Oil Correlations
Subtopics:
AlMarhoun 1985 (Saudi Arabian Oil)
The AlMarhoun correlation contains equations for estimating bubble point pressure, solution gas oil ratio (Rs), and oil formation volume factor (Bo) for Saudi Arabian oils. Seventyfive bottom hole fluid samples from 62 reservoirs in Saudi Arabia were used in the development of these correlations. The author claims that the correlations should be valid for all types of gasoil mixtures that share similar properties as those used in the derivation. According to the author, the average errors and standard deviations were lower with the AlMarhoun correlation than with the Standing and Glaso correlations for Saudi Arabian crude oils.
Bubble Point Pressure
Where:
Solution Gas Oil Ratio
The bubble point pressure equation is reversed to solve for the solution gasoil ratio. The variable x must be solved for using the quadratic equation.
Where:
Oil Formation Volume Factor
Gas Saturated
Where:
Undersaturated
The oil compressibility (co) used in this equation is obtained from the Vasquez and Beggs correlation.
Reference
"PressureVolumeTemperature Correlations for Saudi Crude Oils", M.A. AlMarhoun, SPE 13718, 1985.
De Ghetto et al (Heavy and ExtraHeavy Oils)
The De Ghetto et al correlation contains modified PVT correlations for estimating bubble point pressure, solution gas oil ratio (Rs), oil formation volume factor (Bo), oil compressibility (co), and oil viscosity (mo) for heavy (10 < °API < 22.3) and extraheavy oils (°API < 10). The oils used for developing the correlation came from AGIP’s reservoir fluid samples taken from the Mediterranean Basin, Africa, and the Persian Gulf. When comparing published correlations, De Ghetto et al decided that the Vasquez and Beggs correlation estimated the oil formation volume factor (Bo) with minimal error, and therefore no further modification was needed. Note that in contrast with other correlations, the De Ghetto et al correlation requires the pressure and temperature at the separator.
Bubble Point Pressure
Heavy Oils
A modified Vasquez and Beggs solution gas oil ratio (Rs) correlation is reversed to solve for the bubble point pressure as follows:
Where:
ExtraHeavy Oils
A modified Standing solution gas oil ratio (Rs) correlation is reversed to solve for the bubble point pressure as follows:
Solution Gas Oil Ratio
Heavy Oils
A modified Vasquez and Beggs solution gas oil ratio (Rs) correlation was developed as follows:
Where gg(psp) is calculated the same as above for bubble point pressure.
ExtraHeavy Oils
A modified Standing solution gas oil ratio (Rs) correlation was developed as follows:
Oil Formation Volume Factor
Gas Saturated
A modified Vasquez and Beggs oil formation volume factor (Bo) correlation was developed as follows:
Where:
Coefficient 
go<= 30°API 
go > 30°API 
C1 
4.677x104 
4.670x104 
C2 
1.751x105 
1.100x105 
C3 
1.811x108 
1.377x109 
Undersaturated
Oil Compressibility
Gas Saturated
The derivatives dBo/ dRs and dRs / dp were taken from the Vasquez and Beggs correlation.
Undersaturated
Modified Vasquez and Beggs oil compressibility (co) correlations were developed as follows:
Heavy Oils
ExtraHeavy Oils
Where gg(psp) is calculated the same as above for bubble point pressure.
Oil Viscosity
Dead Oil
Modified EgbogahJack’s oil viscosity (mo) correlations were developed as follows:
HeavyOils
ExtraHeavy Oils
Gas Saturated
Modified Kartoatmodjo’s oil viscosity (mo) correlations were developed as follows:
HeavyOils
Where:
ExtraHeavy Oils
Where:
Undersaturated
Heavy Oils
A modified Kartoatmodjo’s oil viscosity (mo) correlation was developed as follows:
ExtraHeavy Oils
A modified Labedi’s oil viscosity (mo) correlation was developed as follows:
Reference
"PressureVolumeTemperature Correlations for Heavy and Extra Heavy Oils", Giambattista De Ghetto, Francesco Paone, and Marco Villa, SPE 30316, 1995.
Glaso (North Sea Oil)
The Glaso correlation contains equations for estimating bubble point pressure, solution gas oil ratio (Rs), and oil formation volume factor (Bo) for North Sea oils. The author claims that the correlation should be valid for all types of oil & gas mixtures after correcting for nonhydrocarbons in the surface gases, and the paraffinicity of the oil. According to the author, the correlation more accurately predicts the oil properties of North Sea oils than the Standing correlation.
Bubble Point Correlation
Where:
Solution Gas Oil Ratio
The bubble point pressure equation is reversed to solve for the solution gas oil ratio (Rs). The variable x must be solved for using the qua
Where:
Oil Formation Volume Factor
Gas Saturated
Where:
Undersaturated
The oil compressibility (co) used in this equation is obtained from the Vasquez and Beggs correlation.
Reference
"Generalized PressureVolumeTemperature Correlations", Oistein Glaso, Journal of Petroleum Technology, 1980.
Hanafy et al (Egyptian Oil)
The Hanafy et al correlation contains equations for estimating bubble point pressure, solution gas oil ratio (Rs), oil formation volume factor (Bo), oil compressibility (co), oil viscosity (mo), and oil density (ro) for Egyptian oils. The compressibility correlation assumes constant compressibility after the bubble point. This correlation is independent of oil gravity (go) and reservoir temperature (T). The PVT data used in the derivation of the correlations was gathered from the Gulf of Suez, Western Desert, and Sinai regions. The authors claim that the correlations can be used to estimate oil properties for a wide range of crude oils ranging from heavy to volatile oils. However our observations are that it appears to be closer to the properties of light oils.
Bubble Point Pressure
Solution Gas Oil Ratio
To prevent the calculation of a negative solution gas oil ratio (Rs), 0 is returned for pressures less than 157.28 psia.
Oil Formation Volume Factor
Gas Saturated
Undersaturated
Oil Density
Note that the density is calculated in metric units (g / cm3).
Gas Saturated
Undersaturated
Oil Compressibility
Undersaturated
This correlation uses only the oil density (rob) at the bubble point. Therefore the oil compressibility (co) is constant for pressures greater than the bubble point.
Gas Saturated
The derivatives dBo/ dRs and dRs / dP were taken from the Vasquez and Beggs correlation.
Oil Viscosity
This correlation calculates the oil viscosity (mo) at any pressure using the corresponding oil density (ro).
Reference
"A New Approach for Predicting the Crude Oil Properties", H.H. Hanafy, S.M. Macary, Y.M. ElNady, A.A. Bayomi and M.H. El Batanony, SPE 37439, 1997.
Khan et al (Saudi Arabian Oil)
The Khan et al correlation contains equations for estimating oil viscosity (mo) at, above, and below the bubble point for Saudi Arabian oils. The study used data from 75 bottom hole samples, which were taken from 65 Saudi Arabian reservoirs. The authors claim that this correlation gives the most accurate predictions for Saudi Arabian crude oils, as compared to the Beggs and Robinson, Beal, and Chew and Connally correlations.
Oil Viscosity at the Bubble Point
For this correlation oil gravity (go) must be less than 1 (10°API).
Where:
Oil Viscosity above the Bubble Point
Oil Viscosity below the Bubble Point
Reference
"Viscosity Correlations for Saudi Arabian Crude Oils", S.A. Khan, M.A. AlMarhoun, S.O. Duffuaa, and S.A. AbuKhamsin, SPE Paper No. 15720, 1987.
Ng and Egbogah
The Ng and Egbogah correlation contains two methods for calculating dead oil viscosity (mod) using a modified Beggs and Robinson viscosity correlation and a correlation that uses the pour point temperature. Pour point temperature is the lowest temperature at which the oil is observed to flow when cooled and examined under conditions prescribed in ASTM D97. The purpose of introducing the pour point temperature into the correlation is to reflect the chemical composition of crude oil into the viscosity correlation. To obtain the viscosity for live oils, the dead oil correlations are used with the Beggs and Robinson viscosity correlation. The data used to derive the correlations was taken from the Reservoir Fluids Analysis Laboratory of AGAT Engineering Ltd., using a total of 394 oil systems.
Dead Oils
Modified Beggs and Robinson Viscosity Correlation
Pour Point Visc
Note the range for pour point temperature (Tpp) in this equation is from 50 to 15 °C.
Live Oils
GasSaturated
Where:
Undersaturated
Where:
Reference
"An Improved TemperatureViscosity Correlation for Crude Oil Systems", J.T.H. Ng and E.O. Egbogah, Petroleum Society of CIM 833432, 1983.
Petrosky and Farshad (Gulf of Mexico Oil)
The Petrosky and Farshad correlation contains equations for estimating bubble point pressure, solution gas oil ratio (Rs), oil formation volume factor (Bo), and oil compressibility (co) for Gulf of Mexico oils. The correlation was developed using fluid samples taken from offshore regions in Texas and Louisiana (Galveston Island eastward through Main Pass). The authors claim that these correlations provide improved results over other correlations for the Gulf of Mexico, including those published by Standing, Vasquez and Beggs, Glaso, and AlMarhoun.
Bubble Point Pressure
Where:
Solution Gas Oil Ratio
Where:
Oil Formation Volume Factor
Gas Saturated
Undersaturated
Oil Compressibility
Gas Saturated
The derivatives dBo/ dRs and dRs / dP were taken from the Vasquez and Beggs correlation.
Undersaturated
Note that this equation is valid for an oil compressibility (co) between 2.464x105 to 3.507x105.
Reference
"PressureVolumeTemperature Correlations for Gulf of Mexico Crude Oils", G.E. Petrosky Jr. and F.F. Farshad, SPE 26644, 1993.
Standing (California Oil)
The Standing correlation contains equations for estimating bubble point pressure, solution gas oil ratio (Rs), and oil formation volume factor (Bo) for California oils. 105 experimentally determined data points on 22 different oilgas mixtures from California were used in the development of the correlations.
Bubble Point Pressure
Solution Gas Oil Ratio
Oil Formation Volume Factor
Gas Saturated
Undersaturated
The oil compressibility (co) used in this equation is obtained from the Vasquez and Beggs correlation.
Reference
"A PressureVolumeTemperature Correlation for Mixtures of California Oil and Gases", M.B. Standing, Drill. & Prod. Prac., API, 1947.
Vasquez and Beggs (Generally Applicable)
Vasquez and Beggs is a generally applicable correlation containing equations for solution gas oil ratio (Rs), oil formation volume factor (Bo), and oil compressibility (co). The correlation was developed from data obtained from over 600 laboratory PVT analyses gathered from fields all over the world. The data used in the development of the correlation covers a wide range of pressures, temperatures, and oil properties. The correlation divides the data into two groups, one for an oil gravity (go) over 30 API and one at and below 30 API.
Bubble Point Pressure
Where:
Coefficient 
go<= 30°API 
go > 30°API 
C1 
0.0362 
0.0178 
C2 
1.0937 
1.1870 
C3 
25.7240 
23.9310 
Solution Gas Oil Ratio
The coefficients C1, C2, and C3 are the same as for the bubble point pressure equation above.
Oil Formation Volume Factor
Gas Saturated
Where:
Coefficient 
go<= 30°API 
go > 30°API 
C1 
4.677x104 
4.670x104 
C2 
1.751x105 
1.100x105 
C3 
1.811x108 
1.377x109 
Undersaturated
Oil Compressibility
Gas Saturated
The derivatives dBo/ dRs and dRs / dP were taken from the Vasquez and Beggs correlation.
Undersaturated
Reference
"Correlations for Fluid Physical Property Prediction", M.E. Vasquez and H.D. Beggs, JPT 968  70, June 1980.
Velarde et al (Reduced Variable Approach)
The Velarde et al correlation contains equations for estimating bubble point pressure, solution gas oil ratio (Rs), and oil formation volume factor (Bo). The bubble point pressure correlation was based on 728 data sets. The solution gas oil ratio (Rs) was based on 2097 data sets.
Bubble Point Pressure
Where:
Solution Gas Oil Ratio at the Bubble Point Pressure
Starting from the bubble point pressure equation shown above, rearrangement yields the following solution for the solution gas oil ratio (Rs):
Solution Gas Oil Ratio
The correlation for the solution gas oil ratio (Rs) below the bubble point uses a reduced variable approach, which yields the reduced solution gas oil ratio (Rsr) as follows:
Where:
A Coefficients 
B Coefficients 
C Coefficients 
A0 = 9.73x107 
B0 = 0.022339 
C0 = 0.725167 
A1 = 1.672608 
B1 = 1.004750 
C1 = 1.485480 
A2 = 0.929870 
B2 = 0.337711 
C2 = 0.164741 
A3 = 0.247235 
B3 = 0.132795 
C3 = 0.091330 
A4 = 1.056052 
B4 = 0.302065 
C4 = 0.047094 
The reduced solution gas oil ratio (Rsr) is defined as the solution gas oil ratio (Rs) divided by the solution gas oil ratio at the bubble point (Rsb) as follows:
Similarly, the reduced pressure is defined as the pressure divided by the bubble point pressure.
Using the above relationship the reduced solution gas oil ratio (Rsr) and the solution gas oil ratio at the bubble point (Rsb) are used to solve for the actual solution gas oil ratio (Rs) at any pressure below the bubble point.
Oil Formation Volume Factor
Gas Saturated
Where:
In the above equation an initial estimate of rpo is calculated as follows:
After this initial value is known, rpo is calculated through a 10 step iteration process using the following equations. The values from the ninth and tenth iterations are averaged to yield a final value for rpo.
Undersaturated
The oil compressibility (co) used in this equation is obtained from the Vasquez and Beggs correlation.
Correlation Limits
Variable 
Rs Correlation Limits 
Pbp Correlation Limits 
T 
70 to 307 °F 
74 to 327 °F 
pbp 
106 to 5312 psia 
70 to 6700 psia 
Bob 
1.040 to 2.082 Rbbl / stbbl 
N/A 
Rs or Rsb 
102 to 1808 scf / stbbl 
10 to 1870 scf / stbbl 
gg 
0.561 to 1.101 
0.556 to 1.367 
go 
11.6 to 53.4 °API 
12 to 55 °API 
Reference
"Correlation of Black Oil Properties at Pressures Below Bubble Point Pressure – A New Approach", J. Velarde, T.A. Blasingame and W.D. McCain, Jr., The Petroleum Society 93  97, 1997.
Oil Correlation Limits
Correlation 
T (°F) 
p (psia) 
pbp (psia) 
Bo (Rbbl / stbbl) 
Rs (scf / stbbl) 
AlMarhoun 1985 (Saudi Arabian Oil) 
75 – 240 

107 – 4315 
1.02 – 2.42 
24 – 1901 
De Ghetto et al (Heavy and ExtraHeavy Oils) 
131.4 – 250.7 
1038.49 – 7411.54 
208.86 – 4021.96 
1.057 – 1.362 
17.21 – 640.25 
Glaso (North Sea Oil) 
80 – 280 
400 – 4000 
150 – 7127 
1.087 – 2.588 
90 – 2637 
Hanafy et al (Egyptian Oil) 
1038.49 – 7411.54 

36 – 5003 
1.032 – 1.35 
7 – 4272 
Khan et al (Saudi Arabian Oil) 
75 – 240 
14.7 – 5015 
107 – 4315 

24 – 1901 
Ng and Egbogah 
70 – 295 




Petrosky and Farshad (Gulf of Mexico Oil) 
114 – 288 
1700 – 10692 
1574 – 6523 
1.1178 – 1.6229 
217 – 1406 
Standing (California Oil) 
60 – 260 (pbp) 100 – 260 (Bo) 

200 – 6000 
1.024 – 2.15 
20 – 1425 
Vasquez and Beggs (Generally Applicable) 

140.7 – 9514.7 



Velarde et al (Reduced Variable Approach) 
See Velarde et al 

See Velarde et al 
See Velarde et al 
See Velarde et al 
Correlation 
gg 
go (°API) 
Tsp (°F) 
Psp (psia) 
mo (cp) 
AlMarhoun 1985 (Saudi Arabian Oil) 
0.752 – 1.367 
14.3 – 44.6 



De Ghetto et al (Heavy and ExtraHeavy Oils) 
0.623 – 1.517 
6 – 22.3 
59 – 177.8 
14.5 – 752.2 
2.4 – 354.6 
Glaso (North Sea Oil) 
0.65 – 1.276 
22.3 – 48.1 


0.119 – 106.6 
Hanafy et al (Egyptian Oil) 
0.752 – 1.367 
14.3 – 44.6 


0.13 – 71 
Khan et al (Saudi Arabian Oil) 





Ng and Egbogah 

5 – 58 



Petrosky and Farshad (Gulf of Mexico Oil) 
0.5781 – 0.8519 
16.3 – 45 



Standing (California Oil) 
0.5 – 1.5 
16.5 – 63.8 



Vasquez and Beggs (Generally Applicable) 
0.511 – 1.351 
15.3 – 59.5 



Velarde et al (Reduced Variable Approach) 
See Velarde et al 
See Velarde et al 



Correlation 
mod (cp) 
mos (cp) 
mob (cp) 
ro (g / cm3) 
rob (g / cm3) 
AlMarhoun 1985 (Saudi Arabian Oil) 





De Ghetto et al (Heavy and ExtraHeavy Oils) 
7.7 – 1386.9 
2.1 – 295.9 



Glaso (North Sea Oil) 





Hanafy et al (Egyptian Oil) 



0.648 – 1.071 
0.428 – 0.939 
Khan et al (Saudi Arabian Oil) 

0.13 – 77.4 
0.13 – 17.9 


Ng and Egbogah 





Petrosky and Farshad (Gulf of Mexico Oil) 





Standing (California Oil) 





Vasquez and Beggs (Generally Applicable) 





Velarde et al (Reduced Variable Approach) 




