz,1 Standing,2 Lasater,3 and Cronquist.4 For several years, thesecorrelations were the only source available for estimating PVTproperties when experimental data were unavailable. In the last 20years there has been an increasing interest in developing new cor-relations for crude oils obtained from various regions in the world.

Vazquez and Beggs,5 Glaso,6 Al-Marhoun,7,8 and Abdul-Majeedand Salman9 carried out some of the recent studies. The followingpresents a review of the best-known correlation models publishedin the literature. A summary of these published correlation modelsis provided in the Appendix (Tables 1 and 2), including the formsof correlation used, errors reported by each author, and details ofthe data used for each development.

Empirical Correlations. In 1942, Katz1 published a graphical cor-relation for predicting Bo. Katz1 used U.S. midcontinent crude todevelop his correlations. The graphical correlation uses reservoirtemperature, pressure, solution gas/oil ratio (GOR), oil gravity, andgas gravity. The correlations were presented only in graphical formand were hard to use because they required the use of graphs andcalculations in combination.

In 1947, Standing2,10,11 published his correlations for pb andfor Bo. The correlations were based on laboratory experimentscarried out on 105 samples from 22 different crude oils inCalifornia, U.S.A. The correlations treated the pb and the Bo as afunction of the reservoir temperature, GOR, oil gravity, and gasgravity. Standings2,10,11 correlations were the first to use thesefour parameters, which now are commonly used to develop cor-relations. In fact, these correlations are the most widely used inthe oil industry.

Lasater3 in 1958 presented a new correlation model based on158 samples from 137 reservoirs in Canada, the U.S., and SouthAmerica. His correlation was only for pb. It is based on standardphysical chemical equations of solutions. It uses Henrys law con-stant and the observation that the bubblepoint ratio at differenttemperatures is equal to the absolute temperatures ratio for hydro-carbon systems not close to the critical point. The correlation waspresented in graphical form and was used as a lookup chart. Anadvantage of Lasaters3 correlation is the wide variety of datasources used to develop the correlation.

In 1972, Cronquist4 presented a ratio correlation based on 80data points from 30 Gulf Coast reservoirs. The correlation is use-ful for the analysis of depletion-drive reservoirs when PVT analy-sis is not available. The method was presented in graphical formand requires an estimation of average reservoir properties.

In 1976, Vazquez and Beggs5 published correlations for GORand Bo. They started categorizing oil mixtures into two categories,above 30API gravity and below 30API gravity. They also pointedout the strong dependence on gas gravity and developed a corre-lation to normalize the gas-gravity measurement to a referenceseparation pressure of 100 psi. This eliminated its dependence onseparation conditions. More than 6,000 data points from 600 lab-oratory measurements were used in developing the correlations.

Glaso6 in 1978 developed correlations for pb, formation volumefactor, GOR, and oil viscosity for North Sea hydrocarbon mixtures.The main feature of Glasos6 correlations is that they account forparaffinicity by correcting the flash stock-tank-oil gravity to anequivalent corrected value with reservoir temperature and oil vis-cosity. They also account for the presence of nonhydrocarbons onsaturation pressure by using correction factors for the presence ofCO2, N2, and H2S in the total surface gases. A total of 45 oil samples,most of which came from the North Sea region, were used in thedevelopment of these correlations.

In 1988, Al-Marhoun8 published new correlations for estimatingpb and Bo for Middle East oils. A total of 160 data sets from 69Middle Eastern reservoirs were available for the correlation devel-opment. Al-Marhouns7,8 correlations were the first to be developedfor Middle East reservoirs.

146 April 2001 SPE Reservoir Evaluation & Engineering

A Review of Bubblepoint Pressure and OilFormation Volume Factor Correlations

A.A. Al-Shammasi, SPE, Saudi Arabian Texaco

Copyright 2001 Society of Petroleum Engineers

This paper (SPE 71302) was revised for publication from paper SPE 53185, first presentedat the 1999 SPE Middle East Oil Show, Bahrain, 2023 February. Original manuscriptreceived for review 24 June 1999. Revised manuscript received 24 January 2001. Paperpeer approved 15 February 2001.

April 2001 SPE Reservoir Evaluation & Engineering 147

TAB

LE 1

FOR

MA

TION

VO

LUM

E FA

CTO

R C

OR

RE

LATIO

NS

Authors

Correlation

Sam

plesO

rigin

No. of D

ataP

ointsU

sed

Bo

Range(bbl/S

TB)

TR

ange(F

)

Rs

Range(scf/S

TB)

AP

IR

ange(A

PI)

gR

ange(ratio)

Author

AverageE

rror(%

)

Author

Average

AbsoluteE

rror(%

)

Author

Standard

Deviation

Standing

2,10,11 (1947)B

o = a1 +

a2 [ R

s ( g /) a

3 + a4 T

] a5

California,U

.S.A

.105

1.02402.150

100258

201,425

16.563.8

0.590.95

1.17a

1 = 0.972, a2 = 1.472e-4, a

3 = 0.5, a4 = 1.25, a

5 = 1.175V

azquez andB

eggs5 (1980)

Bo = 1+

a1 R

s + a

2 [( A

PI /g )( T 60)] +

a3

[Rs (

AP

I /g ) (T

60)]

Worldw

ide6,004

1.0282.226

7529402,199

15.359.3

0.5111.35

A

PI

30 a1 = 4.677e-4, a

2 = 1.751e-5, a3 = 1.8106e-8

A

PI >30 a

1 = 4.67e-4, a2 = 1.1e-5, a

3 = 1.337e-9

Glaso

6 (1980)B

o = 1+ 10 [a

1 + a2 (log G

) a3 (log G

)2]

G = R

s (g /

) a4+ a

5 TN

orth Sea

411.0322.588

80280902,637

22.348.1

0.651.28

0.432.18

a1 =

6

.58511, a2 = 2.91329, a

3 = 0.27683, a4 = 0.526, a

5 = 0.968

Al-M

arhoun8 (1988)

Bo = a

1 + a

2 (T +460) + a

3 M + a

4 M2

M = R

s a5

g a6 a

7

Middle E

ast160

1.0321.997

74240261,602

19.444.6

0.751.37

0.010.88

1.18

a1 = 0.497069, a

2 = 0.862963e-3, a3 = 0.182594e-2, a

4 = 0.318099e-5, a5 =0.74239, a

6 =0.323294, a7 = 1.20204

Abdul-M

ajeed andS

alman

9(1988)A

l-Marhoun

8 (1988)N

ew calculated constants

420

1.0282.042

7529001,664

9.559.5

0.511.35

0.241.4

1.91

a1 = 0.9657876, a

2 = 7.73e-4, a3 = 4.8141e-5, a

4 = 6.8987e-10, a5 =1.2, a

6 = 0.147, a7 = 5.222

Dokla and

Osm

an17 (1992)

Al-M

arhoun8 (1988)

New

calculated constantsU

AE

511.2162.493

190275

1812,266

28.240.3

0.801.29

0.0231.225

1.681

a1 = 0.431935e-1, a

2 = 0.156667e-2, a3 = 0.139775e-2, a

4 = 0.380525e-5, a5 =0.773572, a

6 =0.404020, a7 =

0.882605

Petrosky and

Farshad

25 (1993)S

tanding

2,10,11 (1947) New

calculated

constantsB

o = a1 +

a2 [ R

s a3 (

g a4/

a5) + a

6 T a

7]a

8G

ulf of Mexico

901.1181.623

114288

2171,406

16.345.0

0.580.85

0.010.64

0.58

a1 = 1.0113, a

2 =7.2046e-5, a3 = 0.3738, a

4 = 0.2914, a5 =0.6265, a

6 =0.24626, a7 = 0.5371, a

8 = 3.0936

Farshad, Leblance,

Garber, and O

sorio21

(1992) (Single S

tage)

Glaso

6 (1980) New

calculated constantsB

o = 1+ 10 [a

1 + a2 (log G

) a3 (log G

)2]

G = R

s a4

g

a5

a6+ a

7 T

Colom

bia107

1.0602.064

9526061,645

18.044.9

0.661.7

13.3237.02

a1 = 2.6541, a

2 =0.5576, a3 = 0.3331, a

4 = 0.5956, a5 =0.2369, a

6 = 1.3282, a7 = 0.0976

Al-M

arhoun20 (1992)

Bo = 1+

a1 R

s + a2 R

s (g /)+

a3 R

s (1

)(T 60) +

a4 (T 60)

Worldw

ide4,012

1.0102.960

7530003,265

9.555.9

0.5752.52

0.000.57

0.6787

a1 = 0.177342e-3, a

2 = 0.220163e-3, a3 = 4.292580e-6, a

4 = 0.528707e-3

Om

ar and Todd

24 (1993)S

tanding 2,10,11 correlation with one change

Bo = a

1 + a

2 [ Rs (

g /) a

3+ a4 T

] x

X = b

1 +b2 (

AP

I / g )+ b

3 g

Malaysia

931.0851.954

125280

1421,440

26.653.2

0.6121.32

1.441.88

b1 = 1.1663, b

2 = 0.762e-3, b3 = 0.0399

Alm

ehaideb27 (1997)

Bo = a

1 + a

2 Rs T

/ 2U

AE

621.1423.562

190306

1283,87130.948.6

0.751.12

1.355.17

a1 = 1.122018, a

2 = 1.41e-6

Macary and

El-B

atanoney22 (1992)

Bo = (a

1 + a

2 T) N

N = exp[a

3 Rs + a

4 (/g )]

Gulf of S

uez,E

gypt90

1.202.00

130290

2001,200

25400.701.00

0.527.04

a1 = 1.0031, a

2 = 0.0008, a3 = 0.0004, a

4 = 0.0006

Kartoatm

odjoand S

chmidt 26(1994)

Standing 2,10,11 (1948) N

ew calculated

constantsB

o = a1 +

a2 [ R

s a3 g

a4/

a5+ a

6 T] a

7

Exactly as P

etrosky and Farshad

25

Worldw

ide5,392

1.0072.144

7532002,890

14.458.9

0.381.71

0.1042.025

a1 = 0.98496, a

2 = 0.0001, a3 = 0.755, a

4 = 0.25, a5 = 1.5, a

6 =0.45, a7 =1.5

o

o

oo

o

o

o

o

oo

o

o

oo

o100


TAB

LE 2

B

UB

BLE

PO

INT

PR

ES

SU

RE

CO

RR

ELA

TIO

NS

Aut

hors

C

orre

latio

n S

ampl

esO

rigin

No.

of

Dat

aP

oint

sU

sed

p bR

ange

(psi

a)

TR

ange

(F)

Rs

Ran

ge(s

cf/S

TB)

AP

I Ran

ge(A

PI)

gR

ange

(rat

io)

Aut

hor

Ave

rage

Err

or(%

)

Aut

hor

Ave

rage

Abs

olut

eE

rror

(%)

Aut

hor

Sta

ndar

dD

evia

tion

Sta

ndin

g2,1

0,11 (1

947)

p b =

a1 [(

Rs/

g) a

2 10

(T a

3 oA

PIa

4 )

a5 ]

Cal

iforn

ia,

U.S

.A.

105

130

7,00

010

025

820

1,

425

16.5

63

.80.

590

.95

4.8

a 1 =

18.

2, a

2 = 0

.83,

a3 =

0.0

0091

, a4 =

0.0

125,

a5 =

1.4

Vaz

quez

an

d B

egg

s5 (1

980)

p b =

{( a

1 Rs/

g) an

tilog

[a 3

AP

I /(46

0+T

)] }a

2W

orld

wid

e6,

004

15

6,05

575

294

02,

199

15.3

59

.30.

511

.35

AP

I 30 a

1 = 2

7.64

, a2 =

1.0

937,

a3 =

11.

172

A

PI >

30 a

1 = 5

6.06

, a2 =

1.1

87, a

3 = 1

0.39

3

Gla

so6 (

1980

)p b

= a

ntilo

g{ a

1+a

2 log

(G)

a3 [

log(

G)]

2 }G

= (R

s/

g) a

4 T

a5

AP

I a6

Nor

th S

ea41

165

7,14

280

280

90

2,63

722

.3

48.1

0.65

1.2

81.

286.

98

a 1 =

1.7

669,

a2 =

1.7

447,

a3 =

0.3

0218

, a4 =

0.8

16, a

5 = 0

.172

, a6 =

0 .

989

Al-M

arho

un8 (

1988

)p b

= a

1 Rs

a2 g

a3

a 4 ( T

+460

)a

5M

iddl

e E

ast

160

20

3,57

374

240

26

1,60

219

.4

44.6

0.75

1.3

70.

033.

664.

536

a 1 =

5.3

8088

e-3,

a2 =

0.7

1508

2, a

3 =

1.87

7840

, a4 =

3.1

4370

0, a

5 = 1

.326

570

Dok

la a

nd O

sman

17 (1

992)

Al-M

arho

un8 (

1988

)N

ew c

alcu

late

d co

nsta

nts

UA

E51

590

4,64

019

027

518

12,

266

28.2

40

.30.

801

.29

0.45

7.61

10.3

78

a 1 =

0.8

3638

6e4,

a2 =

0.7

2404

7, a

3 =

1.01

049,

a4 =

0.1

0799

1, a

5 =

0.95

2584

Pet

rosk

y an

dFa

rsha

d25

Sta

ndin

g 2,

10,1

1 (19

47) N

ew c

alcu

late

d co

nsta

nts

p b =

a1 [

( Rs

a2 /

g a

3) 1

0x

a 4 ]

X=(

a 5 T

a 6

a7

AP

I a8

)

Gul

f of M

exic

o90

1,57

46,

523

114

288

217

1,40

616

.3

45.0

0.58

0.8

60

.17

3.28

2.56

a 1 =

112

.727

, a 2

=0.5

774,

a3 =

0.8

439,

a4 =

12.

340,

a5 =

4.5

61e-

5, a

6=1.

3911

, a7 =

7.9

16e-

4, a

8 = 1

.541

0La

sate

r3 (1

958)

p b =

[(p f

)(T

+459

.67)

]/ g

Yg =

( Rs /

a 1)/

[( R

s /a 1

) +(a

2 /M

)]M

o = a

3 a

4 A

PI+

a5

AP

I2p f

= a

6 a

7 Yg +

a8 Y

g2

Can

ada

Wes

t and

Mid

cont

inen

tU

.S.A

.

158

48

5,78

082

272

32,

905

17.9

51

.10.

571

.23.

8

a 1 =

379

.3, a

2 = 3

50, a

3 = 7

25.3

2143

, a4 =

16.

0333

3, a

5 = 0

.095

24, a

6 = 0

.384

18, a

7 =

1.20

081,

a8 =

9.6

4868

Om

ar a

ndTo

dd24 (1

993)

Sta

ndin

g 2,

10,1

1 cor

rela

tion

with

one

cha

nge

p b =

a1 [

( Rs/ g

) X 1

0(T a

3 A

PIa

4 )

a5 ]

X =

b1+

b 2 B

o+ b

3 g+

b 4 B

o2+

b 5

g2+b

6/ (

Bo

g)

Mal

aysi

a93

790

3,85

112

528

014

21,

440

26.6

53

.20.

611

.32

7.17

9.54

b 1 =

1.4

256,

b2 =

0.

2608

, b3 =

0.

4596

, b4 =

0.0

4481

, b5 =

0.2

360,

b6 =

0.

1077

Fars

had,

Leb

lanc

e,G

arbe

r, an

d O

sorio

21

(199

2) (S

ingl

e S

tage

)

Sta

ndin

g 2,

10,1

1 (19

47) N

ew c

alcu

late

d co

nsta

nts

p b =

a1 (

Rs/

g) a

2 1

0(a

3 T

a

4

AP

I)

Col

ombi

a43

32

4,13

895

260

61,

645

18.0

44

.90.

661

.73

3.4

914

.61

a 1 =

33.

22, a

2=0.

8283

, a3 =

0.0

0003

7, a

4 = 0

.014

2Fa

rsha

d, L

ebla

nce,

Gar

ber,

and

Oso

rio21

(199

2) (S

ingl

e S

tage

)

Gla

so6 (1

980)

New

cal

cula

ted

cons

tant

sp b

= a

ntilo

g{ a

1+a 2

log(

G)

a3 [

log(

G)]

2 }G

=

g a

4 R

s

a 5 1

0 (a

6 T

a

7

AP

I)

Col

ombi

a4

332

4,

138

952

606

1,64

518

.0

44.9

0.66

1.7

313

.32

37.0

2

a 1 =

0.3

058,

a2=

1.9

013,

a3 =

0.2

6, a

4 =

1.37

8, a

5 = 1

.053

, a6=

0.0

0069

, a7 =

0.0

208

Mac

ary

and

El-B

atan

oney

22 (1

992)

p b =

a1 K

[Rs

a2

a3]

K =

exp

[a4T

a 5

A

PI

a6

g ]G

ulf o

f Sue

z90

1,20

04,

600

130

290

200

1,20

025

40

0.70

1.0

00.

527.

04

a 1 =

204

.257

, a2=

0.5

1, a

3 = 4

.792

7, a

4 = 0

.000

77, a

5 = 0

.009

7, a

6= 0

.400

3

Alm

ehai

deb2

7 (19

97)

p b =

a1+

a2 R

s / (

g B

o a3) +

a4T

UA

E6

250

14,

822

190

306

128

3,87

130

.9

48.6

0.75

1.1

24.

997

6.56

a 1 =

62

0.59

2, a

2= 6

.230

87, a

3 = 1

.385

59, a

4 = 2

.898

68K

arto

atm

odjo

and

Sch

mid

t26

(199

4)

Vaz

quez

and

Beg

gs5 c

orre

latio

n (1

980)

New

cal

cula

ted

cons

tant

sp b

= {R

s/[

a 1*

g a2

*10

a 3

/(460

+T) ]}

a4

Wor

ldw

ide

5,39

215

6,

055

753

200

2,89

014

.4

58.9

0.38

1.7

13.

3420

.17

a

1 = 0

.059

58, a

2 = 0

.797

2, a

3 = 1

3.14

05, a

4=0.

9986

AP

I >30

a1 =

0.0

3150

, a2 =

0.7

587,

a3 =

11.

2895

, a4=

0.91

43

o

o o

o

o

o o

o

o o

o

oAP

I

o o

AP

I 30

o o

o

In 1987, Obomanu and Okpobori12 presented new correlationsfor predicting GOR and Bo for Nigerian crude oils. They used 503data points from 100 Nigerian reservoirs in the Niger Delta basin.They used Al-Marhouns7 pb correlation model form and modifiedStandings2 Bo correlation model form. In addition, they developednew correlation coefficients for Nigerian crude oils. The Bo correla-tion divided the crude oils into two ranges according to oil gravity.

In 1988, Abdul-Majeed and Salman9 published a Bo correlationbased on 420 data sets from unpublished sources. The form of thecorrelation is Al-Marhouns8 Bo correlation with new calculatedcoefficients. Al-Fattah and Al-Marhoun13 reported that 259 datasets used by Abdul-Majeed and Salman9 are from Vazquezs14 MSthesis. A total of 256 data sets were found as reported by Al-Fattahand Al-Marhoun.13

In 1989, Asgapur et al.15 published a new set of correlations fordifferent geological reservoirs of western Canadian gases and crudeoils. Correlations for pb, GOR at and below the pb, and Bo at andbelow the pb were developed for four geological reservoirs. Thenew approach of developing correlations for a specific geologictime was justified by the varying behaviors of western Canadianreservoirs. However, little detail was presented concerning thecrude oil differences. The new correlations used Al-Marhouns8 pbcorrelation form and developed a new form for Bo. The newapproach resulted in less average error than the Standing,2Lasater,3 and Vazquez and Beggs5 correlations for all geologicreservoirs studied.

Labedi16 in 1990 published new correlations for Bo, oil density,and fluid compressibility for African crude oils. Labedis16 correla-tions eliminate the need for gas gravity and total GOR by using theseparator pressure and temperature. A total of 97 data sets fromLibya, 28 sets from Nigeria, and four from Angola were available forthe study. The correlations substitute the gas gravity and total GOR,which are very unlikely to be measured in the field, with separationGOR, temperature, and pressure, as these are reported in field tests.

Dokla and Osman17 in 1992 published a new set of correlationsfor estimating pb and Bo for United Arab Emirates crudes. They used51 data sets to calculate new coefficients for Al-Marhouns8 1988Middle East correlations. Al-Yousef and Al-Marhoun18 pointed outthat the Dokla and Osman17,19 pb correlation performance found con-tradicting physical laws, as the pb is decreasing with temperature andis insensitive to oil-gravity changes. The data used in calculating thecoefficients were insufficient to obtain an empirical correlation.

In 1992, Al-Marhoun20 published a second correlation for Bo.The correlation was developed with 11,728 experimentallyobtained formation volume factors at, above, and below pb. Thedata set represents samples from more than 700 reservoirs world-wide, mostly from the Middle East and North America.

In 1992, Farshad et al.21 produced a new set of correlations forpb, GOR, and Bo. They used the number of surface-separator stagesas a criterion for developing the correlations. The main feature ofthe new correlation is that it uses separator gas gravity and GORinstead of the totals, and corrects them for separation temperatureand pressure. Reservoir samples from 98 Colombian reservoirswere available for the study. The new correlations used Standings2and Glasos6 correlation forms and calculated new coefficients forthem. The correlations for a single-stage separation process wereconsidered for this study. The proposed correlations based on cor-rected separator data are more realistic because the stock-tank-gasgravity and GOR are seldom measured in the field.

In 1992, Macary and El-Batanoney22 presented new correla-tions for pb, Bo, and GOR. Ninety data sets from 30 independentreservoirs in the Gulf of Suez, Egypt, were used to develop thecorrelations. The new correlations were tested against otherEgyptian data of Saleh et al.,23 and showed improvement overpublished correlations.

Omar and Todd24 in 1993, based on work similar to Standings2Bo correlation model, calculated a modified set of correlation coef-ficients. Omar and Todd24 also developed a pb correlation that usesthe Bo in addition to oil gravity, gas gravity, GOR, and reservoirtemperature. The new correlation was based on 93 data sets fromMalaysian oil reservoirs. An estimated Bo from the developed cor-relation can be used for bubblepoint prediction if it is not measured.

In 1993, Petrosky and Farshad25 developed new correlationsfor Gulf of Mexico crudes. Standings2 correlations for pb, GOR,and Bo were taken as the basis for developing the new correlationcoefficients. Vazquez and Beggs5 oil-compressibility correlationmodel was used as a base for oil-compressibility correlations. Theapproach that Petrosky and Farshad25 applied to develop the cor-relations was to give the original correlation model maximumflexibility through nonlinear regression to achieve the best empir-ical relation possible with the available data set. The maximumflexibility allows each variable to have a multiplier and exponent,while the original model fixes multipliers and exponents of someof the variables to one. Ninety data sets from the Gulf of Mexicowere used in developing these correlations.

In 1994, Kartoatmodjo and Schmidt26 used a global data bank todevelop new correlations for all PVT properties. Standings2 corre-lation models were taken as the basis for pb and GOR correlations;Vazquez and Beggs5 Bo correlation was considered a base for Bocorrelation. Data from 740 different crude oil samples gatheredfrom all over the world provided 5,392 data sets for correlationdevelopment. These correlations and Al-Marhouns20 1992 Bo corre-lation are the only correlations that used global data for develop-ment. In addition to the global data gathered for the study, a separatedata set collected from the literature was used to verify the finalresults of the correlation models developed and compare them withpublished correlations. The approach used in the development of thenew correlations is similar to Petrosky and Farshads25 approach inproviding the maximum flexibility to the base models to reach thebest empirical relation for the available data.

In 1997, Almehaideb27 published a new set of correlations forUAE crudes. He used 62 data sets from UAE reservoirs to developthe new correlations, for pb, Bo, oil viscosity, and oil compress-ibility. The pb correlation, like Omar and Todds,24 uses the Bo asinput in addition to oil gravity, gas gravity, GOR, and reservoirtemperature. Improvement over published correlations wasachieved with this work.

Neural-Network Correlations. Neural-network uses in petroleumapplications have been increasing in recent years. An overview ofneural-network applications for the petroleum industry is welldocumented by Ali.28 The area of PVT properties modeling usingneural networks is relatively new, and only two studies have beenpublished during the last few years on this subject.

In 1996, Gharbi and Elsharkawy29 presented neural-networkmodels for estimating pb and Bo for Middle East crude oils.Separate models were used for each property, and the modelarchitectures were of two hidden layers. The pb model has eightneurons in the first layer and four neurons in the second. The for-mation volume factor model has six neurons in both layers. Atotal of 498 data sets collected from the literature and unpub-lished sources were used for training the models. Another set of22 data points from the Middle East, not included in the training,were used to verify the resulting network. The results showedimprovement over the conventional correlation methods with atleast a 50% reduction in the average error for the pb and a 30%reduction for Bo.

In 1997, Gharbi and Elsharkawy30 presented another neural-network model for estimating pb and Bo for universal use. The twoproperties are predicted by a model consisting of one hidden layerof five neurons. The study used 5,200 data sets collected from allover the world, representing 350 different crude oils. Another col-lection of data consisting of 234 data sets was used for verifyingthe models results. The reported results for the universal modelshowed less improvement over the conventional correlations thandid the Middle East neural model. The average error for pb was30% less for the training data and 40% less for the test data com-pared to conventional correlations.

On the other hand, the Bo was better than conventional correla-tions only in terms of correlation coefficient. The average error forthe neural-network model is similar to conventional correlationsfor training data and higher for test data than the best-performingconventional correlation. The reported results for test data indicatebetter performance than the training data.


Evaluation Studies of Correlations. As more correlations weredeveloped, researchers compared the previously published correla-tions with the new ones and carried out studies to select the mostaccurate correlation for a particular reservoir or geographic area.The only research done for geologic categorization was done byAsgapur et al.15

In 1983, Ostermann et al.31 evaluated published correlationsbased on eight Alaskan fluid samples. They indicated that Glasos6correlation for pb and Standings2 correlation for Bo showed theleast error for Alaskan crudes. The samples they used were charac-terized by high N2 and CO2 content. The study pointed out the sig-nificant effect of nonhydrocarbons on the pb. Jacobsons31 nitrogencorrection was found to perform better than Glasos6 correction.

In 1987, Saleh et al.23 published an evaluation of empirical cor-relations for Egyptian oils. Glasos6 correlation showed the bestresults for pb and GOR, Standings2 model for Bo, Vazquez andBeggs5 correlation model for viscosity, and Beggs and Robensonsfor compressibility. No details were given about corrections, rangeof data, or number of data.

Sutton and Farshad32,33 in 1990 published an evaluation of Gulfof Mexico crude oils. They used 285 data sets for gas-saturated oiland 134 data sets for undersaturated oil, representing 31 differentcrude oils and natural-gas systems. The results show that Glasos6correlations for pb, GOR, and Bo perform the best for most of thestudy data. It was pointed out that the Vazquez and Beggs5 corre-lation models performed better than Glasos6 correlations at highGOR above 1400 scf/STB and pb greater than 7,000 psia. The over-all average absolute errors for pb and GOR reported for Glasos6correlation models are 25.34% and 27.05%, respectively. Thesevalues are relatively high when compared with what is reported inthe literature.

In 1993, Petrosky and Farshad25 published a new correlationbased on Gulf of Mexico crudes; it had a much lower absoluterelative error for all correlations than what is reported in the 1990study by Sutton and Farshad. The best-performing publishedmodels in the 1993 study are Glasos6 models for pb and GOR.Al-Marhouns8 1988 correlation model for Bo showed the bestperformance of the published models.

In 1991, McCain34 published an evaluation of all reservoirproperties correlations based on a large global database at TexasA&M U. McCain recommended Standings2 correlations for pb andGOR with estimation accuracy of 15% when used with separatorgas gravity and total GOR. For Bo at and below pb, McCain34 rec-ommended Standings2 correlation as well, with an estimationaccuracy of 5.0% when used with total GOR. He also pointed outthe dependence of the estimation accuracy on the data source. Forexample, the accuracy of formation-volume-factor estimation isless if an estimated GOR is used.

In 1994, Al-Fattah and Al-Marhoun13 published an evaluation ofall Bo correlations. They used 674 data sets from published literature.The results recommend Al-Marhouns20 1992 correlation as it showsthe least error for the global data set. The study pointed out the util-ity of trend tests to evaluate the models violations of physicalbehavior. The study indicates the bad performance of all existingcorrelations in the two areas of high GOR and high temperatures.

De Ghetto et al.35 in 1994 published a comprehensive study ofPVT properties correlations based on 195 global data sets repre-senting a full range of hydrocarbon mixtures. The data sources arefrom Agip Oils Inc., collected from the Mediterranean basin,Africa, the Arabian Gulf, and North Sea reservoirs. Standings2correlation for pb gave the best results with an average absoluteerror of 16.1%. This is in close agreement with the results ofMcCains34 study. For the Bo, Vazquez and Beggs5 correlationresults were the best, with an average absolute error of less than3.0%. They categorized oils into four groups according to API oilgravity, and recommended different correlations for each category.

They also investigated the improvement of existing correlationsfor all properties except formation volume factor. This was done byrecalculating new coefficients for the best model selected based onanalysis of the original coefficients. They found improvementscould be achieved in pb models. Reduction of the average absoluteerror to 12.8% for Standings2 correlation was reached. The final

recommendations of the study suggest using the modified,improved correlations with API categorization.

In 1994, Elsharkawy et al.36 published a study for evaluatingPVT correlations for Kuwaiti crude oils. The study used 44 sampleanalyses for the evaluation. Standings2 correlation for pb gave thebest results with an average absolute error of 10.85%. Al-Marhouns8 1988 Bo correlation model performed the best with anaverage absolute error of 2.72%.

In 1996, Mahmood and Al-Marhoun37 presented an evaluationof PVT correlations for Pakistani crude oils. They used 166 datasets from 22 different crude samples for the evaluation. High errorswere obtained for pb. Al-Marhouns8 correlation gave the leasterror with an average absolute error of 31.5%. Al-Marhouns201992 Bo correlation gave the best results with an average absoluteerror of 1.23%. The pb errors reported in this study, for all correla-tions, are among the highest reported in the literature.

In 1997, Hanafy et al.38 published a study evaluating the mostaccurate correlations to apply to Egyptian crude oils. The studyrecommended Macary and El-Batanoneys22 correlations for pband Bo. Macary and El-Batanoneys22 correlation for pb showed anaverage absolute error of 16.6% while Standings,2 Lasaters,3 andLabedis16 models showed 14.1%, 14.8%, and 14.9%, respectively.For formation volume factor, Macary and El-Batanoneys22correlation showed an average absolute error of 4.9%, whileDokla and Osmans17 showed 3.9%. The study strongly sup-ports the approach of developing local correlations as opposedto global correlations.

Data Acquisition and Analysis ProcedureData used for this work is published in the literature and consistsof reservoir temperature, oil gravity, total GOR, and average gasgravity for pb and/or flash Bo at or below pb. This selection is basedon the input requirements for the majority of published correlations.When no information about separation conditions, gas gravity, andGOR are provided, the data are considered as a one-stage separationwith average gas gravity and total GOR reported.

A total of 1,661 data sets from 13 published papers were col-lected and checked for accuracy. Another 48 data sets for Kuwaitireservoirs originated from unpublished sources, for a total of 1,709data sets. Each data set consists of reservoir temperature, pb, for-mation volume factor, gas gravity, GOR, and oil gravity. To ensureaccuracy for each data group collected from a specific source, theresults published in that source were recalculated. Table 3 showsthe data sources and ranges for each parameter and the number ofdata sets collected for each source.

Each data group was checked for duplicates and crosscheckedwith other data groups to avoid repeating data sets in more than onesource. The results are given in Table 4. The data available afterexcluding repeats are 1,243 data sets for pb and 1,345 data sets forformation volume factor. Variable ranges for the two data sets areshown in Table 5.

Thirteen models for each pb and Bo were analyzed with theglobal data sets. The analysis was carried out for each property inthe following sequence.

1. Performance evaluation of correlations with their originalpublished coefficients to determine the degree of accuracy for eachmodel representing global data.

2. Calculation of new coefficients for each correlation modelusing linear or nonlinear regression as models allow. This step isdesigned to test models for global flexibility and to evaluate thepossibility of improving their performance.

3. Development of new correlations.4. Development of new sets of coefficients for each data

group obtained from different geographical locations. This geo-graphically based analysis is meant to evaluate the accuracy ofcategorizing models according to the geographical origin of thecrude used.

5. Performance evaluation of correlations on the basis of oil-gravity grouping. This analysis is used to evaluate the validity ofgrouping correlation models accuracy according to oil gravity.New coefficients for oil-gravity groups will be calculated andtested accordingly.


6. Checking the correlation models from steps 1 through 5against the correct PVT properties trends to determine models con-tradicting physical laws.

Bubblepoint PressureThe statistical analysis parameters for all correlations with originalcoefficients calculated for the 1,243 data sets show that Standings2correlation has the least average absolute error, as shown in the topsection of Table 6. Standings2 correlation has an average absoluteerror of 20.68%, which is 3.22% lower than Al-Marhouns8 correla-tion. When new coefficients are calculated for all correlations basedon global data, the performances of all correlations improve, exceptfor those of Petrosky and Farshad.25 Petrosky and Farshads correla-tion is a recalculation of coefficients based on Standings2 correla-tion, where a nonlinear regression was used and failed to converge.

For Standings2 correlation, two forms were used in the recalcu-lation of new coefficients: the nonlinear form of the original modeland a modified linear form reached by dropping the constant in theoriginal correlation. The modified linear form reached improvementand the nonlinear original form converged to coefficients that gaveless accurate results than the original coefficient. The modified lin-ear form of Standings2 correlation is one of the two correlationspublished by Farshad et al.21 for one-stage separation. This isobserved in Table 6 as a repetition of the results for the two rows.The other one-stage correlation from Farshad et al.21 is a recalcula-tion of coefficients based on Glasos6 correlation, and it failed toconverge. Its results are not included in Table 6. Vazquez andBeggs5 correlation and Kartoatmodjo and Schmidts26 correlationboth show the same results for the recalculation of new coefficients,as the latter one is a development based on the former one.


TABLE 3DATA SUMMARY

GeographicalLocation Index pbmin

pbmax Bomin Bomax Rsmin Rsmax gmin gmax oAPImin oAPImax Tmin Tmax Count

Alaska Ref. 31 515.0 1802.0 1.129 1.236 140.0 435 0.853 1.094 25.40 37.10 122.0 180.0 8

Worldwide Ref. 35 71.0 6613.8 1.034 2.887 8.6 3298 0.624 1.789 6.00 56.80 80.6 341.6 195

Worldwide Ref. 29 408.0 6358.0 1.098 2.887 104.0 3020 0.669 1.188 27.49 52.03 100.0 306.0 22

Worldwide Ref. 9 0.0 0.0 1.028 2.042 9.0 1664 0.511 1.351 9.50 59.50 75.0 294.0 420

Worldwide Ref. 14 126.0 5148.0 1.011 1.962 9.0 1664 0.511 1.041 15.30 59.50 75.0 294.0 259

Colombia Ref. 21 31.7 4137.7 1.045 2.064 6.0 1719 0.657 1.731 18.00 46.50 95.0 260.0 104

Kuwait Unpublished 334.7 2985.0 1.040 1.390 50.5 711 0.750 1.190 15.00 35.17 94.0 176.0 48

Malaysia Ref. 24 790.0 3851.0 1.085 1.954 142.0 1440 0.612 1.750 26.60 53.20 125.0 280.0 93

Middle East Ref. 8 130.0 3573.0 1.032 1.997 26.0 1602 0.752 1.367 19.40 44.60 74.0 240.0 160

Nigeria Ref. 12 58.0 2514.9 1.023 1.723 7.0 1164 0.564 0.929 15.74 43.62 123.0 190.0 48

North Sea,Worldwide

Ref. 6 150.0 7127.0 1.087 2.588 90.0 2637 0.650 1.286 18.10 47.70 80.0 280.0 63

Pakistan Ref. 37 15.0 4975.0 1.067 2.916 92.0 2496 0.825 3.445 29.00 56.50 182.0 296.0 185

UAE Ref. 17 590.0 4640.0 1.216 2.493 181.0 2266 0.798 1.290 28.21 40.31 190.0 275.0 51

U.S.A. Ref. 1 499.0 3950.0 1.070 1.706 6.0 1313 0.575 1.386 21.80 63.70 58.0 255.0 53

TABLE 4CROSS-CHECK OF DATA SETS FOR DUPLICATES AND REPETITIONS

Reference Geographical Location AuthorsDuplicates

Within the Set

1 U.S.A. Katz 0

6 North Sea and Worldwide Glaso 1

8 Middle East Al-Marhoun 0

9* Global Abdul-Majeed and Salman 4

12 Nigeria Obomanu and Okpobori 0

14 Global Vazquez 4

17 UAE Dokla and Osman 0

21 Colombia Farshad, Leblance, Garber,and Osorio

2

24 Malaysia Omar and Todd 0

29** Global Gharbi and Elsharkawy 0

31 Alaska Ostermann, Ehlig-Economides,and Owalabi

0

35 Global De Ghetto and Villa 1

37 Pakistan Mahmood and Al-Marhoun 3

Repeated in other references:*256 data sets found in Abdul-Majeed9 from Vazquezs14 data.**12 data sets found: 2 from Vazquez,14 2 from Dokla and Osman,19 4 from Glaso,6 and 4 from Al-Marhoun.8

With new calculated coefficients, Al-Marhouns8 correlationgave the best fit with an average absolute error of 19.2% for theglobal data used. This was followed by a modified Standing2 cor-relation with 1.15% difference. Al-Marhouns8 gave the bestresults, with new calculated coefficients 1.49% less thanStandings2 original correlation. The linear and nonlinear correla-

tion models reached close average absolute error values, indicatingsimilar flexibility in all models.

Development of New Correlation. The relationships between vari-ables in various forms were explored through plots, and then linearregression analysis was used to test the prediction performance.

After testing many combinations, a new pb correlation,

pb o5.527215

*e1.841408*[o* g]

pb o5.527215

*[Rs*(460T)*g]0.783716, . . . . . . . . . . . . . . . . (1)was reached and found to perform better than all existing modelstested in this study with the global data sets available. The statisticalresults for this new correlation are given in the last section of Table 6.

The performance of the new correlation is better than all othercorrelations with original coefficients or new calculated coefficients.The new correlations statistical measures gave 0.9987 correlationcoefficient, 17.85% average absolute error, 17.17 standard deviation,and 210% maximum error.


TABLE 5pb AND BO DATA RANGES

Units Unitspbmin 31.70 psi pbmax 7127.0 psi

Bomin 1.02 bbl/STB Bomax 2.916 bbl/STB

Rsmin 6.00 scf/STB Rsmax 3298.6 scf/STB

gmin 0.51 ratio gmax 3.44 ratio

oAPImin 6.00 API oAPImax 63.7 API

Tmin 74.0 F Tmax 341.6 F

Bo Data Count: 1345; pb Data Count: 1243

TABLE 6BUBBLEPOINT PRESSURE CORRELATION PERFORMANCE WITHORIGINAL COEFFICIENTS AND WITH NEW CALCULATED COEFFICIENTS

BASED ON GLOBAL DATA

COEFFICIENTS CLASSIFICATION [ORIGINAL COEFFICIENTS]

Correlation NameAverage Absolute

Relative ErrorStandardDeviation Min (%) Max (%)

Standing 20.685 28.50 0.03 372

Farshad, Leblance,Garber, and Osorio(Nonlinear)

22.487 21.63 0.02 173

Al-Marhoun 23.915 28.50 0.01 317

Vazquez 24.084 32.61 0.01 404

Glaso 26.153 26.64 0.00 247

Kartoatmodjo andSchmidt

26.339 37.28 0.02 487

Dokla and Osman 26.415 27.26 0.04 262

Farshad, Leblance,Garber, and Osorio(Linear)

26.844 30.35 0.00 324

Almehaideb 32.648 42.74 0.01 427

Lasater 44.360 91.45 0.02 1214

Macary andEl-Batanoney

45.572 76.11 0.04 767

Petrosky andFarshad

86.635 230.0 0.12 3931

Omar and Todd 267.32 2594. 0.07 54,409

COEFFICIENTS CLASSIFICATION [NEW COEFFICIENTS BASED ON GLOBAL DATA]

Al-Marhoun 19.202 23.36 0.02 237Standing Modified(Linear)

20.358 27.12 0.00 339

Farshad, Leblance,Garber, and Osorio

20.358 27.12 0.00 339

Kartoatmodjo andSchmidt

20.537 28.12 0.04 354

Vazquez 20.537 28.12 0.04 354Glaso 21.621 29.91 0.03 379Macary andEl-Batanoney

21.935 34.79 0.02 479

Standing(Nonlinear)

25.118 45.74 0.03 707

Petrosky andFarshad

127.93 285.7 0.22 4,294

COEFFICIENTS CLASSIFICATION [NEW CORRELATION BASED ON GLOBAL DATA ]

Al-Shammasi 17.849 17.17 0.00 210

Geographical and Gravity-Grouping Analysis. Data sets weregrouped according to their geographical origin. Correlation per-formances for data sets of different origins are calculated for orig-inal published coefficients, new coefficients based on global data,and new coefficients based on individual data groups. The lastclass of coefficients is obtained by calculating the coefficients ofthe correlations for each data group individually. The results showthat regional fitting of correlations to represent a specific geo-graphical region does not always provide the best performancecorrelation. Table 7 shows the average absolute error results forthe three classes of coefficients.

When data were grouped according to API oil gravity, the bestperforming correlation for each geographically classified group ofdata did not show consistent least error over the entire range of grav-ities. Instead, it was observed that the overall least error was a func-tion of the abundance of data points falling in a certain API range.

Results with original coefficients show that the existing corre-lations are highly influenced by the majority of API gravity groups

used to develop them. The new coefficients, on the other hand,show less fluctuation in performance, as globally diverse data setswere used to calculate the coefficients. Fig. 1 shows the perform-ance of the top seven correlations for different API gravity ranges.

Calculating correlation coefficients based on data from a limitedrange of API gravity resulted in lower errors than in original andglobal coefficients cases. Correlations with coefficients based onlimited API gravity data ranges produced slightly better results forall cases except for the range of data above 30API gravity. Themagnitude of the improvement is between 1 and 2%. A summaryof oil-gravity analysis is shown in Table 8.

Sensitivity and Trend Tests. For sensitivity tests, only one variablein the correlation was varied while the rest were held constant to seethe trend of the correlation and check it against the physical laws.Four points were selected, which covered the whole range of reser-voir properties; they are shown in Table 9. These values were takenas the mean of the global data when grouped into four categories


TABLE 7BUBBLEPOINT PRESSURE CORRELATIONS AVERAGE ABSOLUTE ERROR FORGEOGRAPHICAL DATA GROUPS

Ala

ska

Ku

wai

t (U

np

ub

lish

ed)

Mid

dle

Eas

t

Co

lom

bia

U.S

.A.

Wo

rld

wid

e

Mal

aysi

a

Nig

eria

n

No

rth

Sea

an

dW

orl

dw

ide

Pak

ista

n

UA

E

Wo

rld

wid

e

Coefficients Classificationand Correlation Name

Ref.35

Ref.31

Ref.8

Ref.21

Ref.1

Ref.29

Ref.24

Ref.12

Ref.6

Ref.37

Ref.17

Ref.14

Original Coefficients

Farshad, Leblance, Garberand Osorio 19.08 16.49 36.85 31.59 15.75 19.91 15.32 13.49 71.09 16.08 44.06 34.32 21.12Dokla and Osman 33.46 20.47 12.43 20.73 16.48 25.70 14.61 18.64 58.64 29.58 34.40 7.62 26.46Al-Marhoun 26.81 16.28 11.39 3.67 16.30 20.38 22.24 26.43 122.89 13.65 31.50 17.97 19.67Kartoatmodjo and Schmidt 20.31 14.63 18.30 18.09 15.92 16.49 22.90 13.47 36.15 18.50 67.10 50.88 17.39Standing 16.89 17.91 12.36 12.08 13.83 14.37 17.48 12.50 41.85 14.72 45.67 33.56 16.19Lasater 20.52 17.00 19.03 23.87 54.64 21.57 11.43 15.04 39.93 19.62 165.21 41.05 21.80Petrosky and Farshad 136.87 37.12 60.06 162.22 639.62 29.12 12.63 17.58 297.11 72.53 181.97 19.24 111.16Omar and Todd 21.94 16.64 24.02 25.52 19.17 1,133.4 11.28 7.97 48.40 19.06 1,536.89 39.36 17.64Almehaideb 33.26 20.91 35.14 28.85 28.64 72.61 12.67 17.92 78.13 17.53 43.87 13.67 25.50Macary and El-Batanoney 23.96 21.49 20.68 34.45 59.70 26.27 8.69 17.77 89.09 24.63 120.30 43.74 32.47Vazquez and Beggs 17.14 14.74 18.81 18.29 13.37 15.62 19.08 14.16 53.33 15.40 55.34 43.95 16.24Glaso 28.47 15.37 32.56 25.22 19.97 19.61 13.75 17.75 57.40 10.58 32.08 40.91 22.56

New Coefficients Based on Global Data

Al-Marhoun 18.13 16.41 11.23 9.85 11.98 14.33 14.91 14.42 71.80 13.85 31.11 26.28 15.32Al-Shammasi 17.56 16.56 16.08 18.20 13.60 15.44 14.21 12.18 44.56 17.40 15.85 30.00 16.58Standing Modified (Linear) 17.75 16.77 13.22 13.55 11.07 15.33 15.80 12.36 46.14 15.99 42.54 26.84 16.22Farshad, Leblance,Garber, and Osorio 17.75 16.77 13.22 13.55 11.07 15.33 15.80 12.36 46.14 15.99 42.54 26.84 16.22Vazquez and Beggs 18.25 17.41 13.37 13.02 11.09 14.75 15.61 12.28 46.49 15.25 44.64 26.98 15.87Macary and El-Batanoney 17.34 14.40 16.64 16.34 34.65 13.61 8.18 11.90 74.42 15.67 24.49 34.93 18.30Petrosky and Farshad 99.82 51.34 75.83 144.64 248.05 48.52 51.42 32.40 264.90 83.09 225.41 42.90 94.90Kartoatmodjo and Schmidt 18.25 17.41 13.37 13.02 11.09 14.75 15.61 12.28 46.49 15.25 44.64 26.98 15.87Glaso 19.07 15.45 13.52 13.47 14.74 13.96 9.98 13.69 45.25 13.34 48.70 29.24 16.31

New Coefficients Based on Data Group

Kartoatmodjo and Schmidt 15.92 13.57 11.01 10.12 11.47 27.63 16.37 11.91 9.93 13.88 29.31 8.04 16.65Glaso 22.20 10.59 11.37 14.12 17.21 17.46 12.00 19.14 12.51 11.69 28.87 8.34 16.97Standing Modified (Linear) 14.13 9.66 10.60 10.21 11.51 23.61 16.62 11.76 9.34 14.78 25.97 7.68 16.63Vazquez and Beggs 15.92 13.57 11.01 10.12 11.47 27.63 16.37 11.91 9.93 13.88 29.31 8.04 16.65Petrosky and Farshad 99.70 46.85 69.19 177.30 302.52 58.45 79.68 34.67 174.81 127.56 145.93 62.17 16.63Macary and El-Batanoney 22.20 5.71 11.54 5.07 31.95 17.94 16.37 19.19 10.98 11.80 17.48 8.81 17.33Al-Marhoun 14.18 10.51 10.58 3.67 11.41 22.72 15.88 10.86 9.47 13.11 19.32 7.61 16.18Farshad, Leblance,Garber, and Osorio 14.13 9.66 10.60 10.21 11.51 23.61 16.62 11.76 9.34 14.78 25.97 7.68 16.63Al-Shammasi 15.59 10.26 10.85 7.84 13.78 19.80 15.31 11.86 9.94 12.98 16.17 8.53 16.92

Wo

rld

wid

e

(very heavy, heavy, medium, and light oils). The trend results ofcorrelations with original published coefficients confirmed theresults, indicated by Al-Yousef and Al-Marhoun,18 that Dokla andOsmans17 correlation for UAE crudes was contradicting physicallaws. Dokla and Osmans17 correlation shows that the pb decreasesas the temperature increases and has no sensitivity to API gravity.With global data used to calculate coefficients, all models manageto follow the correct trends with changes in variables.

Correlations with coefficients calculated based on limited datafrom a certain origin do not always give the correct trend. This indi-cates that limited data might generate a correlation with coefficientsthat give lower average absolute errors, but with trends that contradictphysical laws. For example, correlations based on UAE and Nigeriandata sets do not conform to physical laws. Fig. 2 shows temperaturetrends for three major correlations, with coefficients calculated basedon these two data groups. For correlations with coefficients devel-oped from a limited range of API gravities, the trend performance suf-fers from the same problem as would limited data sets.

Overall Performance Assessment. The performance of bubble-point correlations depends strongly on three sources of error. Thefirst is error involved in the correlation itself, from the error in thedata used to develop it and from the degree of coverage it providesover the range of reservoir fluid properties. Such error will beimbedded within the coefficient values used in the correlation. Thesecond error source is from the input variables used in the model.The majority of this error comes from the uncertainty of total GORmeasurement because of the strong presence of this variable in thefunction of pb in its various forms. The last source of error iscaused by nonhydrocarbons and impurities not corrected for andnot represented in the correlation. For the correlations presented inthis study, only the first error source is controllable. From theanalysis done, the following points could be generalized for bub-blepoint correlations.

One global correlation model, which could be considered thebest correlation model for all kinds of data, does not exist. This issupported by the observation that there is no correlation modelwith original coefficients or with new calculated coefficients thatperfectly fits the global data.

Classifying crudes by geographical origin and then using cor-relation models for specific geographical areas is usually invalid.Observations that support this conclusion are as follows.

The correlation model with the least overall error for each setof data (geographically classified) does not show consistentleast error over the whole range of API gravity; instead, itwas observed that it is related to the abundance of data pointsfalling in a certain API range. This observation is true forcorrelation models with original coefficients, new coeffi-cients calculated based on the global data, and new coeffi-cients calculated based on each data group.

Calculating new coefficients for the correlation modelsbased on limited data points might result in correlationswith coefficients that contradict the physical behavior ofpetroleum fluids.

It has been observed in the literature23,38 that the correlationmodel recommended for a specific geographical areachanges as the data set changes.

In addition to producing a model that is inconsistent withphysical laws, the practice of calculating new sets of coefficientsfor a specific data set sometimes results in less accurate coeffi-cients than those already published.

The newly developed Al-Shammasi correlation performs bet-ter than all existing correlations with original coefficients or newcalculated coefficients.

The most consistent published correlation model for all datathat exhibits a safe error range over the whole API gravity isStandings2 correlation.

The proper classification of correlation models should bebased on API gravity. This is supported by the observed reductionin error when correlation model coefficients were calculated basedon a limited vs. a full range of API gravity.

The process of developing new coefficients for an existingcorrelation model should always include a check for consistencywith physical laws.

Limited data that does not cover the whole range of fluidproperties should not be used to generate correlations or to calcu-late new coefficients for existing correlations.

Oil Formation Volume Factor CorrelationsThe statistical analysis parameters for all correlations with originalcoefficients calculated for 1,345 data sets indicate that Petroskyand Farshads25 is the best performing correlation model for thedata used in this work. This is supported by the statistical indica-tors, as shown in Table 10.

Petrosky and Farshads25 correlation and Kartoatmodjo andSchmidts26 correlation for Bo modify Standings2 correlation.Standings correlation was modified by recalculation of the corre-lation coefficients with maximum flexibility of the model. Bothcorrelations converge to the same point for the recalculation ofcoefficients based on the global data. The two correlations are bestfor new coefficients, but not better than the Petrosky and Farshad25correlation with original published coefficients. The results of thenew calculated coefficients for all correlation models, along withthe original coefficients, are given in Table 10.

Development of a New Correlation. For the development of newBo correlations from the many forms analyzed, two correlationswere selected. One uses three variables instead of the four vari-ables conventionally used. The gas-gravity variable is not requiredfor this model. The two models with coefficients calculated basedon the global data set are given in Eqs. 2 and 3, and the perform-ance parameters for the new correlations are shown in Table 10.

New correlation with four variables:

Bo15.53*107[Rs*(T60)]0.000181*(Rs/o)Bo0.000449*[(T60)/o]0.000206*(Rs* g/o). . . . . . . (2)New correlation with three variables:

Bo10.000412*(Rs/o)0.000650*[(T60)/o]. . . . . . . (3)Geographical and Gravity-Grouping Analysis. Grouping thedata according to geographical origin, Petrosky and Farshads25


Fig. 1API grouping of average absolute error for pb correla-tions with published coefficients.

API Category

< 10

>= 10

& < 15

>= 15

& < 20

>= 20

& = 25

& < 30

>= 30

& < 35

>= 35

& = 40

& = 45

Ave

rage

Abs

olut

e R

elat

ive

Err

or %

10

15

20

25

30

35

40

45Standing CorrelationVazquez and Beggs CorrelationAl-Shammasi CorrelationFarshad, Leblance, Garber, and Osorio CorrelationKartoatmodjo and Schmidt CorrelationAl-Marhoun CorrelationDokla and Osman Correlation

correlation with original published coefficients performs bet-ter than all data groups except Pakistan data,37 Middle Eastdata from Al-Marhoun,8 Katzs1 data, and UAE19 data. Of thegeographical-grouping results for correlations with coefficientscalculated based on a global data set, Petrosky and Farshads25correlation performs the best, except for the groups indicated.Fig. 3 shows the performance of the top seven correlations withgeographical grouping. In the case of coefficients calculatedbased on data groups, the results show Petrosky and Farshads25correlation best except for UAE19 and Al-Marhouns8 MiddleEast data.


TABLE 8AVERAGE ABSOLUTE ERROR FOR BUBBLEPOINT PRESSURE CORRELATIONS WITH ORIGINAL COEFFICIENTSAND COEFFICIENTS CALCULATED BASED ON GLOBAL DATA WITH API GRAVITY GROUPING

Coefficients Classification: Original Coefficients

Correlation Name API Range < 10 < 2010 and20

20 and30 30

Farshad, Leblance, Garber,and Osorio (Linear)

18.31 31.25 33.87 33.16 24.49

Al-Marhoun 31.85 33.93 34.35 27.76 21.75Almehaideb 48.45 61.08 63.64 37.84 28.22Kartoatmodjo and Schmidt 23.60 21.75 21.37 20.07 28.70Standing 10.54 15.37 16.35 19.20 21.67Glaso 103.66 45.83 34.11 28.03 23.61Lasater 28.20 30.99 31.56 38.55 47.46Dokla and Osman 31.93 34.95 35.56 22.28 26.81Vazquez and Beggs 14.60 20.10 21.21 20.26 25.64Omar and Todd 38.52 29.63 27.83 207.84 309.12Macary and El-Batanoney 29.26 39.32 41.36 42.92 47.00Petrosky and Farshad 124.39 142.47 146.14 128.97 68.22

Al-Shammasi 17.93 20.82 21.41 20.69 16.69

Kartoatmodjo and Schmidt 12.55 18.69 19.94 19.09 21.16

Petrosky and Farshad 127.91 184.10 195.49 181.20 106.18

Al-Marhoun 11.37 19.76 21.46 20.51 18.75

Standing Modified (Linear) 10.29 17.28 18.70 19.17 21.03

Macary and El-Batanoney 18.56 26.66 28.30 29.22 19.26

Glaso 36.28 19.48 16.08 19.94 22.34

Vazquez and Beggs 12.55 18.69 19.94 19.09 21.16

Farshad, Leblance, Garber,and Osorio (Linear)

10.29 17.28 18.70 19.17 21.03

Coefficients Classification: Based on Data Within API Group

Vazquez and Beggs 10.27 19.07 20.76 18.18 21.31

Al-Shammasi 11.13 18.91 20.35 18.21 16.90

Glaso 7.39 16.93 18.08 20.20 22.01

Petrosky and Farshad 127.91 184.10 135.44 168.64 152.12

Macary and El-Batanoney 8.70 14.76 14.35 23.24 20.30

Al-Marhoun 9.58 14.77 15.44 17.99 19.10

Standing Modified (Linear) 10.06 14.37 15.15 18.12 21.22

Count 15 89 74 268 886

New Coefficients Based on Global DataCoefficients Classification:

TABLE 9MEAN VALUES USED FOR THE TREND TESTS

API Grade Very Low Low Medium Light

T (F) 198 157 161 196

oAPI 7.8 16.9 25.9 38.7

g 1.214 1.024 0.942 1.054

Rs (scf/STB) 122 146 270 667 Fig. 2Temperature trend of pb correlations with coefficientscalculated on the basis of UAE and Nigerian data groups.

0

500

1000

1500

2000

2500

3000

3500

4000

107

117

127

137

157

167

177

187

207

217

227

237

257

267

277

287

307

317

327

337

357

367

377

387

407

417

427

437

Temperature

Pre

ssur

e

Al-Marhoun Correlation (Based on UAE Data)Standing Modified Correlation (Based on UAE Data)Glaso Correlation (Based on UAE Data)Standing Original CorrelationAl-Marhoun Correlation (Based on Nigeria Data)Standing Modified Correlation (Based on Nigeria Data)Glaso Correlation (Based on Nigeria Data)

Although Petrosky and Farshads25 correlation is best, the per-formance is not consistent when data are grouped according to APIoil gravity. Petrosky and Farshads25 correlation consistently per-forms better for crude oil below 25API gravity. Higher than25API gravity, the performance is not consistent, but is very closeto the best performer. Fig. 4 shows the performance of the besteight correlations with original coefficients and global-based coef-ficients with API gravity grouping.

Results for correlations with coefficients calculated based ondata from a limited API gravity range show improvement in thevery heavy and light crudes. Petrosky and Farshads25 correlationremains the best performer in the heavy and medium crudes.

Sensitivity and Trend Tests. Trend analysis of Bo correlationswith original published coefficients shows several of them con-tradicting the physical laws. The analysis used the same four cat-


TABLE 10OIL FORMATION VOLUME FACTOR CORRELATIONS PERFORMANCE WITHORIGINAL COEFFICIENTS AND WITH NEW CALCULATED COEFFICIENTS

BASED ON GLOBAL DATA

Coefficients Classification: Original Coefficients

CorrelationName

Average AbsoluteRelative Error Standard Deviation Min (%) Max (%)

Al-Marhoun(1988)

2.126 2.37 0.00 34.8

Kartoatmodjoand Schmidt 1.973 2.22 0.00 33.9

Standing 2.424 2.88 0.00 34.0

Glaso 2.936 2.60 0.00 34.9

Abdul-Majeedand Salman

3.275 4.12 0.00 41.3

Petrosky andFarshad

1.728 1.92 0.00 11.8

Al-Marhoun(1992)

1.769 2.27 0.00 33.7

Omar andTodd

3.392 3.93 0.00 34.6

Almehaideb 7.506 5.76 0.02 37.9


8.096 5.00 0.03 60.9

Vazquez andBeggs

3.700 4.45 0.01 33.5

Dokla andOsman 3.765 3.26 0.00 38.8

Coefficients Classification: New Coefficients Based on Global Data

Petrosky andFarshad

1.760 2.20 0.00 33.2

Kartoatmodjoand Schmidt

1.760 2.20 0.00 33.2

Al-Marhoun(1992) 1.773

2.25 0.00 33.6

Vazquez andBeggs

3.630 3.66 0.00 33.2


2.830 2.92 0.00 33.0

Standing 2.057 2.42 0.00 34.0

Almehaideb 2.747 2.69 0.00 32.3

Glaso 2.064 2.42 0.00 33.5

Al-Marhoun(1988) 1.963

2.28 0.00 34.3

Coefficients Classification: New Correlation Based on Global Data

Al-Shammasi(FourVariables)

1.806 2.27 0.00 33.7

Al-Shammasi(ThreeVariables)

3.033 2.66 0.00 32.9


egories of mean values that were used in pb trend analysis. Thepoints listed below are observations on correlations with originalpublished coefficients; Figs. 5 and 6 show some of these.

Abdul-Majeed and Salmans9 model at high GOR shows adecrease in the Bo as the GOR increases. That contradicts thephysical laws.

Macary and El-Batanoneys22 correlation is insensitive to gasgravity and API gravity changes.

Vazquez and Beggs5, Omar and Todds,24 and Abdul-Majeedand Salmans9 correlations show incorrect trend of Bo with increas-ing gas gravity.The use of limited data to calculate coefficients for correlations,as is the case with geographically based correlations, producescorrelations with incorrect trends because data are not sufficient torepresent the whole range of fluid properties. The trend perform-ance of correlations with coefficients based on API limited-rangedata is more adversely affected.

Overall Performance Assessment. The Bo property of hydrocar-bon mixtures is less influenced by the presence of nonhydrocarbonsand impurities. The gas gravity parameter is of less significance andinfluence on this property. Therefore, the large error involved in thisvariable measurement does not reflect high error in estimation ofBo. Petrosky and Farshads25 correlation with original coefficientsfor Bo shows outstanding performance and could be generalized forglobal use with a high level of confidence. Al-Marhouns20 1992correlation comes second. From the analysis done, the followingpoints could be generalized for Bo.

Petrosky and Farshads25 correlation, with original coeffi-cients, exhibits nearly consistent geographical and API groupingperformance. It can be used for all types of data with acceptableaccuracy; therefore, there is no need for geographical or API-gravity-based classifications.

Calculating new coefficients for correlation models based onlimited data sets might result in coefficients that invalidate thephysical behavior of petroleum fluids, as well as the possibility ofproducing coefficients inconsistent with physical laws. The prac-tice of calculating new sets of coefficients for a specific data setwas found to be not always better than the published coefficients.

The process of developing new coefficients for an existingcorrelation model or developing a new correlation should alwaysbe followed with checks on the trend of the correlation modelagainst the physical laws.

Neural NetworksThe two existing models published in the literature, Gharbi andElsharkawys,29,30 were subjected to validation. Two points mustbe clear about the validation. First, the published models are notclear about the order by which input variables are delivered to themodels. Second, only the sigmoidal transfer function is mentionedas the function used from each layer to the next. Using the sig-moidal transfer function for all layers, and assuming all possiblecombinations of transfer functions commonly used with backprop-

Fig. 3Error distribution for Bo correlations with original andnew calculated coefficients.

Geographical Location of Data Source

Worldw

ide R35

Alaska

n R31

Kuwait

8

Middle

East R

Colomb

ia R21

Worldw

ide R29

Worldw

ide R9

Malays

ian R24

Nigeria

n R12

North S

ea R6

Pakista

n R37

UAE R

17

Worldw

ide R14

Ave

rage

Abs

olut

e R

elat

ive

Err

or %

0

1

2

3

4

5

6Petrosky and Farshad New Coefficients Based on Global DataPetrosky and Farshad Original CoefficientsAl-Marhoun (1992) New Coefficients Based on Global DataAl-Marhoun (1992) Original CoefficientsKartoatmodjo Original CoefficientsStanding Original CoefficientsGlaso New Coefficients Based on Global Data

Fig. 4API grouping of average absolute error for Bo correla-tions with original and new calculated coefficients.

API Category

< 10

>=10 &

=15 &

=20 &

=25 &

=30 &

=35 &

=40 &

=45

Ave

rage

Abs

olut

e R

elat

ive

Err

or %

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0Petrosky and Farshad New Coefficents Based on Global Data Petrosky and Farshad Original CoefficientsAl-Shammasi (4 variables) Based on Global DataAl-Marhoun (1992) New Coefficents Based on Global DataAl-Marhoun (1992) Original CoefficientsKartoatmodjo Original CoefficientsStanding Original CoefficientsGlaso New Coefficents Based on Global Data

Fig. 5Solution GOR trend of oil formation volume factor cor-relations with the original published coefficients.

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

157

322

472

607

715

795

875

9391,

0191,

1151,

1791,

2591,

3311,

4191,

4911,

5711,

6431,

7311,

8111,

8831,

9632,

0432,

1232,

1952,

2752,

3632,

4352,

5152,

5792,

6752,

7392,

8192,

8912,

9793,

0593,

131

Solution GOR

Oil

Fo

rmat

ion

Vo

lum

e F

acto

r

Standing Correlation

Petrosky and Farshad Correlation

Abdul-Majeed and Salman Correlation

Fig. 6Gas-gravity trend of oil formation volume factor corre-lations with the original published coefficients.

1.250

1.350

1.450

1.550

1.650

1.750

1.850

0.675

0.735

0.795

0.855

0.915

0.975

1.035

1.095

1.155

1.215

1.275

1.335

1.395

1.455

1.515

1.575

1.635

1.695

1.755

Gas Gravity

Oil

Fo

rmat

ion

Vo

lum

e F

acto

r

Standing CorrelationPetrosky and Farshad CorrelationVazquez and Beggs CorrelationAbdul-Majeed and Salman CorrelationMacary and El-Batanoney CorrelationOmar and Todd Correlation


agation for all possible delivery sequences of input to the neuralmodel, the models could not be reproduced. Models reported needmore details to be reproduced.

Development of Neural-Network Models. The development ofneural-network models starts with finding the best network struc-ture to represent the complicated relationship between variables.Possible neural-network structures, starting from a low number oflayers and neurons to a higher number of layers and neurons,should be tested. Successful structures are those that converge tothe target error or reach the minimum possible sum square error(SSE) and exhibit stable performance to new data not included inthe training.

Of the global data sets, 137 were randomly selected for testingsuccessfully trained models, leaving 1,106 data sets available forpb training. The best results reached by a model consisted of twohidden layers (five nodes in the first layer and three in the secondlayer) with a training average absolute error of 15.08% and 19.86%for the test data sets. The improvement over the new Al-Shammasicorrelation is 2.77% for training data. The test data averageabsolute error is higher than the numerical correlation models by2.01%. It was observed that several structures reached 15 to 16%average absolute error, which was always the minimum error levelfor each configuration. This is confirmed by a plot of SSE vs.cumulative iterations performed. Most of the high-error points

were observed to be in the low-pressure and low oil-gravity range.Using limited data for training gave similar results, as shown inTable 11.

The overall improvement reached in all cases shows that the quality of the numerical correlation is very close to the neural-network modeling. The difference between the numerical correlations and neural-network models is relatively small.They are not enough to justify field applications, but are worthincorporating in computerized applications if they pass thetrend test.

The model based on the global data, and selected based on errorperformance, will be used for trend testing. Table 12 gives thearchitecture of the model with all necessary details to reproduce it.Figs. 7 through 10 show trend analysis plots of the model. Trendtests clearly show the weakness of the neural-network model, as itis unstable and has the wrong trend for GOR. No other model mettrend analysis criteria that could be presented as a correct trendneural model.

Neural-network model development for Bo used 1,165 data setsfor training, leaving 180 data sets reserved for testing. The best-achieved model has an average absolute error of 11.68%, muchhigher than the conventional numerical correlations. Modelsreached were found to consistently have 12 to 14% absolute averageerror position after few iterations, indicating the strong presence ofthat direction in the training data.

A nonlinear relationship in numerical correlations is com-monly used to represent the Bo relation. Convergence of nonlinearmodels to optimum solutions is very dependent on the startingposition and the data used in the process of nonlinear optimiza-tion. This dependence on both factors is also valid for neural-networks training. The local minimum reached by different modelsis probably caused by the strong presence of that local in thearchitectures used.

The performance of empirical correlations for Bo is acceptable,with an average absolute error of 1.8%. This low error is largelycaused by experimental and human error. Therefore, the improve-ment in performance expected from neural-network modeling islimited and of small magnitude.

TABLE 11PERFORMANCE COMPARISON BETWEENNEURAL-NETWORK AND NUMERICAL CORRELATIONS

Training DataNeural-Network

Best-Model ResultsNumerical

Correlation Results

All data (1,106 sets) 15.08% 17.85%

Al-Marhoun(160 sets)

2.38% 3.67%

Conclusions1. The new developed correlations (Eqs. 1 through 3) are

improvements over existing correlations based on the resultsobtained for the data used in this study. The new pb correlation(Eq. 1) has the lowest average absolute error for global dataused in this study. It significantly outperforms other correla-tions for oil gravity above 30API gravity.

2. Of the published bubblepoint correlations, Standings2 correla-tion is the most stable performance correlation and has an esti-mated average absolute error of approximately 20%. Petroskyand Farshads25 Bo correlation is the best global correlation.Neural-network models have not been proven to perform betterthan numerical correlations for these two fluid properties.

3. Correlation selection for a particular application should bebased on oil-gravity performance criteria, not on geographicalcriteria. Geographical classification of crude oils is not sup-ported by PVT correlation performance. Only data that fullyrepresent the full range of PVT properties should be used todevelop new correlations or perform modifications to existingmodels. Trend analysis is recommended to check correlationperformance over the full range of PVT properties.

4. Caution should always be used in applying PVT correlations,including the ones developed in this study, as the accuracy ofany correlation is not guaranteed for data different from the oneused for developing it.

NomenclatureBo oil formation volume factor, bbl/STBpb bubblepoint pressure, psia

Rs solution gas/oil ratio, scf/STBT temperature, F

Wij weight for input i and neuron j specific gravityo oil specific gravityg gas specific gravity viscosity, cp

AcknowledgmentsThe author wishes to express his sincere appreciation to SaudiArabian Texaco for permission to publish this paper. Appreciationis also extended to the Kuwait U. Computer Services (KUCS) forproviding software used in this study and to the Texaco E&PTechnology Dept. (EPTD) library staff for providing the literaturereferences and for their support throughout the study.

References1. Katz, D.L.: Prediction of shrinkage of crude oils, Drill. Prod. &

Prac., API, Dallas (1942) 137.2. Standing, M.B.: A Pressure Volume Temperature Correlation for

Mixture of California Oils and Gases, Drill. & Prod. Prac., API,Dallas (1947) 275.

3. Lasater, J.S.: Bubble Point Pressure Correlation, Trans., AIME(1958) 213, 379.

4. Cronquist, Chapman.: Dimensionless PVT Behavior of Gulf CoastReservoir Oils, JPT (May 1973) 538.

5. Vazquez, M. and Beggs, H.D.: Correlation for Fluid Physical PropertyPrediction, JPT (June 1980) 968.


Fig. 7Temperature trend for neural-network model.

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

87 107

127

147

167

187

207

227

247

267

287

307

327

347

367

387

407

427

Temperature

Bub

blep

oint

Pre

ssur

e Bubble point Pressure

Fig. 8Oil-gravity trend for neural-network model.

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

6.74

9.14

11.54

13.94

16.34

18.74

21.14

23.54

25.94

28.34

30.74

33.14

35.54

37.94

40.74

43.74

46.74

49.74

52.74

55.74

58.74

61.74

Oil Gravity

Bub

blep

oint

Pre

ssur

e

Bubblepoint Pressure

Fig. 9GOR trend for neural-network model.

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

75 165

255

390

534

337

607

779

923

1,06

71,

211

1,35

51,

499

1,64

31,

787

1,93

12,

075

2,21

92,

363

2,50

72,

651

2,79

52,

939

3,08

3

Solution GOR

Bu

bb

lep

oin

t P

ress

ure


Fig. 10Gas-gravity trend for neural-network model.

0

500

1,000

1,500

2,000

2,500

3,000

0.71

50.

755

0.79

50.

835

0.87

50.

915

0.95

50.

995

1.03

51.

075

1.11

51.

155

1.19

51.

235

1.27

51.

315

1.35

51.

395

1.43

51.

475

1.51

51.

555

1.59

51.

635

1.67

51.

715

1.75

51.

795

Gas Gravity

Bub

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6. Glaso, O.: Generalized Pressure-Volume-Temperature Correlations,JPT (May 1980) 785.

7. Al-Marhoun, M.A.: PVT Correlations for Saudi Crude Oils, paperSPE 13718 presented at the 1985 SPE Middle East Oil Show, Manama,Bahrain, 1114 March.

8. Al-Marhoun, M.A.: PVT Correlations for Middle East Crude Oils,JPT (May 1988) 650; Trans., AIME, 285.

9. Abdul-Majeed, G.H.A. and Salman, N.H.: An Empirical Correlationfor FVF Prediction, J. Cdn. Pet. Tech. (1988) 27, No. 6, 118.

10. Standing, M.B.: Oil-System Correlation, Petroleum ProductionHandbook, T.C. Frick (ed.), McGraw-Hill Book Co., New York City(1962) 2, Chap. 19.

11. Standing, M.B.: Volumetric and Phase Behavior of Oil Field HydrocarbonSystems, Reinhold Publishing Corp., New York City (1952).

12. Obomanu, D.A. and Okpobori, G.A.: Correlating the PVT Propertiesof Nigerian Crudes, Trans., ASME (1987) 109, 214.

13. Al-Fattah, Saud Mohammed and Al-Marhoun, M.A.: Evaluation ofempirical correlation for bubble point oil formation volume factor, J.Pet. Sci. and Eng. (1994) 11, 341.

14. Vazquez, M.E.: Correlation for Fluid Physical Property Prediction,MS thesis, U. of Tulsa, Tulsa, Oklahoma (1976).

15. Asgapur, Soheil et al.: Pressure Volume Temperature Correlation forWestern Canadian gases and Oils, J. Cdn. Pet. Tech. (JulyAugust1989) 28, 103.

16. Labedi, R.: Use of Production Data to Estimate Volume Factor Densityand Compressibility of Reservoir Fluids, J. Pet. Sci. Eng. (1990) 4, 357.

17. Dokla, M. and Osman, M.: Correlation of PVT Properties for UAECrudes, SPEFE (March 1992) 41.

18. Al-Yousef, H.Y. and Al-Marhoun, M.A.: Discussion of Correlation ofPVT Properties for UAE Crudes, SPEFE (March 1993) 80.

19. Dokla, M. and Osman, M.: Authors Reply to Discussion of Correlationof PVT Properties for UAE Crudes, SPEFE (March 1993) 81.

20. Al-Marhoun, M.A.: New Correlation for formation Volume Factor ofoil and gas Mixtures, J. Cdn. Pet. Tech. (March 1992) 31, No. 3, 22.

21. Farshad, F.F. et al.: Empirical PVT Correlations for Colombian CrudeOils, paper SPE 36105 presented at the 1996 SPE Latin American andCaribbean Petroleum Enginerring Conference, Port of Spain, Trinidadand Tobago, 2326 April.

22. Macary, S.M. and El-Batanoney, M.H.: Derivation of PVTCorrelations for the Gulf of Suez Crude Oils, EGPC 11th Pet. Exp. &Prod. Conf. (1992).

23. Saleh, A.M., Mahgoub, I.S., and Asaad, Y.: Evaluation of EmpiricallyDerived PVT Properties for Egyptian Oils, paper SPE 15721 presentedat the 1987 SPE Middle East Oil Show, Manama, Bahrain, 710 March.

24. Omar, M.I. and Todd, A.C.: Development of New Modified BlackOil Correlation for Malaysian Crudes, paper SPE 25338 presentedat the 1993 SPE Asia Pacific Oil and Gas Conference, Singapore,810 February.

25. Petrosky, G. and Farshad, F.: Pressure-Volume-TemperatureCorrelation for the Gulf of Mexico, paper SPE 26644 presented atthe 1993 SPE Annual Technical Conference and Exhibition, Houston,36 October.

26. Kartoatmodjo, Trijana and Schmidt, Zelimie: Large data bank improvescrude physical property correlations, Oil & Gas J. (4 July 1994) 51.

27. Almehaideb, R.A.: Improved PVT Correlations for UAE Crude Oils,paper SPE 37691 presented at the 1997 SPE Middle East Oil Show,Manama, Bahrain, 1518 March.

28. Ali, J.K.: Neural Networks: A New Tool for the Petroleum Industry,paper SPE 27561 presented at the 1994 European Petroleum ComputerConference, Aberdeen, 1517 March.

29. Gharbi, R.B. and Elsharkawy, A.M.: Neural Network Model forEstimating the PVT Properties of Middle East Crude Oils, paper SPE37695 presented at the 1997 SPE Middle East Oil Show, Manama,Bahrain, 1518 March.

30. Gharbi, R.B. and Elsharkawy, A.M.: Universal Neural Network BasedModel for Estimating the PVT Properties of Crude Oil Systems, paperSPE 38099 presented at the 1997 SPE Asia Pacific Oil and GasConference, Kuala Lumpur, 1416 April.

31. Ostermann, R.D., Ehlig-Economides, C.A., and Owalabi, O.O.:Correlations for the Reservoir Fluid Properties of Alaskan Crudes,paper SPE 11703 presented at the 1983 SPE California RegionalMeeting, Ventura, California, 2325 March.

32. Sutton, Robert P. and Farshad, F.: Evaluation of Empirically Derived PVTProperties for Gulf of Mexico Crude Oils, SPERE (February 1990) 79.

33. Sutton, R.P. and Farshad, F.: Supplement to SPE 1372, Evaluation ofEmpirically Derived PVT Properties for Gulf of Mexico Crude Oils,paper SPE 20277 available from SPE, Richardson, Texas (1989).

34. McCain, W.D.: Reservoir-Fluid Property CorrelationsState of theArt, SPERE (May 1991) 266.

35. De Ghetto, Giambattista and Villa, Marco: Reliability Analysis onPVT Correlations, paper SPE 28904 presented at the 1994 SPEEuropean Petroleum Conference, London, 2527 October.

36. Elsharkawy, A.M. et al.: Assessment of the PVT Correlations forPredicting the Properties of the Kuwaiti Crude Oils, J. Pet. Sci. Eng.(1995) 13, 219.

37. Mahmood, M.M. and Al-Marhoun, M.A.: Evaluation of empiricallyderived PVT properties for Pakistani crude oils, J. Pet. Sci. and Eng.(1996) 16, 275.

38. Hanafy, H.H. et al.: Empirical PVT Correlations Applied to EgyptianCrude Oils Exemplify Significance of Using Regional Correlations,paper SPE 37295 presented at the 1997 SPE International Symposiumon Oilfield Chemistry, Houston, 1821 February.

SI Metric Conversion FactorsAPI 41.5/(131.5 API) g/cm3

bbl 1.589 873 E 01 m3F (F 32 )/ 1.8 CF (F 459.67)/1.8 KF F 459.67 R

psi 6.894 757 E 00 kPascf/bbl 1.801 175 E 01 std m3/m3

*Conversion factor is exact.

A.A. Al-Shammasi is currently a petroleum engineer withSaudi Arabian Texaco, PNZ, Kuwait, where he has workedsince 1996. e-mail: [email protected]. Previously, heworked for Schlumberger as a wireline logging engineer. Al-Shammasi holds a BS degree in petroleum engineeringfrom the King Fahad U. of Petroleum and Minerals inDhahran, Saudi Arabia, and an MS degree in chemical engi-neering from Kuwait U.

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