assessment of oil reservoir properties empirical correlations · assessment of oil reservoir...

@IJMTER-2016 All rights Reserved 129

Assessment of Oil Reservoir Properties Empirical Correlations Salem O. Baarimah

1, Mohamed Mustafa

2,Hamid Khattab

3,Mahmoud Tantawy

4 and

Ahmed A. Gawish5

1,2,3,4,5Petroleum Engineering Department ,Suez University, Egypt

Abstract—Reservoir fluid properties such as oil bubble point pressure, oil formation volume factor,

solution gas-oil ratio, gas formation volume factor, and gas and oil viscosities are very important in

reservoir engineering computations. Perfectly, these properties should be obtained from actual

laboratory measurements on samples collected from the bottom of the wellbore or at the surface. Quite

often, however, these measurements are either not available, or very costly to obtain. For these reasons,

it is necessary for the petroleum engineer to find a accurate, quick and reliable method for predicting

the reservoir fluid properties.Therefore, the concept of numerical correlation equations has been

proposed to the petroleum industry to alleviate all difficulties in reservoir fluid properties

determination.For this study, 63 published black oil empirical correlations for oil bubble point pressure

and oil formation volume factorwere collected and summarized from 1946 till now in chronological

order.A huge database of crude oil properties wereused to evaluate these correlations against whole

range of API gravity and each class of API gravity.

Keywords—Reservoir fluid properties;empirical correlations;oil bubble point pressure; oil formation

volume factor; Assessment.

I. INTRODUCTION

Reservoir fluid properties are very important physical properties that control the flow of oil

through porous media and pipes. They used comprehensively in most of petroleum engineering

applications such as drilling engineering, reservoir engineering, and production engineering. Accurate

reservoir fluid properties are very important in reservoir engineering computations and a requirement for

all types of petroleum calculations such as determination of initial hydrocarbons in place, optimum

production schemes, ultimate hydrocarbon recovery, design of fluid handling equipment, and enhanced

oil recovery methods.

Actually, the reservoir fluid properties depend on pressure, temperature, and chemical

compositions. For the development of a correlation, geological condition is considered important

because the chemical composition of crude oil differs from region to region. For this reason, it is

difficult to obtain the same accurate results through empirical correlations for different oil samples

having different physical and chemical characteristics. Engineers should be modified these correlations

for their application by recalculating the correlation constants for the region of interest. The purposeof

this work is to study the performance of oil bubble point pressure and oil formation volume factor

models available inthe literature, based on 3000 data sets collected from different published literature

papers and PVT reports from different oil fields in the Saudi Arabia and Yemen.

II. LITERATURE REVIEW

The history of reservoir fluid properties correlation equations in the petroleum industry started

more than five decades ago. Several reliable empirical correlations for calculating the reservoir fluid

properties such as crude oil viscosity, oil formation volume factor, oil bubble point pressure, solution

gas-oil ratio, gas formation volume factor and isothermal compressibility have been proposed over the

International Journal of Modern Trends in Engineering and Research (IJMTER) Volume 03, Issue 02, [February – 2016] ISSN (Online):2349–9745; ISSN (Print):2393-8161


years.Since the 1940’s engineers have realized the importance of developing empirical correlation for oil

bubble point pressure and oil formation volume factor. Studies carried out in this field resulted in the

development of new correlations. Several studies of this kind were published by Katz(1942)[1],

Standing (May, 1947)[2], Lasater (May, 1958)[3]. For several years, these correlations were the only

source available for estimating bubble point pressureand oil formation volume factor when experimental

data were unavailable. In the last thirty years there has been an increasing interest in developing new

correlations for crude oils obtained from the various regions in the world. Glaso (May,

1980)[4],Vazquez andBeggs(1980)[5], Al-Marhoun(1988)[7],Abdul-Majeed and Salman (November,

1988)[8],Kartoatmodjo and Schmidt (June, 1991)[9],Dokla and Osman (March, 1992)[10],Al-Marhoun

(March, 1992)[11],Macary and El-Batanoney (January, 1993)[12],Omar and Todd (February,

1993)[13],Petrosky and Farshad (October, 1993)[14],De Ghetto et al ( October, 1994)[15],Farshad et al

(April, 1996)[16],Hanafy et al ( February, 1997)[17],Almehaideb ( March, 1997)[18],Elsharkawy and

Alikhan (May, 1997)[19],Velarde et al ( June, 1997)[20],Khairy et al (May, 1998)[21],Movagharnejad

and Fasih (January, 1999)[22],Al-Shammasi ( February, 1999)[23],Dindoruk and Christman

(September, 2001)[24],Boukadi et al (January, 2004)[25],Bolondarzadeh et al (2006)[26],Mehran et al

(2006)[27],Hemmati and Kharrat ( March, 2007)[28],Mazandarani and Asghari (September,

2007)[29],Khamechi et al (March, 2009)[30],Ikiensikimama and Ogboja (August,2009)[31],Moradi et al

(June, 2010)[32],Okoduwa and Ikiensikimama (July, 2010)[33],Elmabrouk((December

2010)[34],Moradi et al (2013)[35],Karimnezhad et al (2014)[36]andSulaimon et al

(August,2014)[37]carried out some of the recent studies. A summary of bubble point pressureand oil

formation volume factormodels are provided in Appendix B and Appendix Cincluding the formsof

correlation used authors, and detailsof the data used for each development.

III. Research Methodology

To acheive this work,MATLAB statistical error analysis and MATLAB cross plot error analysis

were usedto compare the performance and accuracy of oil bubble point pressure and oil formation

volume factor models.The statistical parameters used for comparison are: average absolute percent

relative error, standard deviationand the correlation coefficient

IV. Data Acquisition and Analysis

To achieve this study, the 3000 data sets used for this work were collected from different

published literature papers and conventional PVT reports that derive the various fluid properties through

differential liberation process from different oil fields in the Saudi Arabia and Yemen.

Each data set contains bubble point pressure, formation volume factor, total solution gas oil ratio,

average gas gravity, oil gravity, crude oil density, reservoir temperature and reservoir pressure.

Statistical distributions such as maximum, minimum, mean, range, mid-range, variation and standard

deviation of the input data are shown in Tables1.

As can be seen from Table3.1, bubble-point pressure of the data ranged between 10.416 psi a to

8647 psia. For formation volume factor, the data ranged between 1.028 bbl/stb to 2.588 bbl/stb.

Corresponding solution gas oil ratio ranged from 4.951 scf/stb to 2637 scf/stb. Similar to solution gas oil

ratio, oil gravity, crude oil density and average gas gravity varied between 15.3 to 63.7 API, 25.022 to

62.37 lb/ft3 and 0.511 to 1.731, respectively. The reservoir temperature ranged between 58 0F to 294

0F.

Corresponding reservoir pressure ranged from 165 psia to 2637 psia.

3000 data sets have been divided into the following three different API gravity classes: heavy oils

for 0API˂ 22, medium oils for 22≤

0API˂ 31 and light oils for

0API≥31.



Table 1- Statistical descriptions of all data

Property Min Max Mean Range Mid-Ran. St. Dev.

�� 10.416 8647 1809.3 8636.6 4328.7 1151.2

�� 1.028 2.588 1.330 1.56 1.808 0.230

�� 4.951 2637 534 2632 1321 389.4

API 15.3 63.7 35.31 48.4 39.5 7.5

�� 25.022 62.37 48.58 37.3476 43.6962 5.8

� 0.511 1.731 0.896 1.22 1.121 0.167

� 58 294 172 236 176 49.1

P 165 7411.54 2911.7 7246.54 3788.27 1631.7

V. Results and Discussion

A large database consisting of data from oil PVT reports and literature sources has been compiled

in order to evaluate bubble-point pressure and formation volume factormethods using statistical and

graphical error analysis.

5.1Bubble Point Pressure CorrelationsAssessment

Most bubble-point pressure correlations are a function of oil and gas gravity, solution gas-oil ratio

and temperature. 28 methods for calculating bubble-point pressure have been evaluated using a large

database consisting of data from oil PVT reports and literature sources.

The best three correlations for each class and for the whole range of API gravity for bubble-point

pressure have been summarized in Tables 2.

As can be seen from Tables 2, Standing (1947) correlation outperforms the most common

published empirical correlations followed by Vazquez and Beggs (1980) and Velarde et al (997)

correlationsfor whole data sets.Standing (1947) correlation has an average absolute error of 19.83%,

standard deviation of 44.58% and correlation coefficient of 0.921.

For heavy oils, the statistical analysis for all correlations indicate that Mehran et al (2006)

correlation model is the best performing correlation model for heavy oils for 0API˂ 22 with least

average absolute error of 20.34%, least standard deviation of 41.69% and the highest correlation

coefficient of 0.824 followed by Velarde et al (1997) and Al-Shammasi (1999) correlations.

The statistical analysis for bubble point pressure correlations for medium oils for 22≤ 0API˂ 31

indicate Standing (1947) correlation outperforms the bubble point pressure published empirical

correlations with least average absolute error of 25.84%, least standard deviation of 65.06 % and the

highest correlation coefficient of 0.847 followed by Al-Shammasi (1999) and Vazquez and

Beggs(1980) correlations.

For light oils, the statistical analysis for all correlations illustrate that Vazquez and Beggs(1980)

correlation model is the best performing correlation model for light oils for 0API ≥ 31 with least average

absolute error of 18.10%, least standard deviation of 31.19% and the highest correlation coefficient of

0.938 followed by Standing (1947) and Al- Kartoatmodjo and Schmidt (1991) correlations.

The statistical accuracy of for all correlations for the 3000 data sets is summarized

inTablesA1(Appendix A).

The crossplots of estimated values against experimental values for the best three performing

bubble-point pressure models (Standing, Vazquez and Beggs and Velarde et al) are presented in Figures

1 through 3. The plotted points of the best three correlations fall very close to the perfect correlation of

the 45° line.



Table 2Bubble point pressure correlations assessment summary

Bubble point pressure correlations assessment summary for whole data sets

Method Year No. of data AARE Std R2

Standing 1947 3000 19.83 44.58 0.921

Vazquez and Beggs- 1 1980 3000 20.39 48.46 0.910

Velarde et al 1997 3000 21.21 50.56 0.902

Bubble point pressure correlations assessment summary for heavy oils( 0API˂ 22)

Mehran et al 2006 115 20.34 41.69 0.824

Velarde et al 1997 115 21.00 42.38 0.819

Al-Shammasi 1999 115 21.22 46.36 0.809

Bubble point pressure correlations assessment summary for medium oils( 22≤ 0API˂ 31)

Standing 1947 627 25.84 65.06 0.847

Al-Shammasi 1999 627 27.94 67.63 0.820


Bubble point pressure correlations assessment summary for light oils( 0API≥31)


Standing 1947 2243 18.10 31.19 0.938

Kartoatmodjo and Schmidt- 1 1991 2243 18.84 26.50 0.930

Figure 1 Accuracy of Standing correlation

Figure 2 Accuracy of Vazquez and Beggs-1 correlation



Figure 3 Accuracy of Velarde et al correlation

5.2 Oil Formation Volume Factor Correlations Assessment

Statistical and graphical comparative were used to check the accuracy of oil formation volume

factor correlations.The best three correlations for each class and for the whole range of API gravity for

oil formation volume factor have been summarized in Tables 3.

FromTables 3, the statistical analysis parameters for all correlations indicate that Al-Shammasi-2

(1999) correlation model is the best performing correlation model for the data used in this work

followed by Kartoatmodjo and Schmidt (1991) and Farshad et al (1996) correlations.Al-Shammasi

(1999) correlation has an average absolute error of 3.14%, standard deviation of 4.70% and correlation

coefficient of 0.948.

The statistical analysis for all correlations indicate that Al-Shammasi-2 (1999) correlation model is

the best performing correlation model for heavy oils with least average absolute error of 1.63%, least

standard deviation of 2.55% and the highest correlation coefficient of 0.914 followed by Farshad et al

(1996) and Al-Marhoun-2 (1992) correlations.

For medium oils, the statistical analysis for oil formation volume factor correlations indicate that

Al-Shammasi-2 (1999) correlation model is the best performing correlation model for medium oils with

least average absolute error of 1.78%, least standard deviation of 2.71% and the highest correlation

coefficient of 0.941 followed by Kartoatmodjo and Schmidt (1991) and Farshad et al (1996)

correlations.

The statistical analysis for oil formation volume factor correlations for light oils indicate Al-

Shammasi-2 (1999) correlation outperforms the bubble point pressure published empirical correlations

with least average absolute error of 3.59%, least standard deviation of 5.19 % and the highest correlation

coefficient of 0.934 followed by Kartoatmodjo and Schmidt(1991) and Mehran et al(2006) correlations.

The statistical accuracy of for all formation volume factor for the 3000 data sets is summarized in

TablesA2 (Appendix A).

The crossplots of estimated values against experimental values for the best three performing

formation volume factor models (Al-Shammasi, and Kartoatmodjo and Schmidt, Farshad et al) are

presented in Figures 4 through 6.



Table 3 Oil formation volume factor correlations assessment summary

Oil formation volume factor correlations assessment summary for whole data sets

Method Year No. of data AARE Std R2

Al-Shammasi-2 1999 3000 3.14 4.70 0.948

Kartoatmodjo and Schmidt 1991 3000 3.16 4.76 0.945

Farshad et al 1996 3000 3.22 4.87 0.942

Oil formation volume factor correlations assessment summary for heavy oils 0API˂ 22

Al-Shammasi-2 1999 115 1.63 2.55 0.914

Farshad et al 1996 115 1.71 2.72 0.902

Al-Marhoun-2 1992 115 1.72 2.60 0.905

Oil formation volume factor correlations assessment summary for medium oils 22≤ 0API˂

31

Al-Shammasi-2 1999 627 1.78 2.71 0.941


Farshad et al 1996 627 1.91 2.76 0.940

Oil formation volume factor correlations assessment summary for light oils 0API≥31

Al-Shammasi-2 1999 2243 3.59 5.19 0.934


Mehran et al 2006 2243 3.74 5.29 0.931

Figure 4 Accuracy of Al-Shammasi-2 correlation

Figure 5 Accuracy of Kartoatmodjo and Schmidt correlation



Figure 6 Accuracy of Farshad et al correlation

VI. Conclusions

Based on the analysis of the results obtained in this research study, the following conclusions can be

made:-

1. Totally,63published black oil empirical correlations for oil bubble point pressure and oil formation

volume factor were collected, summarized, evaluated.

2. A large database of crude oil properties was collected.

3. Standing (1947) correlation outperforms the most common publishedbubble point pressure

empirical correlations followed by Vazquez and Beggs (1980) and Velarde et al (997) correlations

for whole data sets.

4. For heavy oils, the statistical analysis for all bubble point pressure correlations indicate that Mehran

et al (2006) correlation model is the best performing correlation model with least average absolute

error, least standard deviation and the highest correlation coefficient followed by Velarde et al

(1997) and Al-Shammasi (1999) correlations.

5. The statistical analysis for bubble point pressure correlations for medium oils indicate that Standing

(1947) correlation outperforms the bubble point pressure published empirical correlations followed

by Al-Shammasi (1999) and Vazquez and Beggs(1980) correlations.

6. 6- For light oils, the statistical analysis for all bubble point pressure correlations illustrate that

Vazquez and Beggs(1980) correlation model is the best performing correlation model with least

average absolute error of, least standard deviation and the highest correlation coefficient followed

by Standing (1947) and Al- Kartoatmodjoand Schmidt (1991) correlations.

7. Foroil formation volume factor correlations,the statistical analysis parameters for all correlations

indicate that Al-Shammasi (1999) correlation model is the best performing correlation model for for

whole data sets used in this work followed by Kartoatmodjo and Schmidt (1991) and Farshad et al

(1996) correlations.

8. The statistical analysis for all oil formation volume factor correlations indicate that Al-Shammasi

(1999) correlation model is the best performing correlation model for heavy oils followed by

Farshad et al (1996) and Al-Marhoun-2 (1992) correlations.

9. For medium oils, the statistical analysis for oil formation volume factor correlations indicate that

Al-Shammasi (1999) correlation model is the best performing correlation model for medium oils

with least average absolute error, least standard deviation and the highest correlation coefficient

followed by Kartoatmodjo and Schmidt (1991) and Farshad et al (1996) correlations.

10. The statistical analysis for oil formation volume factor correlations for light oils indicate Al-

Shammasi (1999) correlation outperforms the bubble point pressure published empirical



correlations

11. followed by Kartoatmodjo and Schmidt(1991) and Mehran et al(2006) correlations.

References [1] Katz, D. L., “Prediction of Shrinkage of Crude Oils,” Drill & Prod. Pract., API,pp. 137-147November,1942.

[2] Standing, M.B., “A Pressure Volume Temperature Correlation for Mixture of California Oils and Gases,” Drill. & Prod.

Prac., API, Dallas ,pp. 275-287 , May,1947.

[3] Lasater, J.S.,“Bubble Point Pressure Correlation,” Trans., AIME,1958.

[4] Glaso, O., “Generalized Pressure-Volume-Temperature Correlations,” JPT,pp. 785-795, May, 1980.

[5] Vasquez, M. and Beggs, H.D.,“Correlation for Fluid Physical Property Predictions,” JPT,pp. 968-970, June, 1980.

[6] Standing, M. B, Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, 9th ed. Dallas: Society of

Petroleum Engineers,1981.

[7] Al-Marhoun, M.A., “PVT Correlations for Middle East Crude Oils,” JPT,pp. 650-666, (May, 1988).

[8] Abdul-Majeed, G. H. A. and Salman, N. H.: “An Empirical Correlation for FVF Prediction,” J Can. Pet. Tech.,pp. 118-

122, November, 1988.

[9] Kartoatmodjo, R.S.T. and Schmidt, Z., “New Correlations for Crude Oil Physical Properties,” paper SPE 23556

available from SPE Book Order Dept., Richardson, Texas 1991.

[10] Dokla, M. and Osman, M.,“Correlation of PVT Properties for UAE Crudes,” SPE Formation Evaluation,pp. 41-46,

March, 1992.

[11] Al-Marhoun, M. A.,“New Correlation for formation Volume Factor of oil and gas Mixtures,” Journal of Canadian

Petroleum Technology,pp. 22-26, March, 1992.

[12] Macary, S.M. and El-Batanoney, M.H., “Derivation of PVT Correlations for the Gulf of Suez Crude Oils,” Journal of

The Japan Petroleum Institute, Vol. 36,pp. 472-478, (1993).

[13] Omar, M.I. and Todd, A.C.,“Development of New Modified Black Oil Correlation for Malaysian Crudes,” paper SPE

25338 presented at the SPE Asia Pacific Oil and Gas Conference, Singapore, February,1993.

[14] Petrosky, G. and Farshad, F., “Pressure-Volume-Temperature Correlation for the Gulf of Mexico,” paper SPE 26644

presented at the SPE Annual Technical Conference and Exhibition, Houston, October,1993.

[15] De Ghetto, G., Paone, F. and Villa, M., “Reliability Analysis on PVT Correlations,” paper SPE 28904presented at the

European Petroleum Conference in London U.K., October, 1994.

[16] Farshad, F. F, Leblance, J. L, Garber, J. D. and Osorio, J. G., “Empirical PVT Correlations for Colombian Crude Oils,”

paper SPE 36105 presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Port of

Spain, Trinidad and Tobago,April, 1996.

[17] Hanafy, H. H., Macary, S. A., Elnady, Y. M., Bayomi, A. A. and El-Batanoney, M. H.,“Empirical PVT Correlations

Applied to Egyptian Crude Oils Exemplify Significance of Using Regional Correlations,” paper SPE 37295 presented at

the SPE International Symposium on Oilfield Chemistry, Houston,February, 1997.

[18] Almehaideb, R.A., “Improved PVT Correlations for UAE Crude Oil,” paper SPE 37691 presented at the Middle East

Oil Conference and Exhibition, Manama, Bahrain,March, 1997.

[19] Elsharkawy, A.M. and Alikhan, A.A.,“Correlations for Predicting Solution Gas/Oil Ratio, Oil Formation Volume

Factor, and Undersaturated Oil Compressibility,” J. Pet. Sci. Eng.,pp.291–302.,May, 1997.

[20] Velarde, J. J., Blasingame, T. A., and McCain, W.D., Jr., “Correlation of Black Oil Properties at Pressure Below Bubble

Point Pressure – A New Approach,” Paper 97-93 presented at the 48thATM of The Petroleum Society, Calgary,pp. , 1-

7, June ,1997.

[21] Khairy, M., El-Tayeb, S., and Hamdallah, M., “PVT Correlations Developed for Egyptian Crudes,” Oil and Gas J.,pp.

114–116, May, 1998.

[22] Movagharnejad and Fasih .,“The New Correlation for Prediction Bubble Point pressure and Oil Formation Volume

Factor for Iranian Reservoirs”, Research Institute of Petroleum Industry ,National Iranian Oil Company, January 1999.

[23] Al-Shammasi, A.A.,“Bubble Point Pressure and Oil Formation Volume Factor Correlations,” paper SPE 53185

presented at the SPE Middle East Oil Show, Bahrain, February1999.

[24] Dindoruk, B. and Christman, P.G.,“PVT Properties and Viscosity Correlations for Gulf of Mexico Oil,” paper SPE

71633 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, October2001.

[25] Boukadi, F.H., Bemani, A.S and Hashemi, A., “Pressure- Volume- Temperature Empirical Formulations for

Understaturated Omani Oils,” Petroleum Science and Technology, Online Publication Date: Petroleum Science and

Technology,January, 2004.

[26] Bolondarzadeh, A. and et al,“The New PVT Generated correlations of Iranian Oil properties”, 4th Iranian Petroleum

Engineering Student conference,2006.

[27] Mehran, F. Movagharnejad, K. and Didanloo, A.,“New Correlation for Estimation of Formation Volume Factor and

Bubble Point Pressure for Iranian Oil Fields”, First Iranian Petroleum Engineering conference, Tehran, 2006.



[28] Hemmati, M. N. and Kharrat, R., “A correlation Approach for Prediction of Crude-Oil PVT Properties,” paper SPE

15721 prepared for presentation at the 15th SPE Middle East Oil & Gas Show and Conference held in Bahrain

International Exhibition Centre, Kingdom of Bahrain, March, 2007.

[29] Mazandarani, M.T. and Asghari, S.M.,” Correlations for predicting solution gas-oil ratio, bubble point pressure and oil

formation volume factor at bubble-point of Iran crude oils,” European Congress of Chemical Engineering (ECCE-

6)Copenhagen, September, 2007.

[30] Khamehchi, R. and Ebrahimian, R.,“Novel empirical correlations for estimation of bubble point pressure, saturated

viscosity and gas solubility of crude oils,” Pet. Sci.,pp. 86-90 ,( March,2009),.

[31] Ikiensikimama, S. and Ogboja, O.,“New bubble point pressure empirical pvt correlation,” paper SPE 128893 presented

at the SPE technical conference and exhibition in Abuja, Nigeria, August, 2009.

[32] Moradi, B., Malekzadeh, E., Amani, M., Boukadi, F.H, and Kharrat, R.,“Bubble Point Pressure Empirical Correlation,”

paper SPE 132756 prepared for presentation at the Trinidad and Tobago Energy Resources Conference held in Port of

Spain, Trinidad, June 2010.

[33] Okoduwa, I.G. and Ikiensikimama, S.S. “Bubble point Pressure Correlations for Niger Delta Crude Oils,” paper SPE

136968 prepared for presentation at the 34th Annual SPE International Conference and Exhibition held in Tinapa,

Calabar, Nigeria, August 2010.

[34] Elmabrouk, S., Zekri,A. and Shirif, E.,” Prediction of Bubble-point Pressure and Bubble-point Oil Formation Volume

Factor in the Absence of PVT Analysis,” paper SPE 137368 prepared for presentation at the SPE Latin American &

Caribbean Petroleum Engineering Conference held in Lima, Peru,December 2010.

[35] Moradi, B., Malekzadeh, E., Mohammad, A S. , Awang, M. and Moradie, P.,” New Oil Formation Volume Factor

Empirical Correlation for Middle East Crude Oils,” International Journal of Petroleum and Geoscience Engineering

(IJPGE),pp. 12-23,( 2013).

[36] Karimnezhad, M., Heidarian, M., Kamari, M. and Jalalifar, H.,” A new empirical correlation for estimating bubble point

oil formation volume factor,” Journal of Natural Gas Science and Engineering ,pp. 329-335 , March,2014.

[37] Sulaimon, A.A., Ramli, N., Adeyemi, B.J. and Saaid, I.M.,” New Correlation for Oil Formation Volume Factor,” paper

SPE 172396 prepared for presentation at the SPE Nigeria Annual International Conference and Exhibition held in

Lagos, Nigeria, August 2014.

Nomenclature ��= Bubble- point pressure, psia ��= Formation volume factor at the bubble- point pressure, RB/STB ��= Solution gas oil ratio, SCF/STB

API = Oil density ��=crude oil density,lb/ft3 �= Gas relative density (air=1.0)

T= Reservoir temperature, degrees Fahrenheit

P=Reservoir pressure,psia γ ��=gas gravity (air = 1) that would result from separator conditions of 100 psig

γ ��=gas gravity obtained at separator conditions.

P��=actual separator pressure, psia

T��=actual separator temperature, 0F

R��= Separator solution gas oil ratio, SCF/STB. γ ��=Gas Specific gravity at separator pressure of 114.7 psia.

Min=minimum

Max=maximum

AARE = Average absolute percent relative error

Std = Standard deviation error

R2= Correlation coefficient



Appendix A

Table A1 Statistical error analysis for bubble-point pressure correlations for whole data

No. Method Year No. of

data

AARE Std R

1 Standing 1947 3000 19.83 44.58 0.921

2 Lasater 1958 3000 26.84 65.08 0.917

3 Glaso 1980 3000 26.68 48.89 0.912

4 Vazquez and Beggs-1 1980 3000 20.39 48.46 0.910

5 Vazquez and Beggs-2 1980 3000 25.45 53.41 0.916

6 Al-Marhoun 1988 3000 26.00 60.00 0.869

7 Kartoatmodjo and Schmidt-1 1991 3000 21.33 49.93 0.898

8 Kartoatmodjo and Schmidt-2 1991 3000 24.49 52.60 0.913

9 Dokla and Osman 1992 3000 30.60 56.67 0.834

10 Macary and El-Batanoney 1992 3000 40.54 85.88 0.895

11 Omar and Todd 1993 3000 27.35 52.68 0.883

12 Petrosky and Farshad 1993 3000 89.61 411.43 0.914

13 De Ghetto et al-1 1994 3000 23.85 45.63 0.911

14 De Ghetto et al-2 1994 3000 26.24 55.52 0.917

15 De Ghetto et al-3 1994 3000 25.10 52.39 0.924

16 Farshad et al 1996 3000 23.35 41.94 0.905

17 Hanafy et al 1997 3000 38.14 79.35 0.829

18 Almehaideb 1997 3000 34.54 58.61 0.832

19 Velarde et al 1997 3000 21.21 50.56 0.902

20 Khairy et al 1998 3000 32.23 67.90 0.857

21 Movagharnejad and Fasih 1999 3000 41.81 57.72 0.827

22 Al-Shammasi 1999 3000 22.53 46.24 0.921

23 Dindoruk and Christman 2001 3000 26.30 60.12 0.851

24 Boukadi et al 2004 3000 58.00 81.65 0.829

25 Bolondarzadeh et al 2006 3000 54.76 228.55 0.906

26 Mehran et al 2006 3000 22.83 51.78 0.905

27 Hemmati and Kharrat 2007 3000 51.63 73.30 0.829

28 Mazandarani and Asghari 2007 3000 50.07 70.96 0.829

29 Khamechi et al 2009 3000 32.59 57.35 0.909

30 Ikiensikimama and Ogboja 2009 3000 58.79 82.59 0.829

31 Moradi et al 2010 3000 50.67 37.13 0.789

32 Okoduwa and Ikiensikimama-1 2010 3000 52.21 74.15 0.829







Table A2 Statistical error analysis for oil formation volume factor correlations for whole data

No. Method Year No. of

data

AARE Std R

1 Standing 1947 3000 3.46 5.19 0.941

2 Glaso 1980 3000 4.02 5.14 0.940

3 Vazquez and Beggs 1980 3000 3.60 4.96 0.943

4 Al-Marhoun-1 1988 3000 5.15 7.02 0.880

5 Abdul-Majeed and Salman 1988 3000 5.11 6.98 0.880

6 Kartoatmodjo and Schmidt 1991 3000 3.16 4.76 0.945

7 Dokla and Osman 1991 3000 5.51 6.96 0.907

8 Al-Marhoun-2 1992 3000 3.49 4.88 0.942

9 Macary and El-Batanony 1993 3000 8.10 5.49 0.944

10 Omar and Todd 1993 3000 8.57 11.29 0.918

11 Petrosky and Farshad 1993 3000 8.32 7.21 0.881

12 Farshad et al 1996 3000 3.22 4.87 0.942

13 Hanafy et al 1997 3000 6.51 6.09 0.927

14 Almehaideb 1997 3000 4.41 5.87 0.930

15 Elsharkawy and Alikhan 1999 3000 4.43 5.89 0.930

16 Al-Shammasi-1 1999 3000 3.78 4.81 0.947

17 Al-Shammasi-2 1999 3000 3.14 4.70 0.948

18 Dindoruk and Christman 2001 3000 8.57 11.29 0.918

19 Mehran et al 2006 3000 3.39 4.83 0.946

20 Hemmati and Kharrat 2007 3000 3.36 4.95 0.941

21 Mazandarani and Asghari 2007 3000 8.37 7.19 0.881

22 Elmabrouk 2010 3000 4.03 5.37 0.939

23 Moradi et al 2013 3000 3.55 4.80 0.947

24 Karimnezhad et al-1 2014 3000 3.92 5.15 0.946



27 Sulaimon et al 2014 3000 8.45 7.24 0.881

Appendix B

Bubble Point Pressure Empirical Correlationssummary

Standing Correlation (May, 1947&1981)1,6

��=18.2*[(��)�.!" ∗ (10&) − 1.4]

) = 0.00091 ∗ – 0.0125 ∗ )�/

Lasater Correlation (May, 1958)3

�� = 0��1 ∗ ( + 459.67)5

�� = 0.3841 − 1.2008 ∗ � + 9.648 ∗ �8



9: = 725.321 − 16.0333 ∗ )�/ + 0.09524 ∗ )�/8

5 = ( ��379. 3) ( ��350 + 3509�; )

Glaso Correlation (May, 1980)4

log�� = 1.7669 + 1.7447 ∗ log(�∗) − 0.30218 ∗ (log�∗)8

�∗ = (�� )�.!�? ∗ �.�@8)�/�.A!A

Vazquez and Beggs Correlation (June, 1980)5

API≤30

�� = [C27.624 ∗ ��D ∗ 10&)]��.A�F"8!

) = (11.172 ∗ )�/ + 460)

API≥30

�� = [C56.18 ∗ ��D ∗ 10&)]�.!F8F?

) = (10.393 ∗ )�/ + 460)

�� = ��GH ∗ [1 + 5.915 ∗ 10IJ ∗ )�/ ∗ �GH ∗ log( ��GH114.7)] Al-Marhoun Correlation (May, 1988)

7

�� = 5.38089 ∗ 10I" ∗ ��.@�J�!8 ∗ �I�.!@@!F� ∗ ��".�F"@�� ∗ �."8?J@�

Kartoatmodjo and Schmidt Correlation (June, 1991) 9

For API≤30

�� = [ ��0.05958 ∗ (��))�.@A@8 ∗ 10�".�F�J∗&KL/(NOF?�)]�.AA!?

For API≥30

�� = [ ��0.03150 ∗ (��))�.@J!@ ∗ 10��.8!A∗&KL/(NOF?�)]�.A�F"

�� = ��GH ∗ [1 + 0.1595 ∗ )�/�.F�@! ∗ �GHI�.8F?? ∗ �GH ∗ log( ��GH114.7)] Dokla and Osman Correlation (March, 1992)

10

�� = 0.836386 ∗ 10F ∗ ��.@8F�F@ ∗ �–�.��FA ∗ ��.��@AA� ∗ –�.AJ8J!F

Macary and El-Batanoney Correlation (January, 1993)12



�� = 204.257 ∗ P ∗ (��.J� − 4.7927)

P = exp[(0.00077 ∗ ) − (0.0097 ∗ )�/) − (0.4003 ∗ �)] Omar and Todd Correlation (February, 1993)

13

��=18.2*[(��)T ∗ )UVWXYZ(0.00091 ∗ – 0.0125 ∗ )�/) − 1.4]

[ = 1.4256 − (0.2608 ∗ �:) − (0.45960 ∗ �) + (0.04481 ∗ ��8) + \

\ = (0.2360 ∗ �8)– 0.1077 ∗ ( 1� ∗ ��)

Petrosky and Farshad Correlation (October, 1993)14

��=112.727*[((�]^._``a��^.bacd) ∗ 10&) − 12.340]

) = 4.561 ∗ 10IJ ∗ �."A�� − 7.916 ∗ 10IF ∗ )�/�.JF��

De Ghetto et al Correlation ( October, 1994)15

Heavy oils

��=15.7286 *[(��)�.@!!J ∗ ��^.^^e^∗f

��^.^gae∗hij]

Medium-oils:

�� = [ ��0.09902 ∗ (�k�ll))�.8�!� ∗ [email protected]�J"∗&KL/(NOF?�)]�.AAA@

�k�ll = ��GH ∗ ��GH ∗ [1 + 0.1595 ∗ )�/�.F�@! ∗ �GHI�.8F?? ∗ log( ��GH114.7)] Light oils

��=31.7648*[(��)�.@!J@ ∗ ��h

��m]

) = 0.0009 ∗ ,o = 0.0148 ∗ )�/

Agip’s sample

��=21.4729*[(��)�.@?F? ∗ ��h

��m]

) = 0.00119 ∗ ,o = 0.0101 ∗ )�/

Farshad et al Correlation (April, 1996)16

�� = 10&

) = 0.3058 + 1.9013 ∗ XYZ(p) − 0.26 ∗ (XYZp)8

p=�–�."@!��.�J" ∗ 10�.��?A∗NI�.�8�!∗&KL Hanafy et al Correlation ( February, 1997)

17



�� = 3.205 ∗ �� + 157.27

Almehaideb Correlation ( March, 1997)18

�� =– 620.592 + 6.23087 ∗ ) + 2.89868 ∗

) = �� ∗ �� ∗ ��.!A!?!

Velarde et al Correlation ( June, 1997)20

��=1091.47 ∗ [(��.�!�F?J ∗ �I�.�?�F!! ∗ 10T) − 0.740152]J."JF!A�

[ = 0.013098 ∗ �.8!8"@8 − 8.2 ∗ 10I? ∗ )�/8.�@?�8F

Khairy et al Correlation (May, 1998)21

�� = 49.3647 ∗ ��.J@@F ∗ �I�.F?@? ∗ ��I�.�"�J ∗ �.??F�

Movagharnejad and Fasih Correlation (January, 1999)22

�� = 86.233589 + 0.576808 ∗ 10IJ ∗ [ − 3.1535 ∗ 10I�F ∗ [8

[ = ��.�!F8?A ∗ ��.?!!�J? ∗ ��I�.@?J"A? ∗ �.?"88�8

Al-Shammasi Correlation ( February, 1999)23

�� = ��J.J8@8�J ∗ [exp0−1.841408 ∗ ��1 ∗ (�� ∗ � ∗ ( + 460))�.@!"@�?] Dindoruk and Christman Empirical Correlation (September, 2001)

24

��=1.869979257 ∗ (��.88�F!?J8F ∗ �I�."@�J�!"FA ∗ 10&) + 0.011688308

) = [q

[ = 1.42828 ∗ 10I�� ∗ 8.!FFJA�@A@ − 6.74896 ∗ 10IF ∗ )�/�.88J88?F"?

q = (0.033383304 + (2 ∗ ��I�.8@8AFJAJ@ ∗ ��.�!F88?�?A))8

Boukadi et al Correlation (January, 2004)25

log(6.894757 ∗ ��) = −172.29 + ) + o + \ + r − s + t − p − u − / − v

) = 148.41 ∗ log(�� ∗ 0.1801175) , o = 404.22 ∗ log(��),\ = 968.94 ∗ log(�)

r = 30.24 ∗ log(( − 32)/1.8),s = 1.66 ∗ [log(�� ∗ 0.1801175) ∗ XYZ(��)] t = 3.06 ∗ [log(�� ∗ 0.1801175) ∗ XYZ(�)] p = 25.28 ∗ [log(�� ∗ 0.1801175) ∗ XY Z0�1 ∗ XYZ(( − 32)/1.8)] u = 17.14 ∗ XY Z(��) ∗ log(�), / = 69.21 ∗ XY Z(��) ∗ XYZ(( − 32)/1.8)

v = 168.71 ∗ XY Z0�1 ∗ XYZ(( − 32)/1.8)

Bolondarzadeh et al Correlation (2006)26

��=27.16[w&xy ∗ wz

{y − 30.28]



) = 3.4394 ∗ ��.J@��8, o = 0.56807 ∗ ��.A88�A8

\ = 3.7387 ∗ �.8"�F, r = 6.27605 ∗ )�/�.F8F?A

Mehran et al Correlation (2006)27

�� = 3.146 ∗ ��.!�"J ∗ �I�."��F ∗ ��"."A8J ∗ �."F??

Hemmati and Kharrat Correlation ( March, 2007)28

��=10.4566*[(��)T ∗ )UVWXYZ(0.0008 ∗ – 0.0098 ∗ )�/) − 8.6817]

[ = 1.5897 − (0.2735 ∗ �:) − (0.4429 ∗ �) + (0.04692 ∗ ��8) + )

) = (0.1440 ∗ �8)– 0.1596 ∗ ( 1� ∗ ��)

Mazandarani and Asghari Correlation (September, 2007)29

�� = 1.09373 ∗ 10IF ∗ ��.JJ�8 ∗ �I�.@�AJ? ∗ ��8.JF!? ∗ ( + 460)8.�A?@

Khamechi et al Correlation (March, 2009)30

�� = 107.93 ∗ ��.A�8A ∗ �I�.??? ∗ )�/�.�! ∗ �.8�88

Ikiensikimama and Ogboja Correlation (August, 2009)31

�� = �∗ ∗ ( + 635.4152349)�

�∗ = 0.243181338 − (2.316548789 ∗ |) + 10.60657909 ∗ |�.J�!�"�F?J

} = (47.57094772 − 0.677706662 ∗ )�/)�.J"�A"J?�A

| = ~9

~ = ��336.0064009 , 9 = ( ��336.0064009) + (6.7063984 ∗ ��} )

Moradi et al Correlation (June, 2010)32

�� = −65.853149 ∗ 9 + 0.00040668902 ∗ 98 − 0.00000015472455 ∗ 9"

9 = 1.1038 ∗ log()�/) ∗ (141.5�� − 131.5)�.��"! ∗ o

o = exp0−1.8406 ∗ � ∗ �1 ∗ (�� ∗ ( + 460) ∗ �)�.?!!@J

Okoduwa and Ikiensikimama Correlation (July, 2010)33

API≤21 (Heavy Oil)

�� = 4.58925593 ∗ ��.A8""F"@@ ∗ �I8.J"AF!?A ∗ ��J.?!8@@@@8 ∗ �.��JA!8F

21<API ≤ 26 (Medium Oil)

�� = 10.6356181 ∗ ��.��A?J"?A ∗ �I�."8��8?J ∗ ��?.!?�"8AJ� ∗ �.��!8F!"



26<API ≤ 35 (Blend Oil)

�� = 0.00007735 ∗ ��.AJ�@�J8� ∗ �I�.?�@@JJJ� ∗ ��.!�!�J8F? ∗ �.@8FF�@?!

35<API ≤ 45 (Light Oil)

�� = �∗ ∗ ( + 635.415989)�

�∗ = 0.32747598 − (2.26538201 ∗ |) + 10.6528063 ∗ |�.JFJ�8AF@

} = (47.5717698 − 0.68631461 ∗ )�/)�.J8@8!"J8

| = ~9

~ = ��336.006423 , 9 = ( ��336.0064009) + (306.706423 ∗ ��} )

API>45 (Very Light Oil

�� = 0.12357834 ∗ ��.?A"!@"A� ∗ �I�.J??�8A8" ∗ ��A.FA�"!��8 ∗ �.�@!@J"�"

Appendix C

Oil Formation Volume Factor Empirical Correlationssummary

Standing Correlation (May, 1947&1981)1,6

�� = 0.9759 + 0.00012 ∗ [�� ∗ (��)�.J + 1.25 ∗ ]�.8

Glaso Correlation (May, 1980)4

log(�� − 1) = −6.58511 + 2.91329 ∗ log(��∗) − 0.30218 ∗ (log��∗)8

��∗ = �� ∗ (��)�.J8A + 0.968 ∗

Vazquez and Beggs Correlation ( June, 1980)5

API≤30

β� = 1 + 4.677 ∗ 10IF ∗ R� + 1.751 ∗ 10IJ ∗ (T − 60) ∗ wAPI γ �� y + F

t = −1.811 ∗ 10I! ∗ R� ∗ (T − 60) ∗ wAPI γ �� y

API≥30

β� = 1 + 4.670 ∗ 10IF ∗ R� + 1.100 ∗ 10IJ ∗ (T − 60) ∗ wAPI γ �� y + F

t = 1.337 ∗ 10IA ∗ R� ∗ (T − 60) ∗ wAPI γ �� y

γ � = γ �� ∗ [1 + 5.915 ∗ 10IJ ∗ API ∗ T�� ∗ log( P��114.7)]



Al-Marhoun Correlation (May, 1988)7 β� = 0.497069 + 0.86296 ∗ 10I" ∗ + 0.182594 ∗ 10I8 ∗ t + 0.318099 ∗ 10IJ ∗ t8

t = ��.@F8"A��."8"8AF��I�.8�8�F

Abdul-Majeed and Salman Correlation (November, 1988)8 β� = 0.965787 + 7.73 ∗ 10IF ∗ + 4.8141 ∗ 10IJ ∗ t − 6.8987 ∗ 10I�� ∗ t8

t = ��.8�I�.�F@��IJ.888

Kartoatmodjo and Schmidt Correlation (June, 1991)9 β� = 0.98496 + 0.0001 ∗ t�.J

t = ��.@JJ��.8J��I�.J + 0.45 ∗

�� = ��GH ∗ [1 + 0.1595 ∗ )�/�.F�@! ∗ �GHI�.8F?? ∗ �GH ∗ log( ��GH114.7)] Dokla and Osman Correlation (March, 1992)

10 β� = 0.0431935 + 0.15667 ∗ 10I8 ∗ + 0.13977 ∗ 10I8 ∗ t − 0.38052 ∗ 10IJ ∗ t8

t = ��.@@"J@8��.F�F�8��I�.!!8?�J

Al-Marhoun Correlation (March, 1992)11

β� = 1 + 0.177342 ∗ 10I" ∗ �� + 0.220163 ∗ 10I" ∗ �� ∗ �� + t

t = 4.292580 ∗ 10I? ∗ �� ∗ (1 − ��)( − 60) + 0.528707 ∗ 10I" ∗ ( − 60)

Macary and El-Batanoney Correlation (January, 1993)12

β� = [1 + 1.0031 ∗ ] ∗ ~

~ = exp[0.0004 ∗ �� + 0.0006 ∗ (��)] Omar and Todd Correlation ( February, 1993)

13

�� = 0.9759 + 0.00012 ∗ [�� ∗ (��)�.J + 1.25 ∗ ]�~ = 1.1663 + 0.762 ∗ 10I" ∗ )�/

� − 0.0399 ∗ �Petrosky and Farshad Correlation ( October, 1993)

14 β� = 1.0113 + 7.2046 ∗ 10IJ ∗ ~

~ = [��."@"! ∗ (��.8A�F��.?8?J) + 0.24626 ∗ �.J"@�]".�A"?

Farshad et al Correlation (April,1996)16

�� = 1 + 10&) = −2.6541 + 0.5576 ∗ XYZ(9) + 0.3331 ∗ (XYZ9)8



9 = ��.JAJ?��.8"?A��I�."8!8 + 0.0976 ∗ Hanafy et al Correlation (February, 1997)

17 �� = 0.0006 ∗ �� + 1.079

Almehaideb Correlation ( March, 1997)18

�� = 1.122018 + 1.41 ∗ 10I? ∗ �� ∗ ��8

Elsharkawy and Alikhan Empirical Correlation (May, 1997)19

�� = 1 + 40.428 ∗ 10IJ ∗ �� + 63.802 ∗ 10IJ ∗ ( − 60) + 9

9 = 0.780 ∗ 10IJ ∗ [�� ∗ ( − 60) ∗ ��] Al-Shammasi Correlation ( February, 1999)

23

�� = 1 + 5.53.∗ 10I@ ∗ (��( − 60)) + 0.000181 ∗ �� + ~

~ = 0.000449 ∗ ( − 60�� ) + 0.000206 ∗ �� ∗ ��

Dindoruk and Christman Correlation (September, 2001)24

�� = 0.9871 + 7.8651 ∗ 10IF ∗ ) + 2.6891 ∗ 10I? ∗ )8 + 1.1 ∗ 10IJ ∗ ( − 60) ∗ )�/�

o = [��8.J��@JJ ∗ �IF.!J8J��.!"J + 1.3654210J ∗ ( − 60)8.8J8!! + 10.071 ∗ ��]�.FFJ

\ = [5.352624 + ( 8∗�]�^.�c^d^��^.^^^`∗(NI?�))]8 , ) = x

z

Mehran et al Correlation (2006)27

�� = 1 + 10&

) = −4.7486 + 1.587 ∗ XYZ(9) − 0.0495 ∗ (XYZ9)8

9 = �� ∗ [��]�.F8�� + 2.035 ∗

Hemmati and Kharrat Correlation ( March, 2007)28

�� = 1 + 10&

) = −4.6862 + 1.5959 ∗ XYZ(9) − 0566 ∗ (XYZ9)8

9 = �� ∗ [��]�.JAF? + 1.7439 ∗

Mazandarani and Asghari Correlation (September, 2007)29

�� = 0.99117 + 0.00021 ∗ �� − 2.32 ∗ 10I? ∗ �� ∗ �� + 0.00071 ∗ ( − 60) − ~

~ = 4.30 ∗ 10I@ ∗ ( − 60) ∗ (1 − �)



Elmabrouk Correlation (2010)34

�� = 1.6624 + 0.00051 ∗ ��K + 0.00015 ∗ ��K − 0.802 ∗ �:�N + 0.0005 ∗ �

Moradi et al Correlation (2013)35

�� = 0.965278 + [0.0001 ∗ )�/�.�?@8?�J ∗ �I�.F?J"�@ ∗ ~] ~ = [�� ∗ [��]�.?F"�F� + 2.27448 ∗ ]�.�JF�?

Karimnezhad et al Correlation (2014)36

�� = 9.7 ∗ 10I@ ∗ [�� ∗ �� + (��( + 460))] + 1.0367

�� = 1.66 ∗ �� ∗ ��I�.�" + [0.0000044 ∗ (��( + 460))�.!AF]

�� = 1.166 ∗ �� ∗ ��I�.�" + [0.0000044 ∗ (��( + 460))�.!AF]�

u = ( + 460)I�.�FF�I�.J8��.�?�

Sulaimon et al Correlation (August, 2014)37

�� = 1.08199 − (0.00805 ∗ ��) + 00.29401 ∗ �1 + (0.00009 ∗ ��) + ) + o

) = −00.004029 ∗ �� ∗ �1+(9.11296 ∗ 10I? ∗ �� ∗ ��)+ (0.00020 ∗ �� ∗ �)

o = (0.00013 ∗ ��8) − 00.11166 ∗ �81 − (5.2423 ∗ 10I! ∗ ��)

assessment of oil reservoir properties empirical correlations · assessment of oil reservoir...

Documents