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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
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@IJMTER-2016 All rights Reserved 130
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.
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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.
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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
Vazquez and Beggs- 1 1980 627 28.48 91.89 0.791
Bubble point pressure correlations assessment summary for light oils( 0API≥31)
Vazquez and Beggs- 1 1980 2243 17.98 29.53 0.938
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
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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.
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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
Kartoatmodjo and Schmidt 1991 627 1.81 2.74 0.940
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
Kartoatmodjo and Schmidt 1991 2243 3.61 5.26 0.931
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
International Journal of Modern Trends in Engineering and Research (IJMTER) Volume 03, Issue 02, [February – 2016] ISSN (Online):2349–9745; ISSN (Print):2393-8161
@IJMTER-2016 All rights Reserved 135
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
International Journal of Modern Trends in Engineering and Research (IJMTER) Volume 03, Issue 02, [February – 2016] ISSN (Online):2349–9745; ISSN (Print):2393-8161
@IJMTER-2016 All rights Reserved 136
correlations
11. followed by Kartoatmodjo and Schmidt(1991) and Mehran et al(2006) correlations.
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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
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@IJMTER-2016 All rights Reserved 138
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
33 Okoduwa and Ikiensikimama-2 2010 3000 28.68 55.39 0.882
34 Okoduwa and Ikiensikimama-3 2010 3000 50.93 72.27 0.829
35 Okoduwa and Ikiensikimama-4 2010 3000 25.52 72.67 0.908
36 Okoduwa and Ikiensikimama-5 2010 3000 52.02 35.89 0.789
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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
25 Karimnezhad et al-2 2014 3000 8.87 7.31 0.880
26 Karimnezhad et al-3 2014 3000 3.86 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
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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
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�� = 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
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�� = 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]
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@IJMTER-2016 All rights Reserved 143
) = 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!"
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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)]
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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
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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 − �)
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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! ∗ ��)