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Comparison of the Performance of Empirical ModelsUsed for the Prediction of the PVT Properties of CrudeOils of the Niger DeltaO. O. Bello ab; K. M. Reinicke b; P. A. Patil ba Department of Chemical Engineering, Obafemi Awolowo University, Ile-Ife, Nigeriab Institute of Petroleum Engineering, Technische Universität Clausthal, Germany

Online Publication Date: 01 January 2008To cite this Article: Bello, O. O., Reinicke, K. M. and Patil, P. A. (2008) 'Comparisonof the Performance of Empirical Models Used for the Prediction of the PVTProperties of Crude Oils of the Niger Delta', Petroleum Science and Technology,26:5, 593 - 609To link to this article: DOI: 10.1080/10916460701204685

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Petroleum Science and Technology, 26:593–609, 2008

Copyright © Taylor & Francis Group, LLC

ISSN: 1091-6466 print/1532-2459 online

DOI: 10.1080/10916460701204685

Comparison of the Performance of Empirical

Models Used for the Prediction of the PVT

Properties of Crude Oils of the Niger Delta

O. O. Bello,1;2 K. M. Reinicke,2 and P. A. Patil2

1Department of Chemical Engineering, Obafemi Awolowo University,

Ile-Ife, Nigeria2Institute of Petroleum Engineering, Technische Universität Clausthal, Germany

Abstract: A review of the literature has revealed the lack of a formal analysis of the

performance of empirical methods for the prediction of pressure volume temperature

(PVT) properties of Niger delta crude oils. This study presents an assessment of the

predictive accuracy of five bubble-point pressure (Pb ) correlations and five bubble-

point oil formation volume factor (Bob) correlations against a large measured PVT

data bank from Niger Delta crude oils. Statistical analysis techniques were used to

evaluate the performance and the accuracy of the commonly used empirical models for

estimating PVT properties of Niger crude oil in order to guide designers and operators

in selecting the best correlations for their particular applications. Agreement between

calculated and measured Pb and Bob values for the various models was very poor.

The model predictions of Pb and Bob can be different from the measured values

by 56% and 242%, respectively. Development of improved models for predicting the

PVT properties of Niger delta crude oils is urgently required.

Keywords: empirical models, Niger delta crude oil, PVT properties, statistical

analysis

INTRODUCTION

The prediction of pressure volume temperature (PVT) properties of crude

oil such as bubble-point pressure, bubble-point oil formation volume fac-

tor, isothermal compressibility, viscosity, density, saturation pressures, and

compressibility factor, among others, is achieved by one of three approaches:

Address correspondence to O. O. Bello, Institute of Petroleum Engineering,

Technische Universität Clausthal, Clausthal-Zellerfeld 38678, Germany. E-mail:

booladele@spemail.org

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594 O. O. Bello et al.

equation of state or compositional models (Elsharkawy et al., 2001, 2003;

Elsharkawy, 1999, 2002), neural network models (Elsharkawy and Gharbi,

2000; Gharbi and Elsharkawy, 1997, 1999; Gharbi, 1997), and empirical

models (Standing, 1947; Lasater, 1958; Vazuquez and Beggs, 1980; Glaso,

1980; Pedersen and Fredenslund, 1987; Al-Marhoun, 1988, 1992; Abdul-

Majeed and Salman, 1988; Asgapur et al., 1989; Labedi, 1990; Dokla and

Osman, 1992; Farshad et al., 1992; Macary and El-Batanoney, 1992; Saleh

et al., 1987; Omar and Todd, 1993; Ostermann et al., 1983; Mahmood and

Al-Marhoun, 1996; Elsharkawy et al., 1995; Hanafy et al., 1997; Ozdogan

and Yucel, 2001; Elsharkawy, 2003; Shanshool and Niazi, 2004; Al-Fattah

and Al-Marhoun, 1994; Almehaided, 1997a; Almehaided, 1997b; Petrosky,

1990).

Although the advantages of the existing empirical models are clear, no

quantitative analysis has been published in the literature to validate their accu-

racy with measured PVT properties of crude oils of the Niger Delta. A lack of

trust in design procedures using PVT empirical models has been related to the

range of PVT data available for correlation development (Elsharkawy, 2003b;

Ahmed et al., 1986; Elsharkawy and Elkamel, 2001; Abdul-Majeed, 1985;

Saleh et al., 1987; Sutton and Farshad, 1984, Petrosky and Farshad, 1993;

Boukadi et al., 2002; Elsharkawy et al., 1995), and few of the researchers have

provided information on the accuracy and limitations of their correlations.

This creates a problem for designers who wish to use a correlation but

do not know the limits of its applicability as far as accuracy is concerned.

The problem is even more acute if one tries to decide which of the many

available PVT correlations to use in a particular situation under invidious

choice.

With a production of 2.1 million barrels per day, Nigeria is the world’s

sixth largest oil producer. It has the ambition to increase this production to

5.0 million barrels per day by the year 2008. The most important technical

issues to be addressed in the context of these potential recovery increases of

Nigerian oil deposits is the evaluation of oil and gas reserves; fluid flow

through porous media; multiphase flow in pipes, surface, and subsurface

equipment design; and production system optimization, which depend heavily

upon reservoir fluid physical properties. The objective of this study was to

provide performance evaluation of the PVT empirical models of bubble-point

pressure and bubble-point oil formation volume factor against measured PVT

data of Nigerian crude oils.

METHODS OF COMPARISON

Various statistical methods may be used to determine the relative accuracy

of the PVT empirical models. This can be shown in terms of (1) the relative

average percentage error (APE), (2) the average absolute percentage error

(AAPE), and (3) the standard deviations (SDs). Equations for these measures

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Performance of PVT Models for Niger Delta Crude Oils 595

are given as follows:

PE D

�

Estimated � Measured

Measured

�

� 100; (1)

APE D

nX

iD1

.PEi /

n; (2)

APE D

nX

iD1

jPEi j

n; (3)

SD D

v

u

u

u

u

t

n

nX

iD1

.PEi /2 �

nX

iD1

PEi

!2

n2: (4)

The statistical results for the empirical models and the measured PVT data

from crude oils of the Niger delta are listed in Tables 4 and 5, respectively.

The accuracy of the empirical models was also checked by cross plots of

measured versus estimated PVT parameters and plots of error distribution

curve.

DATA SETS USED FOR THE STUDY

The data bank used in the comparisons contained a total of 23 measured black

oil PVT data points, representing different crude oil and gas systems from

oil fields of the Niger delta. Each data point contains bubble-point pressure

(Pb), the bubble-point oil formation volume factor (Bob), the solution gas-

oil ratio (Rs), the temperature (T ), the gas specific gravity ( g), and the oil

specific gravity ( o). The range of the data is shown in Table 1, while the

Table 1. Range of the PVT data

Bubble-point pressure, psia 2,000–5,000

Bubble-point formation volume factor, reservoir barrel per

stock tank barrel (Rb/STB)

1.000–2.612

Solution gas-oil ratio, standard cubic feet per stock tank barrel

(SCF/STB)

400–2,300

Gas relative density (air D 1) 0.552–0.950

Stock tank oil gravity, ıAPI 30.144–45.186

Reservoir temperature, ıF 130–250

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Table 2. PVT data used for correlations evaluation

Serial

no.

Boi ,

Rb/STB

Pb ,

psia

Rs ,

SCF/STB T , ıF g o

ıAPI

gravity

1 1.978 4,229 2,142 200 0.67 0.817 41.7

2 2.215 4,455 2,049 203 0.65 0.802 44.93

3 1.788 4,557 1,395 206 0.65 0.832 38.57

4 1.278 3,233 571 144 0.61 0.873 30.58

5 1.33 2,956 600 150 0.65 0.845 35.96

6 1.603 3,885 1,236 182 0.61 0.825 40.02

7 1.633 4,158 1,238 189 0.65 0.827 39.6

8 1.651 4,443 1,240 195 0.65 0.837 37.56

9 1.577 3,824 1,296 170 0.69 0.814 42.33

10 1.204 3,863 1,321 170 0.65 0.814 42.33

11 1.66 4,041 1,428 177 0.65 0.814 42.33

12 1.736 4,513 1,432 194 0.65 0.83 38.98

13 1.585 3,663 1,235 178 0.69 0.814 42.33

14 1.624 3,961 1,238 190 0.7 0.825 40.02

15 1.844 4,533 1,694 194 0.7 0.83 38.98

16 1.333 2,646 501 186 0.7 0.85 34.97

17 1.359 2,926 552 187 0.7 0.85 34.97

18 1.34 4,424 2,278 203 0.65 0.83 38.98

19 2.49 4,655 2,315 215 0.65 0.829 39.19

20 1.369 2,287.7 626 174 0.851 0.8271 40.7

21 1.577 4,011 1,052 193 0.838 0.767 37.4

22 1.596 3,158 1,039 210 0.829 0.946 39.2

23 1.846 4,498 1,450 245 0.811 0.793 42.9

measured PVT data used for correlation evaluation is given in Table 2 in

Appendix C.

THE PVT MODELS TESTED

The PVT models used in the comparative study are listed below.

Bubble-point Pressure Correlations

The bubble-point pressure correlations tested against the measured PVT data

points from crude oils of the Niger delta were as follows:

(i) Standing

(ii) Lasater

(iii) Glaso

(iv) Al-Marhoun

(v) Dokla and Osman

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Performance of PVT Models for Niger Delta Crude Oils 597

Bubble-point Oil Formation Volume Factor Correlations

The bubble-point oil formation volume factor correlations used in the com-

parison were:

(i) Standing

(ii) Glaso

(iii) Al-Marhoun

(iv) Dokla and Osman

(v) Labedi

All the above-mentioned correlations are commonly used in the Nigerian

petroleum industry. The PVT equations used in predicting bubble-point pres-

sures and bubble-point oil formation volume factor are given in Appendixes A

and B, respectively.

RESULTS AND DISCUSSION

The bubble-point pressure and bubble-point oil formation volume factor com-

parison results are shown in terms of the APE, the AAPE, and the SD.

The accuracy of the correlations were also checked by scattered diagram

(cross plots) of estimated versus measured PVT parameters and plots of error

distribution curve.

Evaluation of Bubble-point Pressure Models

Table 3 compares the 23 measured bubble-point pressures with those pre-

dicted by the various bubble-point pressure correlations (Standing, 1947;

Lasater, 1958; Glaso, 1980; Al-Marhoun, 1988; Dokla and Osman, 1992).

The parameter “Er” represents percent of relative error between the measured

and the estimated data by a given correlation. It is clear from Table 4 that

Lasater’s correlation gives the best prediction performance based on its lowest

errors and SD with tendency to over-predict all the measured data. Dokla and

Osman’s correlation takes second place in terms of the degree of accuracy

with tendency to under-predict some of the measured data. The Glaso and

Standing correlations take the third and fourth positions, respectively, as good

predictors. Al-Marhoun’s correlation shows poor accuracy in predicting the

bubble-point pressure.

The scatter diagram (cross plots) of Figures 1a–1e compares the mea-

sured Pb versus the estimated Pb obtained from all the correlations studied.

As shown in Figures 1a–1e, a tighter cloud of points about the 45ı line was

obtained by the Lasater correlation (Figure 1b) compared to that obtained

by the other four tested correlations (Figures 1a, 1c–1e). The Al-Marhoun

and Dokla and Osman correlations showed wide scatter around the 45ı line,

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Table 3. Calculated Pb and relative error percent for the Pb correlations

Serialno.

ExpPb

psia

StandingCal Pb

psia

LasaterCal Pb

psia

GlasoCal Pb

psia

Al-MarhounCal Pb

psia

Doklaand

OsmanCal Pb

psiaStanding

Er

LasaterEr

GlasoEr

Al-Marhoun

Er

Doklaand

OsmanEr

1 4,229 6,731.606 4,703.276 6,693.12 8,010.15 6,523.71 59.1773 11.21 58.26 89.41 54.262 4,455 6,098.562 4,586.39 6,287.12 7,796.22 6,472.78 36.8925 2.94 41.12 74.99 45.293 4,557 5,353.314 4,409.15 5,540.93 6,686.95 4,898.38 17.4745 �3.24 21.59 46.74 7.494 3,233 2,960.216 3,233.78 3,546.92 4,064.41 3,018.01 �8.4374 0.02 9.71 25.71 �6.645 2,956 2,534.395 3,148.92 3,025.99 3,418.01 2,896.06 �14.2626 6.52 2.36 15.62 �2.026 3,885 4,651.796 4,070.71 5,083.27 6,408.61 4,950.62 19.7373 4.78 30.84 64.95 27.427 4,158 4,538.056 4,131.26 4,941.66 5,821.33 4,601.75 9.1403 �0.64 18.84 40.01 10.678 4,443 4,881.828 4,238.72 5,192.13 6,126.82 4,572.82 9.8768 �4.59 16.86 37.89 2.929 3,824 3,981.93 3,969.2 4,552.66 4,917.99 4,598.98 4.1299 3.79 19.05 28.61 20.26

10 3,863 4,252.883 3,990.61 4,812.33 5,577.31 4,953.11 10.0928 3.31 24.57 44.37 28.2111 4,041 4,606.031 4,121.45 5,107.59 5,983.82 5,185.58 13.9825 1.99 26.39 48.07 28.3212 4,513 5,272.081 4,344.91 5,543.54 6,600.81 5,078.01 16.8199 �3.72 22.83 46.26 12.5113 3,663 3,889.822 3,964.19 4,429.16 4,831.52 4,388.14 6.1922 8.22 20.91 31.91 19.7914 3,961 4,223.143 4,123.31 4,654.61 5,036.93 4,262.36 6.6181 4.09 17.51 27.16 7.6115 4,533 5,701.533 4,516.93 5,893.68 6,476.48 5,321.15 25.7784 �0.35 30.01 42.87 17.3816 2,646 2,274.057 3,130.08 2,620.89 2,873.58 2,234.28 �14.0568 18.29 �0.94 8.61 �15.5517 2,926 2,471.956 3,265.01 2,842.28 3,086.18 2,393.21 �15.5175 11.58 �2.86 5.47 �18.2118 4,424 7,910.542 4,848.94 7,432.81 9,367.83 7,014.79 78.8097 9.61 68.01 111.75 58.5619 4,655 8,172.477 4,945.11 7,526.26 9,667.88 6,975.96 75.5634 6.23 61.68 107.68 49.8520 2,287.7 1,919.775 3,139.91 2,267.08 2,090.31 2,187.43 �16.0827 37.25 �0.91 �8.62 �4.3821 4,011 3,443.341 4,144.44 3,859.69 2,558.51 3,120.08 �14.1525 3.32 �3.77 �36.21 �22.2122 3,158 3,383.01 3,896.99 3,742.78 5,177.46 3,120.33 7.1255 23.41 18.51 63.94 �1.1923 4,498 4,402.641 4,586.23 4,590.04 4,207.28 3,795.79 �2.12 1.96 2.04 �6.46 �15.61

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Performance of PVT Models for Niger Delta Crude Oils 599

Table 4. Statistical parameters for the Pb correlations

Standing Lasater Glaso Al-Marhoun

Dokla and

Osman

APE (E) 13.59 6.34 21.85 39.59 13.25

AAPE 20.95 7.43 22.59 44.05 20.71

Percent SD 65.97 30.77 106.07 192.19 64.32

Figure 1. Comparison of the estimated versus experimental bubble point pressure.

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600 O. O. Bello et al.

while the Glaso and Standing largely overestimated. The error distribution

plots associated with the various correlations is shown in Figure 2. These plots

reveal that Lasater’s correlation has the smallest relative error range from

�16.0 to 35.62%, followed by Dokla and Osman’s correlation with relative

error range from �30.0 to 50.0%. The Glaso and Standing correlation showed

relative error range of �20.0 to 60.0% and �20.0 to 70.0%, respectively. The

comparison of the statistical parameters for each correlation is shown in

Table 4. The Lasater correlation has an SD of 30.77 while the other four

tested correlations show relatively high values of SDs.

Figure 2. Error distribution for bubble point pressure.

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Performance of PVT Models for Niger Delta Crude Oils 601

Evaluation of Bubble-point Oil Formation Volume Factor Models

Table 5 presents the measured versus the estimated Bob for the 23 data

points, along with the relative percent error for each of the data points. The

comparison of statistical parameters for each correlation is shown in Table 6.

The Al-Marhoun’s correlation prediction of Bob was the most accurate, with

a relative error ranging between �30.0 and 50.0% and an SD of 34.67. The

scatter diagram (cross plot) of calculated versus measured value of Bob are

shown in Figure 3. This figure also shows that the Al-Marhoun, Standing,

Glaso, and Dokla and Osman correlations have closer scatter to the united

slope line of perfect correlation. The model by Labedi largely tends toward

over-prediction of measured Bob values.

The error distribution plots are shown in Figure 4. The figure portrays

that Standing’s correlation has the smallest error range, with normal curve

peak being close to zero. The other correlations also exhibit comparable

error range and skewness. A comparison of Figures 2 and 4 appears to

indicate that all bubble-point oil formation volume factor correlations show

better prediction performance than bubble-point pressure correlations. This

is presumably due to the fact that all bubble-point oil formation volume

factor correlations have a narrow range of values compared to their absolute

values. Also, the bubble-point oil formation volume factor correlations have

better accuracy based on their lowest values of the statistical parameters.

However, the differences between the bubble-point pressure values have a

wide range when compared to their possible absolute values. The prediction

capabilities of bubble-point oil formation volume factor correlations seem to

be much closer to the measured values than those given by the bubble-point

pressure correlations. Generally, the error associated with the bubble-point

oil formation volume factor correlations is lowest when compared to the

bubble-point pressure correlations.

CONCLUSIONS

The predictive capabilities of five bubble-point pressure correlations and five

bubble-point oil formation volume factor correlations have been assessed

against measured black oil PVT data obtained from some crude oils of the

Niger delta. A computer program was developed to calculate bubble-point oil

formation volume factor and bubble-point pressure predictions based on the

empirical models.

The errors associated with the bubble-point pressure prediction are quite

high for all the bubble-point pressure correlations tested in this study. Bubble-

point oil formation volume factor predictions are generally better than bubble-

point pressure predictions. However, bubble-point oil formation volume factor

prediction errors are not significantly reduced as well. Because of the very

low precision of the PVT properties predictive techniques investigated in this

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Table 5. Calculated Bob and relative error percent for the Bob correlations

Serialno.

ExpBoi ,

Rb/STB

StandingCal Boi ,Rb/STB

GlasoCal Boi ,Rb/STB

Al-MarhounCal Boi ,Rb/STB

Doklaand

OsmanCal Boi ,Rb/STB

LabediCal Boi

Rb/STBStanding

Er

GlasoEr

Al-Marhoun

Er

Doklaand

OsmanEr

LabediEr

1 1,978 2,209 2,110 2,020 2,170 3,650 11.66 6.41 2.43 9.86 84.612 2,215 2,148 2,050 2,010 2,120 3,520 �3.01 �7.31 �9.61 �3.88 58.993 1,788 1,759 1,710 1,670 1,730 2,680 �1.62 �4.55 �6.33 �3.07 50.094 1,278 1,273 1,240 1,260 1,220 1,630 �0.41 �2.81 �1.25 �4.21 28.095 1,330 1,303 1,270 1,290 1,260 1,710 �2.01 �4.32 �2.54 �5.05 28.026 1,603 1,636 1,590 1,580 1,610 2,410 2.07 �0.54 �1.34 �0.11 50.947 1,633 1,663 1,610 1,610 1,630 2,470 1.81 �0.84 �2.01 �0.07 51.648 1,651 1,664 1,610 1,590 1,630 2,470 0.81 �1.91 �3.31 �1.04 50.219 1,577 1,797 1,660 1,630 1,660 2,570 8.22 5.57 3.78 5.54 63.03

10 1,204 1,699 1,650 1,630 1,650 2,550 41.01 37.58 35.61 37.54 112.1311 1,660 1,763 1,710 1,680 1,720 2,690 6.21 3.34 1.48 3.79 62.2112 1,736 1,771 1,710 1,680 1,730 2,710 2.01 �0.94 �3.11 �0.04 56.0713 1,585 1,678 1,630 1,610 1,640 2,510 5.89 3.28 2.01 3.74 58.3614 1,624 1,690 1,640 1,620 1,650 2,530 4.03 1.33 �0.23 2.19 56.0515 1,844 1,953 1,880 1,820 1,910 3,110 5.92 2.29 �1.54 3.52 68.1916 1,333 1,289 1,250 1,290 1,280 1,670 �3.31 �6.01 �3.04 �3.71 24.4117 1,359 1,315 1,270 1,310 1,310 1,720 �3.25 �5.91 �3.31 �3.76 27.1118 1,340 2,262 2,140 2,050 2,210 3,760 68.81 60.22 53.08 65.22 181.0519 2,490 2,295 2,170 2,070 2,250 3,830 �7.84 �12.76 �16.47 �9.38 54.0820 1,369 1,380 1,340 1,360 1,360 1,860 0.81 �1.51 �0.08 �0.57 36.4721 1,577 1,667 1,620 1,640 1,670 2,480 5.71 3.23 4.05 6.13 57.6122 1,596 1,693 1,560 1,490 1,550 2,340 0.44 �2.22 �6.56 �2.64 47.1123 1,846 1,937 1,860 1,840 1,960 3,060 4.91 1.18 0.03 6.38 66.11

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Performance of PVT Models for Niger Delta Crude Oils 603

Table 6. Statistical parameters for the Bob correlations

Standing Glaso Al-Marhoun

Dokla and

Osman Labedi

APE 6.47 3.16 1.81 4.62 59.67

AAPE 8.33 7.65 7.09 7.89 59.67

Percent SD 40.53 37.35 34.67 38.45 289.67

Figure 3. Comparison of estimated versus experimental bubble-point oil formation

volume factor.

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604 O. O. Bello et al.

Figure 4. Error distribution for bubble-point oil formation volume factor.

study, development of more accurate bubble-point pressure and bubble-point

oil formation volume factor correlations are recommended for Niger delta

crude oil systems.

ACKNOWLEDGMENT

The authors are grateful to the management of the Department of Petroleum

Resources (DPR) Nigeria, for providing the data used in this study.

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Performance of PVT Models for Niger Delta Crude Oils 605

REFERENCES

Abdul-Majeed, G. H. (1985). Evaluation of PVT correlations. SPE Paper

no. 14478. Dallas, TX: Society of Petroleum Engineers.

Abdul-Majeed, G. H. A., and Salman, N. H. (1988). An empirical correlation

for FVF prediction. J. Can. Pet. Tech. 27:118–122.

Ahmed, Y., Sugie, H., and Lu, B. C. Y. (1986). Comparative study of eight

equations of state for predicting hydrocarbon volumetric phase behaviour.

SPE Paper no. 15673. 61st SPE Annual Technical Conference and Ex-

hibition, October 5–8.

Al-Fattah, S. M., and Al-Marhoun, M. A. (1994). Evaluation of empirical

correlation for bubble-point oil formation volume factor. J. Pet. Sci. Eng.

11:341–350.

Al-Marhoun, M. A. (1988). PVT correlations for Middle East crude oils. J.

Pet. Technol. Tarns. AIME, 285, May 1988, pp. 650–666.

Al-Marhoun, M. A. (1992). New correlation for formation volume of oil and

gas mixtures. J. Can. Pet. Technol. 31:22–26.

Almehaided, R. A. (1997a). Improved PVT correlations for UAE crude oils.

SPE Paper no. 37691. SPE Middle East Oil Show and Conference,

Manamah, Bahrain, March 15–18, pp. 106–120.

Almehaided, R. A. (1997b). Improved correlations for fluid properties of

UAE crude oils. Pet. Sci. Technol. 21:1811–1831.

Asgapur, S., McLauchlin, L., Wong, D., and Cheung, V. (1989). Pressure

volume temperature correlation for Western Canadian gases and oils. J.

Can. Pet. Technol. 28:103–113.

Boukadi, F. H., Beniani, A. S., and Hashim, A. (2002). PVT empirical models

for saturated Omani crude oils. Pet. Sci. Technol. 20:89–100.

Dokla, M. E., and Osman, M. E. (1992). Correlation of PVT properties for

UAE crudes. SPE Paper no. 21342. SPE Formation Eval., March:41–46,

Elsharkawy, A. M. (1999). Models for predicting the viscosity of Middle-East

crude oils. Fuel 78:891–903.

Elsharkawy, A. M. (2002). Predicting the dew-point pressure for gas con-

densate reservoirs: Empirical models and equation of states. Fluid Phase

Equilibria 193:147–165.

Elsharkawy, A. M. (2003a). An empirical model for estimating the saturation

pressure of crude oils. J. Pet. Sci. Eng. 38:57–77.

Elsharkawy, A. M. (2003b). Predicting volumetric and transport properties of

sour gases and gas condensate using equation of states, corresponding

state models and empirical correlation. Pet. Sci. Technol. 21:1759–1787.

Elsharkawy, A. M., and Elkamel, A. (2001). The accuracy of predicting the

compressibility for sour natural gas. Pet. Sci. Technol. 19:711–731.

Elsharkawy, A. M., and Gharbi, R. B. (2000). Comparing classical and neural

regression techniques in modeling crude oil viscosity. Adv. Eng. Software

32:215–224.

Dow

nloa

ded

By:

[Bel

lo, O

. O.]

At:

11:1

6 22

Mar

ch 2

008

606 O. O. Bello et al.

Elsharkawy, A. M., Elgibaly, A. A., and Alikhan, A. A. (1995). Assessment

of PVT correlations for predicting the properties of Kuwaiti crude oils.

J. Pet. Sci. Eng. 13:219–232.

Elsharkawy, A. M., Hashim, Y. S. K., and Alikhan, A. A. (2001). Compress-

ibility factor for gas condensates. Energy Fuels 15:807–816.

Elsharkawy, A. M., Hassan, S. A., Hashim, Y. S. K., and Fahim, M. A.

(2003). New compositional models for calculating the viscosity of crude

oils. Ind. Eng. Chem. Res. 42:4132–4142.

Farshad, F. F., Leblance, J. L., Garber, J. D., and Osorio, J. G. (1992).

Empirical correlation for Columbian crude oils. SPE Paper no. 24538.

4th Latin American and Caribbean Petroleum Engineering Conference,

Port-of-Spain, Trinidad and Tobago, April 23–26, 1996.

Gharbi, R. B. C. (1997). Estimating the isothermal compressibility coefficient

of under-saturated Middle-East crudes using neural networks. Energy

Fuels 11:372–378.

Gharbi, R. B., and Elsharkawy, A. M. (1997). Neural network model for

estimating the PVT properties of Middle East crude oils. SPE paper

no. 37995. Proc. SPE Middle East Oil Show Conference, Vol. 1, Man-

amah, Bahrain, March 15–18, pp. 151–166.

Gharbi, R. B., and Elsharkawy, A. M. (1999). Universal network model for

estimating the PVT properties of crude oil systems. Energy Fuels 13:454–

458.

Glaso, O. (1980). Generalized pressure volume temperature correlations. Pet.

Technol. Trans., AIME 785–795.

Hanafy, H. H., Macary, S. A., Elnady, Y. M., Bayomi, A. A., and El-Bata-

money, M. H. (1997). Empirical PVT correlation applied to Egyptian

crude oils exemplify significance of using regional correlations. SPE Pa-

per no. 37295. SPE Oilfied Chemistry International Symposium, Febru-

ary 18–21.

Labedi, R. (1990). Use of production data to estimate volume factor, density

and compressibility of reservoir fluids. J. Pet. Sci. Eng. 4:357–390.

Lasater, J. A. (1958). Bubble point pressure correlation. Trans. AIME 213:

379–381.

Macary, S. M., and El-Batanoney, M. H. (1992). Derivation of PVT correla-

tions for the Gulf of Suez crude oils. EGPC, 11th Petroleum Exploration

and Production Conference.

Mahmood, M. M., and Al-Marhoun, M. A. (1996). Evaluation of empirically

derived PVT properties for Pakistani crude oils. J. Pet. Sci. Eng. 16:

275–290.

Omar, M. I., and Todd, A. C. (1993). Development of new modified black

oil correlation for Malaysian crudes. SPE Paper no. 25338. SPE Asia

Pacific Oil and Gas Conference, Singapore, February 8–10.

Ostermann, R. D., Ehlig-Economides, C. A., and Owalabi, O. O. (1983).

Correlation for the reservoir fluid properties of Alaskan crudes. SPE

Paper no. 11703.

Dow

nloa

ded

By:

[Bel

lo, O

. O.]

At:

11:1

6 22

Mar

ch 2

008

Performance of PVT Models for Niger Delta Crude Oils 607

Ozdogan, S., and Yucel, H. G. (2001). Correlations towards prediction of

petroleum fraction viscosities: An empirical approach. Fuel 80:447–449.

Pedersen, K. S., and Fredensluud, A. (1987). An improved corresponding

state model for the prediction of oil and gas viscosities and thermal

conductivities. Chem. Eng. Sci. 42:182–186.

Petrosky, J. (1990). PVT correlations for Gulf of Mexico crude oil. M.Sc.

Thesis, Lafayette, LA: University of Southern Louisiana.

Petrosky, G. E., and Farshad, F. F. (1993). Pressure volume temperature

correlation for the Gulf of Mexico crude oils. SPE Paper no. 26644.

Dallas, TX: Society of Petroleum Engineers.

Saleh, A. M., Maggoub, I. S., and Asaad, Y. (1987). Evaluation of dmpirically

derived PVT properties for Egyptian oils. SPE Paper no. 15721. Dallas,

TX: Society of Petroleum Engineers.

Shanshool, J., and Niazi, E. (2004). Viscosity-temperature correlation crude

oils. Oil Gas Eur. Mag. 4:185–187.

Standing, M. B. (1947). A pressure-volume-temperature correlation for mix-

ture of California oils and gases. Drilling and Production Practices,

Dallas, TX: API, pp. 275–287.

Sutton, R. P., and Farshad, F. F. (1984). Evaluation of empirical derived PVT

properties for Gulf of Mexico crude oils. SPE Paper no. 13172. Dallas,

TX: Society of Petroleum Engineers.

Vazuquez, M., and Beggs, H. D. (1980). Correlation for fluid physical prop-

erties prediction. J. Pet. Technol., Trans. AIME, 269:968–970.

APPENDIX A

Bubble-point Pressure Correlations

Standing (1947):

Pb D 18:2

"

�

Rs

g

�0:83

� anti log.0:00091 � T � 0:0125 � API/ � 1:4

#

:

Lasater (1958):

Pb Dpf � .T C 459:67/

g

;

Mo D 725:32143 � 16:03333 API C 0:09524 2API;

yg D

�

Rs

379:3

�

��

Rs

379:3

�

C

�

350 o

Mo

�� ;

pf D 0:38414 � 1:20081yg C 9:64868y2g:

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Glaso (1980):

Pb D anti log.1:7669 C 1:7447 � log p�

b � 0:302118 � .log p�

b /2/;

p�

b D

�

Rs

g

�0:816

� T 0:172 � �0:989API :

Al-Marhoun (1988):

Pb D 5:38088 � 10�3 � �1:877840g � 3:1437

o � T 1:32657r � R0:715082

s :

Dokla and Osman (1992):

Pb D 0:836386 � 104 � �1:01049g � 0:107991

o � T �0:952584r � R0:724047

s :

APPENDIX B

Oil Formation Volume Factor

Standing (1947):

Bob D 0:972 C 1:47 � 10�4

Rs �

�

g

o

�0:5

C 1:25 � T

#1:175

Glaso (1980):

Bob D 1:0 C anti log

� f�6:58511 C 2:91329 � log B�

ob � 0:27683 � .log B�

ob/2g;

B�

ob D Rs �

�

g

o

�0:526

C 0:968 � T:

Al-Marhoun (1992):

Bob D 0:497069 C 0:862963 � 10�3 � Tr

C 0:182594 � 10�2 � F C 0:318099 � 10�5 � F 2;

F D R0:742390s � 0:323294

g � �1:202040o :

Dokla and Osman (1992):

Bob D 0:431935 C 0:156667 � 10�2 � Tr

C 0:139775 � 10�2 � F C 0:380525 � 10�5 � F 2;

F D R0:773572s � 0:404020

g � �0:882605o :

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Performance of PVT Models for Niger Delta Crude Oils 609

Labedi (1990):

Bo D 0:9897 C 0:0003164

"

Rs �

�

g

o

�0:5

C 1:25T

#1:175

:

APPENDIX C

NOMENCLATURE

Bob oil formation volume factor at bubble point pressure, Rb/STB

B�

ob correlating number for calculating Bob

API tank oil gravity, ıAPI

g total gas specific gravity, air D 1.0

o tank oil specific gravity, water D 1.0

Mo effective tank oil molecular weight

Pb bubble-point pressure, psia

P �

bcorrelating number for bubble point

Rs solution GOR, SCF/STB, Std m3/stock tank m3

T reservoir temperature, ıF (ıC)

Tr reservoir temperature, ıR (ıK)

yg mole fraction of gas

n number of observations

Er percentage relative error, %

APE relative average percentage error, %

AAPE average absolute percentage error, %

SD standard deviation