Correlation Eqns for PVT Toolbox
Schlumberger Private
Prepared by Oilphase-DBR
Written by Tara Davies
February, 2004
Table of Contents
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Overview............................................................................................................................. 5
Document Division: .................................................................................................... 5
Correlation Selection: ................................................................................................. 5
Equation References: .................................................................................................. 6
Special Notations: ....................................................................................................... 6
Correlations in the PVT Toolbox........................................................................................ 7
Part 1-Oil Correlations...................................................................................................... 10
General Eqns and Knowledge:.................................................................................. 10
Stock Tank Oil Gravity (γAPI):............................................................................... 10
Specific Gravity of stock tank oil: ........................................................................ 10
Specific Gravity of Gas......................................................................................... 10
1.1. Oil Density Correlations ........................................................................................ 11
1.1.1 McCain & Hill (1995)...................................................................................... 11
1.1.2 Standing (1951)................................................................................................ 11
1.1.3 McCain density mass balance.......................................................................... 12
1.1.4 Oil Density at Pressures Above Pb .................................................................. 12
1.2. Oil FVF (Bo).......................................................................................................... 13
1.2.1 Glaso (1980)..................................................................................................... 13
1.2.2 Standing (1947)................................................................................................ 13
1.2.3 Vasquez and Beggs (1980) .............................................................................. 13
1.2.3.1 Gas Corrected Gravity Eqn- Vasquez Beggs............................................ 14
1.2.4 Petrosky & Farshad (1993) .............................................................................. 14
1.2.5 Farshad & Leblanc (1992) ............................................................................... 14
1.2.6 Al-Marhoun (2) (1992) .................................................................................... 14
1.2.7 Kartoatmodjo and Schmidt (1994)................................................................... 15
1.2.7.1 Separator Gas Corrected Gravity, Kartoatmodjo...................................... 15
1.2.8 Casey and Cronquist (1992)............................................................................. 15
1.2.9 Almedhaideb (1997) ........................................................................................ 16
1.2.10 Al-Shammasi (1999)...................................................................................... 16
1.2.11 Elksharkawy & Alikhan (1997) ..................................................................... 16
1.2.12 McCain mass balance formation volume factor ............................................ 16
1.2.13 Oil Formation Volume Factor at Pressures Above Pb................................... 17
1.3
Bubble Point Pressure (Pb, aka Psat)................................................................ 17
1.3.1 Glasø (1980)..................................................................................................... 17
1.3.2 Standing (1947)................................................................................................ 17
1.3.4 Vazquez and Beggs (1980) .............................................................................. 19
1.3.5 Al-Marhoun (1988).......................................................................................... 20
1.3.6 Petrosky and Farshad (1993) ........................................................................... 20
1.3.7 Farshad & Leblanc (1992) ............................................................................... 20
1.3.8. Kartoatmodjo and Schmidt (1994).................................................................. 20
1.3.9. Valkó & McCain (2003) ................................................................................. 21
1.3.10 Velarde, Blasingame, McCain (1997) ........................................................... 22
1.3.11 Labedi (1990)................................................................................................. 22
1.3.12 Al-Shammasi (1999)...................................................................................... 22
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1.4 Gas Oil Ratio (GOR, aka Rs).................................................................................. 23
1.4.1 Glaso (1980)..................................................................................................... 23
1.4.2 Standing (1947)................................................................................................ 23
1.4.3 Vazquez-Beggs (1980)..................................................................................... 24
1.4.4 Lasater (1958) .................................................................................................. 24
1.4.5 Petrosky and Farshad (1993) ........................................................................... 25
1.4.6 Kartoatmodjo-Schmidt (1994) ......................................................................... 25
1.4.7 Casey-Cronquist (1992) ................................................................................... 26
1.4.8 Velarde, Basingame, McCain (1999)............................................................... 26
1.5 Dead Oil Viscosity (µod)........................................................................................ 28
1.5.1 Beggs and Robinson (1975)............................................................................ 28
1.5.2 Glaso (1980)..................................................................................................... 28
1.5.3 Ng and Egbogah (1983) ................................................................................... 28
1.5.4 Beal (1946)....................................................................................................... 29
1.6 Saturated Oil Viscosity (µosat) ................................................................................ 29
1.6.1 Beggs and Robinson (1975)............................................................................. 29
1.6.2 Khan (1987) ..................................................................................................... 29
1.6.3 Chew and Connally (1959) .............................................................................. 30
1.6.4 Hanafy et al (1997) .......................................................................................... 30
1.7 UnSaturated Oil Viscosity (µounsat)......................................................................... 31
1.7.1 Khan (1987) ..................................................................................................... 31
1.7.2 Vasquez & Beggs (1980) ................................................................................. 31
1.7.3 Beal (1946)....................................................................................................... 32
1.7.4 Hanafy et al (1997) .......................................................................................... 32
1.8 Saturated Oil Compressibility (cosat) ...................................................................... 33
1.8.1 McCain, Rollins, and Villena (1988)............................................................... 33
1.8.2 Spivey, Valkó, McCain (2003) ........................................................................ 33
1.9 UnSaturated Oil Compressibility (counsat)............................................................... 34
1.9.1 Spivey, Valkó, McCain (2003) ........................................................................ 34
1.9.2 Vasquez and Beggs (1980) .............................................................................. 35
1.9.3 Petrosky and Farshad ....................................................................................... 36
1.9.4 Calhoun (1947) ................................................................................................ 36
1.9.5 Trube (1957)- not included .............................................................................. 37
Part 2-Gas Correlations..................................................................................................... 39
General Eqns and Knowledge................................................................................... 39
Stock-Tank Gas-Oil Ratio (Rst)............................................................................ 39
Solution Gas Oil Ratio at Pb (Rsb) ....................................................................... 39
Weighted Gas Gravity (γgwt.ave): ............................................................................ 39
Stock-Tank Gas Gravity (γgST).............................................................................. 40
Gas density (ρg).................................................................................................... 40
Gas Formation Volume Factor (Bg) ..................................................................... 40
Z factor.................................................................................................................. 41
2.1.1 Calculating Tc, Pc from known gas gravity......................................................... 42
2.1.1.1 Sutton (1985) ................................................................................................ 42
2.1.1.2. Standing (1977)............................................................................................ 43
2.1.1.3 Piper, McCain, Corredor (1993) ................................................................... 44
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2.1.2 Calculating Tc, Pc from known gas composition:............................................... 45
2.1.2.1 Piper, McCain, Corredor (1993) ................................................................... 45
2.1.2.2 Stewart, Burkhardt, and Voo (1959)............................................................. 45
2.1.2.3 Sutton (1985) ................................................................................................ 47
2.2 Calculating Z Factor ............................................................................................... 48
2.2.1 Dranchuk (1975) .............................................................................................. 48
2.2.2 Hall and Yarborough (1973)............................................................................ 49
2.3 Calculating Gas Viscosity....................................................................................... 49
2.3.1 Lee, Gonzales, Eakin (1966)............................................................................ 49
2.3.2 Carr, Kobayashi, Burroughs (1954)................................................................. 50
2.4 Calculating Gas Compressibility ............................................................................ 51
2.4.1 Hall, Yarborough (1973).................................................................................. 51
2.4.2 Dranchuk, Abou-Kassem (1975) ..................................................................... 52
3. Water Correlations ........................................................................................................ 53
3.1 Water Density ......................................................................................................... 53
3.2 Solution Gas-Water Ratio ....................................................................................... 53
3.2.1 McCain (1990) ................................................................................................. 53
3.3 Water FVF .............................................................................................................. 54
3.3.1 Meehan (1980) ................................................................................................. 54
3.3.2
McCain (1990) Bw above Pb.................................................................... 55
3.3.3 McCain (1990) Bw below Pb .......................................................................... 55
3.4 Water Viscosity....................................................................................................... 56
3.4.1 Meehan (1980) ................................................................................................. 56
3.4.2 McCain (1990) ................................................................................................ 56
3.4.3 Kestin, Khalifa, Correia (1981) ....................................................................... 57
3.5 Water Compressibility ............................................................................................ 59
3.5.1 Osif revised by Spivey, Valko and McCain, Unsaturated (P>Pb)................... 59
3.5.2 Meehan (1980) ................................................................................................. 59
3.5.3 McCain (1990) Saturated cw (P < Pb)............................................................. 60
Nomenclature.................................................................................................................... 61
Latin ...................................................................................................................... 61
Greek..................................................................................................................... 62
Subscripts and Superscripts .................................................................................. 62
References:.................................................................................................................... 63
Overview
Over 75 Black Oil, Gas and Water correlations have been incorporated into the PVT
Toolbox. Equation of State (EOS) Flash and Psat calculations based on PVTi routines has
also been incorporated.
Oil and Gas correlations were studied using a collective database from two main sources,
Dr. McCain and SRPC’s PVTz database.
Document Division:
This document represents all the correlation eqns used in the PVT Toolbox. The
correlation validation study and results are presented in a series of other documents that
can be found on the project website at :
<http://www.abingdon.geoquest.slb.com/data/sim-workflows/pvttoolbox/index.htm>.
This correlation eqns document is divided into 3 main sections:
Section numbers are broken down by Part # (ie Oil/Water/Gas); Correlation Type (FVF,
Rs etc); Correlation Name within correlation type section.
Correlation Selection:
Correlation selection criteria for this study were two fold. First, a global review of
correlations used in SLB applications was performed and the most common were
selected. Second, the best correlations tested by independent studies previously
performed by SLB’s Paul Guieze and world reknown PVT correlation author, Dr.
McCain were included in the study.
The objective of this project was to present the best correlations available in the industry
today. These correlations were coded into a dll that can be connected to any SLB
application and used as the SLB standard, improving consistency across OFS and
reducing support costs through centralized PVT expertise.
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Part 1: Oil Correlations
Part 2: Gas Correlations
Part 3: Water Correlations
Equation References:
1) Spivey, John and McCain, W.D.; “Recommended Correlations for Fluid Property
Estimation”, document based on correlation study done for SLB’s BorFlow software,
unpublished, 2003
2) Guieze, Paul and Segeral, G.; “Review of Bubble Point Pressure and Oil Formation
Volume Factor Correlations against Schlumberger PVT Database”, SLB internal
study, unpublished, 2002
3) OFM Online Manual, 2002
4) Eclipse Manual, 2002
Special Notations:
Some correlations are divided into above and below the bubble point pressure:
“Saturated” refers to the fluid below bubble point pressure (Pb)
“Unsaturated” refers to the fluid above bubble point pressure (Pb)
Standard Conditions: psc = 1 atm (14.7 psia, 101 325 Pa)
and
Tsc = 60 °F (15.56 °C)
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Previous tested has also been done on the correlations added in the toolbox. Under the
“Correlation in the PVT Toolbox section”, a * is added for McCain’s independent studied
correlations and a ** is added for Guieze studied correlations.
Correlations in the PVT Toolbox
1. Oil Correlations
1.1. Oil Density
1.1.1. *McCain & Hill
1.1.2. Standing
1.1.3. *Density above Psat
1.1.4. *McCain mass balance (FVF/ Density relationship)
1.3. Oil Pb
1.3.1. *Glaso
1.3.2. *&** Standing
1.3.3. *Laseter
1.3.4. *&** Vasquez
1.3.5. **Al-Marhoun
1.3.6. Petrosky (* & **-tested poor)
1.3.7. **Farshad
1.3.8. *Kartoatmodjo and Schmidt(**-tested poor)
1.3.9. *Valco and McCain
1.3.10. *Velarde, Basingame, McCain,
1.3.11. *Labedi
1.3.12. ** Al-Shammasi
1.4. Gas Oil Ratio, GOR (aka Rs)
1.4.1. Glaso
1.4.2. *Standing
1.4.3. Lasater
1.4.4. *Vasquez
1.4.5. Petrosky
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1.2. FVF-Bo
1.2.1. Glaso
1.2.2. *Standing
1.2.3. Vasquez
1.2.3.1. Separator Gas Corrected Gravity, Vasquez
1.2.4. Petrosky
1.2.5. Farshad
1.2.6. **Al-Marhoun (2)
1.2.7. **Kartoatmodjo and Schmidt
1.2.7.1. Separator Gas Corrected Gravity, Kartoatmodjo
1.2.8. *Casey and Cronquist
1.2.9. **Almedhaideb
1.2.10. **Al-Shammasi
1.2.11. **Elksharkawy & Alikhan
1.2.12. *McCain mass balance (FVF/ Density relationship)
1.2.13. *Oil Formation Volume Factor at Pressures Above the Pb
1.4.6. *Kartoatmodjo and Shmidt
1.4.7. *Casey-Cronquist
1.4.8. *Velarde, Basingame, McCain
Oil Viscosity
1.5. Dead Oil Viscosity
1.5.1. Beggs
1.5.2. Glaso
1.5.3. *Ng and Egbogah
1.5.4. *Beal
1.6. Live Oil Viscosity (Saturated)
1.6.1. Beggs
1.6.2. Khan
1.6.3. Chew and Connally
1.6.4. *Hanafy
1.8. Live Oil Compressibility (Saturated)
1.8.1. *McCain
1.8.2. *Spivey
1.9. Live Oil Compressibility (Unsaturated)
1.9.1. *Spivey, Valko, McCain
1.9.2. *Vasquez
1.9.3. Petrosky
1.9.4. Calhoun
1.9.5. Trube
2. Gas Correlations
2.1. Tc, Pc Critical Properties
2.1.1. known gas gravity
2.1.1.1.*Sutton
2.1.1.2.*Standing
2.1.1.3.*Piper, McCain, Corridor
2.1.2. known gas composition
2.1.2.1.*Piper, McCain, Corridor
2.1.2.2.*Stewart, Burkhardt and Voo
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1.7. Live Oil Viscosity (Unsaturated)
1.7.1. Khan
1.7.2. *Vasquez & Beggs
1.7.3. *Beal
1.7.4. *Hanafy
2.1.2.3.*Sutton
2.2. Z Factor
2.2.1. *Dranchuk
2.2.2. *Hall and Yarborough
2.3. Gas Viscosity
2.3.1. *Lee
2.3.2. *Carr
2.4. Gas Compressibility
2.4.1. *Dranchuk
2.4.2. *Hall and Yarborough
3. Water Correlations
3.1. Water Density
3.3. Water FVF
3.3.1. Meehan
3.3.2. McCain (P>Pb)
3.3.3. McCain (P<Pb)
3.4. Water Viscosity
3.4.1. Meehan
3.4.2. McCain
3.4.3. *Kestin, Khalifa, Correia
3.5. Water Compressibility
3.5.1. *Osif-revised Unsaturated
3.5.2. Meehan
3.5.3. *McCain Saturated
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3.2. Solution Gas Water Ratio
3.2.1. *McCain
Part 1-Oil Correlations
General Eqns and Knowledge:
Stock Tank Oil Gravity (γAPI):
The API gravity and the specific gravity of the stock tank oil are related by:
141.5
γ API ≡
− 131.5
γo
The units for API gravity are °API.
Specific Gravity of stock tank oil:
γ oil = ρ oil / ρ w ater
and ρwater = 1000 kg/m^3
Note: relative density of oil will be the same value as oil density when expressed in
g/cm^3 since it is divided by a value of 1 (ρwater = 1 g/cm^3)
 MWgas 
γg =
 where the MW of air is 28.9635 kg/m^3
 MWair 
There are four forms of γg used:
1. γg- If a correlation only denotes γg, take this as the gas SG at stnd conditions
(14.7 psi and 60F) (aka γgST-stock tank gas gravity)
2. γg sp (separator gas specific gravity)is the specific gravity of the gas from the
separator, referenced to air
3. γgwt.ave: the weighted average surface gas specific gravity, which is defined as the
specific gravity of the surface gases including both separator gas and stock-tank
vent gas
4. γg 100 psi (separator gas specific gravity for a specific separator pressure separator
gas specific gravity for a specific separator pressure, typically 100 psig)
Eqns for the different types of gas gravity can be found in the gas- part 2 general eqns
section.
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Specific Gravity of Gas
γg (reference to air): (a.k.a relative density of gas)
1.1. Oil Density Correlations
Four eqns were tested and added to the PVT Toolbox. These are:
1. McCain & Hill
2. Standing
3. Density above Psat
4. McCain mass balance (FVF/ Density relationship)
Note: The McCain mass balance is designed to predict either FVF or density when a
correlation is used to determine the other variable.
1.1.1 McCain & Hill (1995)
Note: reference taken from McCain document, pg 101-102
The McCain-Hill correlation for density requires an iterative procedure on the
pseudoliquid density.
Successive substitution is used in Eqs. below until successive trial values agree within
0.001:
2
2
ρ a = ao + a1γ g SP + a 2γ g SP ρ po + a3γ g SP ρ po + a 4 ρ po + a5 ρ po
ρ po =
Rs γ g SP + 4600γ STO
73.71 + Rs γ g SP ρ a
The pseudoliquid density is then used to calculate the reservoir liquid density from Eqs.
listed below:
16.181  p 
263  p 


∆ρ p =  0.167 + 0.0425 ρ po 
 − 0.01 0.299 + 0.0603 ρ po 

10
10

 1000 

 1000 
ρbs = ρ po + ∆ρ p
2

1.505 
0.0233 

0.938
0.475
∆ρT =  0.00302 + 0.951 (T − 60)
−  0.0216 − 0.0161ρ bs (T − 60)
10
ρ bs




ρ o = ρbs − ∆ρT
1.1.2 Standing (1951)
Note: reference taken from McCain document, pg 102
Standing’s density correlation is evaluated using Eqs. Below:
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The initial trial value is obtained from
ρ po = 52.8 − 0.01Rs
+ (94.75 − 33.93 log10 (γ API ))log10 (γ g SP )
10
Rs γ g SP + 4600γ STO
=
73.71 + Rs γ g SP ρ a
ρa =
ρ po
38.52
0.00326γ API
263  p 
16.181  p 


∆ρ p =  0.167 + 0.0425 ρ po 

 − 0.01 0.299 + 0.0603 ρ po 
10
10

 1000 

 1000 
ρ p = ρ po + ∆ρ p

152.4 
0.0622

∆ρT =  0.0133 + 2.45 (T − 60 ) −  0.0000081 − 0.0764 ρ p


ρp 
10


ρ o = ρ p − ∆ρT
2

2
(T − 60 )

1.1.3 McCain density mass balance
Note: reference taken from McCain document, pg 102
This equation is:
ρ STO + 0.01357 Rs γ g wtave
ρo =
Bo
1.1.4 Oil Density at Pressures Above Pb
Note: reference taken from McCain document, pg 102
For unsaturated oils (P>Pb), the oil density is calculated from the density at the bubblepoint using the average oil compressibility between the bubble point pressure and the
pressure of interest:
ρ o = ρ ob exp(co ( p − pb ))
where average compressibility is defined by the Spivey, Valkó, McCain (2003)
correlation found in sections 1.9.1.
Note: The accuracy of the density of oil depends on the accuracy of the correlation used
to estimate the average oil compressibility.
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The McCain mass balance density equation is used when the user chooses a formation
volume factor correlation.
1.2. Oil FVF (Bo)
1.2.1 Glaso (1980)
Note: reference taken from Paul Gueize p.13, cross referenced with Eclipse
[
]
Bo = 1 +10^ a1 + a2 logG − a3 log2 G G = Rs (γ g / γ o ) a 4+ a5 T
a1 = −6.58511, a2 = 2.91329, a3 = 0.27683, a4 = 0.526, a5 = 0.968
where:
Rs=the solution GOR, scf/STB
γg= the gas gravity (air=1.0)
γo=the oil specific gravity
T= temperature, F
1.2.2 Standing (1947)
Note: reference taken from McCain doc, pg. 103; slight variances in equations from
OFM, Pipesim and Eclipse
C N = Rs
γ g SP
γo
Schlumberger Private
Bo = 0.9759 + 0.00012 C N
1.2
+ 1.25 T f
where Bo=oil FVF, bbl/STB
Rs= soln GOR, scf/STB
T= temperature of the fluid, F
1.2.3 Vasquez and Beggs (1980)
Note: reference from Paul Guieze document pg 12, confirmed with Eclipse and OFM
documentation
[(
Bo = 1 + a1 Rs + a 2 γ oAPI / γ
100
)(T − 60)]+ a [R (γ
3
s
oAPI
/ γ 100 ) (T − 60)]
γ oAPI ≤ 30 a1 = 4.677 × 10−4 , a2 = 1.751× 10−5 , a3 = −1.8106 × 10−8
γ oAPI > 30 a1 = 4.67 × 10−4 , a2 = 1.1× 10−5 , a3 = 1.337 × 10−9
where:
Bo= oil FVF, bbl/STB
Rs= soln GOR, scf/STB
T= temperature of the fluid, F
γ100= corrected gas gravity, note: if sep.cond. aren’t known, then use the uncorrected gas
gravity (γg)
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1.2.3.1 Gas Corrected Gravity Eqn- Vasquez Beggs
[ (
where: γ 100 = γ g 1 + 5.912 x10 −5 γ API Ts ep log( Psep / 114.7
)]
γ100= gas gravity that would result from separator at 100 psig
Psep=actual separator pressure, psia
Tsep=actual separator temperature, F
γAPI= oil API gravity, API
1.2.4 Petrosky & Farshad (1993)
Note: reference taken from Paul Gueize p.15, cross referenced with Eclipse
[ (
Bo = a1 + a 2 Rs 3 γ g 4 / γ o
a
a
a5
)+ a
6
T a7
]
a8
a1 = 1.0113, a2 = 7.2046 × 10 −5 , a3 = 0.3738, a4 = 0.2914, a5 = 0.6265, a6 = 0.24626,
a7 = 0.5371, a8 = 3.0936
Schlumberger Private
where:
Rs=the solution GOR, scf/STB
γg= the gas gravity (air=1.0)
γo=the oil specific gravity
T= temperature, F
1.2.5 Farshad & Leblanc (1992)
Note: reference taken from Paul Gueize p.15
[
B o = 1 + 10 ^ a1 + a 2 log G + a 3 log 2 G
]
G = Rs 4 γ g
a
a5
γo
a6
+ a7 T
a1 = −2.6541, a2 = 0.5576, a3 = 0.3331, a4 = 0.5956, a5 = 0.2369, a6 = −1.3282, a7 = 0.0976
1.2.6 Al-Marhoun (2) (1992)
Note: reference taken from Paul Gueize p.16
Bo = 1 + a1 Rs + a2 Rs (γ g / γ o ) + a3 Rs (1 − γ o ) (T − 60 ) + a4 (T − 60 )
a1 = 0.177342 × 10 −3 , a2 = 0.220163 ×10 −3 , a3 = 4.292580 × 10 −6 , a4 = 0.528707 ×10 −3
where:
Rs=the solution GOR, scf/STB
γg= the gas gravity (air=1.0)
γo=the oil specific gravity
T= temperature, F
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1.2.7 Kartoatmodjo and Schmidt (1994)
Note: reference taken from Paul Gueize p.18
(
4
Bo = a1 + a 2 R s 3 γ ga100
/ γ oa5 + a 6 T
a
)
a7
a1 = 0.98496, a 2 = 0.0001, a 3 = 0.755, a 4 = 0.25, a 5 = 1.5, a 6 = 0.45, a 7 = 1.5
where :
1.2.7.1 Separator Gas Corrected Gravity, Kartoatmodjo
The Bo correlation is based on the separator gas specific gravity for separator pressure of
100 psig. If the separator conditions are known, the separator gas specific gravity is
corrected to a separator pressure of 100 psig, using Eq.:

 p sep  
0.4078
− 0.2466
 
γ g100 = γ g SP 1 + 0.1595γ API
Tsep
log10 

114
.
7



1.2.8 Casey and Cronquist (1992)
Note- reference taken from McCain, pg 103
The Casey-Cronquist formation volume factor correlation is evaluated with Eqs. Below:
pD =
p − 14.7
pb − 14.7
B1 = −1.6009 − 0.00073368γ API − 0.00058765γ API
2
B2 = 0.023155 + 0.00013137γ API − 0.0000085933γ API
2
B3 = 0.000047456 − 0.00000054827γ API + 0.0000000049953γ API
Boa = 1 +
2
(B + B T + B T )
2
1
2
3
100
2
3
Bob = C0 + C1Rsb + C2 Rsb + C3 Rsb Boa
(
)
BoD = D0 + D1 pD + D2 pD + D3 pD + D4 pD + D5 pD
Bo = Bob − (Bob − Boa )BoD
2
3
4
5
The coefficients for Eqs:.
C0 =
1.006933
D0 =
0.98949
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Note: If the separator conditions are not known, the separator gas specific gravity is used
with no correction.
C1 =
C2 =
C3 =
4.340923×10-4
6.960178×10-8
-1.088361×10-11
D1 =
D2 =
D3 =
D4 =
D5 =
-1.8061
4.4637
-9.6368
9.3994
-3.4122
Note that the coefficients in Eq. for r sum to 0.00132. Thus, the solution gas-oil ratio
calculated at the bubble point pressure will be 0.13% too low.
1.2.9 Almedhaideb (1997)
Note: reference taken from Paul Gueize p.17
Bo = a1 + a 2 Rs T / γ o
a1 = 1.122018, a 2 = 1.41e − 6
2
Bo = 1 + a1 [Rs (T − 60 )] + a2 (Rs / γ o ) + a3 [(T − 60 ) / γ o ] + a4 (Rs γ g / γ o )
a1 = 5.53 ×10−7 , a2 = 0.000181, a3 = 0.000449, a4 = 0.000206
1.2.11 Elksharkawy & Alikhan (1997)
Note: reference taken from Paul Gueize p.19
Bo = 1 + a1 Rs + a 2 (T − 60) + a3 Rs (T − 60)γ g / γ o
a1 = 40.428 × 10 −5 , a 2 = 63.802 × 10 −5 , a3 = 0.780 × 10 −6
1.2.12 McCain mass balance formation volume factor
Note- reference taken from McCain, pg 104
The McCain mass balance formation volume factor equation is used when the user
chooses a density correlation. This equation is:
ρ STO + 0.01357 Rsγ g wtave
Bo =
ρo
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1.2.10 Al-Shammasi (1999)
Note: reference taken from Paul Gueize p.18
1.2.13 Oil Formation Volume Factor at Pressures Above Pb
Note- reference taken from McCain, pg 104
For unsaturated oils, Bo is calculated from the bubble-point formation volume factor
using the average oil compressibility between the bubble point pressure and the pressure
of interest:
Bo = Bob exp(− co ( p − pb ))
where:
Average compressibility is defined by the Spivey, Valkó, McCain (2003), McCain pg.
105-106 or by the Vasquez-Beggs correlation pg. 106.
Note: The accuracy of Bo obtained depends on the accuracy of the correlation used to
estimate the average oil compressibility.
1.3 Bubble Point Pressure (Pb, aka Psat)
Note: For all Pb correlations, Rs is the total initial producing oil gas ratio, Rsb
Glasø correlated bubble point pressure as a function of weighted average surface gas
gravity rather than separator gas gravity. Glasø’s correlation is evaluated by:
pb = 10 −0.30218 x
2
+1.7447 x +1.7669
0.816
 Rsb 

 T 0.172
 γ g wt avg 

x=
0.989
γ API
1.3.2 Standing (1947)
Note: reference taken from Paul Gueize p.23, cross referenced with Eclipse p. 460
[
]
pb = a1 (Rs / γ g ) 2 ×10X − a5 X = a3T − a4γ oAPI
a
a1 = 18.2, a 2 = 0.83, a 3 = 0.00091, a 4 = 0.0125, a 5 = 1.4
pb= bubble point pressure, psia
Rsb=solution GOR at p≥pb, scf/STB
γg=gas gravity (air=1.0)
T=reservoir temperature, F
γAPI=stock tank oil gravity, API
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1.3.1 Glasø (1980)
Note- reference taken from McCain, pg 94
1.3.3 Laseter (1958)
Note- reference taken from McCain, pg 95-96
Rsb
379.5
yg =
350γ o
Rsb
+
379.5
Mo
where:
yg is the gas mole fraction
Mo is the effective molecular weight of the stock-tank oil. Lasater presented a graphical
correlation to estimate Mo from γAPI.
The bubble point pressure is then calculated:
T + 459.6
pb = p f
γ g wt avg
where:
pf is a correlating factor, and is calculated by linear interpolation from the table below:
Gas Mole
Fraction
Bubble Point
Pressure Factor
pf
yg
0.05
0.1
0.15
0.2
0.25
0.17
0.3
0.43
0.58
0.75
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Mo is calculated by linear interpolation from the table below:
Effective
Stock tank
Molecular
gravity
Weight
Mo
°API
15
486
20
440
25
384
30
331
35
281
40
234
45
184
50
161
55
142
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.94
1.19
1.47
1.74
2.1
2.7
3.29
3.8
4.3
4.9
5.7
6.7
1.3.4 Vazquez and Beggs (1980)
Note- reference taken from McCain, pg 97-98
The Vazquez-Beggs bubble point pressure correlation is based on the separator gas
specific gravity for separator pressure of 100 psig. If the separator conditions are known,
the separator gas specific gravity is corrected to a separator pressure of 100 psig, using:

 p sep  
 
γ g100 = γ g SP 1 + 5.912 × 10 −5 γ API Tsep log10 

114
.
7



Note: If the separator conditions are not known, the separator gas specific gravity is used
with no correction.
•
For oils having API gravity less than or equal to 30 °API use:
R
pb =  sb
 CN
where:
1
 1.0937


 25.7240γ API 
C N = 0.0362γ g100 exp

 T + 460 
•
For oils with API gravity greater than 30 °API use:
R
pb =  sb
 CN
1
 1.1870


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The Vazquez-Beggs bubble point pressure correlation is a rearrangement of the VazquezBeggs solution gas-oil ratio correlation. If the Vazquez-Beggs solution gas-oil ratio
correlation is used, the Vazquez-Beggs bubble point pressure correlation must also be
used for consistency.
where:
 23.9310γ API 
C N = 0.0178γ g100 exp

 T + 460 
1.3.5 Al-Marhoun (1988)
Note: reference taken from Paul Gueize p.24
pb = a1 Rs 2 γ g 3 γ o
a
a
a4
(T + 460)a
5
a1 = 5.38088 ×10 −3 , a2 = 0.715082, a3 = −1.877840, a4 = 3.143700 a5 = 1.326570
where:
Pb= bubble point pressure, psia
T= temperature,F
Rs=solution GOR, scf/STB
[(
pb = a1 Rs 2 / γ g
a
a3
)×10
X
]
a8
− a4 X = a5T a6 − a7γ oAPI
a1 = 112.727, a 2 = 0.5774, a3 = 0.8439, a 4 = 12.340, a5 = 4.561× 10 −5 , a6 = 1.3911,
a7 = 7.916 × 10 −4 , a8 = 1.5410
1.3.7 Farshad & Leblanc (1992)
Note: reference taken from Paul Gueize p.27
pb = a1 (Rs / γ g ) a2 × 10(a3T −a4γ oAPI )
a1 = 33.22, a2 = 0.8283, a3 = 0.000037, a4 = 0.0142
1.3.8. Kartoatmodjo and Schmidt (1994)
Note- reference taken from McCain, pg 96-97
The Kartoatmodjo-Schmidt bubble point pressure correlation is a rearrangement of the
Kartoatmodjo-Schmidt solution gas-oil ratio correlation. If the Kartoatmodjo-Schmidt
solution gas-oil ratio correlation is used, the Kartoatmodjo-Schmidt bubble point pressure
correlation must also be used for consistency.
The Kartoatmodjo-Schmidt bubble point pressure correlation is based on the separator
gas specific gravity for separator pressure of 100 psig. If the separator conditions are
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1.3.6 Petrosky and Farshad (1993)
Note: reference taken from Paul Gueize p.25 , cross ref with Eclipse
known, the separator gas specific gravity is corrected to a separator pressure of 100 psig,
using:

 p sep  
0.4078
− 0.2466
 
γ g100 = γ g SP 1 + 0.1595γ API
Tsep
log10 

114
.
7



If the separator conditions are not known, the separator gas specific gravity is used with
no correction.
•
For oils with API gravity less than or equal to 30 °API use:

Rsb
pb = 
 0.05958γ 100 0.7972 C
g
N

where:
C N = 10 x
x=
13.1405γ API
T + 460
For oils with API gravity greater than 30 °API use:

Rsb
pb = 
 0.03150γ g100 0.7587 C N

where:
C N = 10 x




1
1.0937
11.2895γ API
T + 460
1.3.9. Valkó & McCain (2003)
Note- reference taken from McCain, pg 93-94
The Valkó-McCain bubble point correlation is given by:
2
3
A = A0 + A1γ API + A2γ API + A3γ API
B = B0 + B1γ g SP + B2γ g SP + B3γ g SP
2
3
C = C 0 + C1T + C 2T 2 + C 3T 3
D = D0 + D1 ln (Rsb ) + D2 ln (Rsb ) + D3 ln (Rsb )
y = A+ B+C + D
pb = exp(E 0 + E1 y + E 2 y 2 )
2
3
where:
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•
x=
1
 1.0014



Coefficients for Valkó, McCain Bubble Point Pressure Correlation
A0 =1.27
B0 =4.51
C0 =-0.7835
D0 =-5.48
E0 =7.475
A2 =4.36×10-4
B2 =8.39
C2 =-1.22×10-5
D2 =0.281
E2 = 0.0075
A1 =-0.0449
B1 =-10.84
C1 =6.23×10-3
D1 =-0.0378
E1 =0.713
A3 =-4.76×10-6
B3 =-2.34
C3 =1.03×10-8
D3 =-0.0206
1.3.10 Velarde, Blasingame, McCain (1997)
Note- reference taken from McCain, pg 94
The Velarde, Blasingame, McCain correlation for bubble point pressure is:
x = 0.013098 T 0.282372 − 8.2 × 10 −6 γ API
(
pb = 1091.47 Rsb
0.081465
γ g SP
− 0.161488
2.176124
10 x − 0.740152
)
5.354891
Labedi’s correlation is a modified version of the Standing bubble point pressure
correlation. Labedi’s correlation is evaluated:
0.83
 R 
C pb =  sb  10 0.0091 T − 0.0125γ API
γ

 g SP 
0.9653
pb = 21.38 C pb
1.3.12 Al-Shammasi (1999)
Note- reference taken from Guieze, pg 30
a γ γ
2 o g
p = γ a1 e
b
o
 R (460 + T )γ 
 s
g 
a3
a1 = 5.527215, a2 = −1.841408, a3 = 0.783716
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1.3.11 Labedi (1990)
Note- reference taken from McCain, pg 95
1.4 Gas Oil Ratio (GOR, aka Rs)
1.4.1 Glaso (1980)
Note: Glaso did extremely poor while testing and was not included in toolbox.dll. Glaso’s
original paper did not include Rs and it is believed to be a rearrangement of the Pb
correlation. Reference taken from Eclipse, pg. 466- Eqn may be source of error and is
referenced below:
 γ 0.989 

Rs = γ g  API0.172  Pb *  1.2255
 TF


Where:
0.5
Pb * = 10 [2.8869−(14.1811−3.3093 log( pbc )) ]
Pb
CorrN 2 + CorrCO2 + CorrH 2 S
where:
CorrN 2 = 1 + 2.65x10 −4 γ API + 5.5 x10 −3 TF + 0.0391γ API − 0.8295 YN 2
[
[
+ 1.954 x10 −11 γ API
TF + 4.699γ API
4.699
CorrCO 2 = 1 + 693.8YCO 2TF
0.027
]
− 2.366 YN 2
]
2
−1.553
CorrH 2 S = 1 − (0.9035 + 0.0015γ API )YH 2 S + 0.019(45 − γ API )YH 2 S
where:
γg= the specific gravity of the soln gas
TF= the reservoir temperature, F
γAPI=the stock tank oil gravity=API
YN2= mole fraction of N2
YCO2= mole fraction of CO2
YH2S=mole fraction of H2S
1.4.2 Standing (1947)
Note: reference taken from OFM’s documentation, cross-referenced by Eclipse
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Pbc =


P
R =γ 
s
g
y

g
 18 x10
1.204





Where:
Rs= Solution GOR (scf/stb)
γg=gas specific gravity
yg =0.00091T-.0125γ , where γ is API gravity and yg= the mole fraction of gas
T= Reservior Temperature (F)
1.4.3 Vazquez-Beggs (1980)
Note- reference taken from McCain, pg 100
The Vazquez-Beggs bubble point pressure correlation is a rearrangement of the VazquezBeggs solution gas-oil ratio correlation. If the Vazquez-Beggs solution gas-oil ratio
correlation is used, the Vazquez-Beggs bubble point pressure correlation must also be
used for consistency.

 p sep  
 
γ g100 = γ g SP 1 + 5.912 × 10 −5 γ API Tsep log10 

114
.
7



If the separator conditions are not known, the separator gas specific gravity is used with
no correction.
• For oils having API gravity less than or equal to 30 °API use:
R s = C N p 1.0937
where:
 25.7240γ API 
C N = 0.0362γ g100 exp

 T + 460 
• For oils with API gravity greater than 30 °API use:
R s = C N p 1.1870
where:
 23.9310γ API 
C N = 0.0178γ g100 exp

 T + 460 
1.4.4 Lasater (1958)
Note: referenced from OFM’s documentation, crossed referenced by Eclipse
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The Vazquez-Beggs bubble point pressure correlation is based on the separator gas
specific gravity for separator pressure of 100 psig. If the separator conditions are known,
the separator gas specific gravity is corrected to a separator pressure of 100 psig.
Rs =
132,755γ o y g
M oe (1 − y g )
Where:
γo = specific gravity of oil
γg= Specific gravity of gas
Moe = effective molecular weight of stocktank oil
yg= mole fraction of gas in the system
T=Temperature, R
Where:
γAPI ≤ 40, Moe =630-10γAPI
γAPI >40, Moe =73110(γAPI)-1.562
(Pγg)/T < 3.29, yg= 0.359ln[(1.473 Pγg)/T +0.476]
(Pγg)/T ≥3.29, yg= [(0.121 Pγg)/T –0.236)]0.281
1.4.5 Petrosky and Farshad (1993)
Note: reference taken from Eclipse p.467
 Pb
 0.8439 x
Rs = 
+ 12.340 γ g
10
 112.727

1.73184
where:
X=(7.916x10-4 γAPI1.5410)-(4.561x10-5 T1.3911)
Pb=bubble point pressure, psia
T=temperature, F
1.4.6 Kartoatmodjo-Schmidt (1994)
Note- reference taken from McCain, pg 99-100
If the Kartoatmodjo-Schmidt solution gas-oil ratio correlation is used, the KartoatmodjoSchmidt bubble point pressure correlation must also be used for consistency.
The Kartoatmodjo-Schmidt solution gas-oil ratio correlation is based on the separator gas
specific gravity for separator pressure of 100 psig. If the separator conditions are known,
the separator gas specific gravity is corrected to a separator pressure of 100 psig, using:
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where P= pressure, psia
T= Temperature, R
yg= mole fraction of the gas

 p sep  
0.4078
− 0.2466
 
γ g100 = γ g SP 1 + 0.1595γ API
Tsep
log10 

114
.
7



If the separator conditions are not known, the separator gas specific gravity is used with
no correction.
• For oils with API gravity less than or equal to 30 °API
13.1405γ API
x=
T + 460
C N = 10 x
Rs = 0.05958 C N γ g100
0.7972
p 1.0014
• For oils with API gravity greater than 30 °API:
11.2895γ API
x=
T + 460
C N = 10 x
Rs = 0.03150 C N γ g100
0.7587
p 1.0937
Rs = (1 − r )Rsb
where
2
3
4
5
r = 0.99632 - 1.3078 p D + 1.7964 p D - 4.1124 p D + 4.3031 p D - 1.6743 p D
p − 14.7
pD =
pb − 14.7
1.4.8 Velarde, Basingame, McCain (1999)
Note- reference taken from McCain, pg 98-99
A
A A
A
A = A0γ g SP 1 γ API 2 T f 3 ( pb − 14.7 ) 4
B B
B
B = B0γ g SP B1 γ API 2 T f 3 ( pb − 14.7 ) 4
C
C C
C
C = C 0γ g SP 1γ API 2 T f 3 ( pb − 14.7 ) 4
pr =
p − 14.7
pb − 14.7
Rsr = Ap r + (1 − A) p r
Rs = Rsr Rsb
B
C
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1.4.7 Casey-Cronquist (1992)
Note- reference taken from McCain, pg 99
A0 =
A1 =
A2 =
A3 =
A4 =
9.73×10-7
1.672608
0.929870
0.247235
1.056052
B0 =
B1 =
B2 =
B3 =
B4 =
0.022339
-1.004750
0.337711
0.132795
0.302065
C0 =
C1 =
C2 =
C3 =
C4 =
0.725167
-1.485480
-0.164741
-0.091330
0.047094
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1.5 Dead Oil Viscosity (µod)
1.5.1 Beggs and Robinson (1975)
Note: Reference taken from Eclipse, pg 456
µ od = 10 x − 1
where:
x = T −1.168 exp(6.9824 − .04658γ API )
µod=the dead oil viscosity, cp
γAPI=stock tank oil API gravity, API
T= Temperature, F
1.5.2 Glaso (1980)
Note: Reference taken from Eclipse, pg 457
µ od = 3.141x1010 (T − 460) −3.444 (log γ API ) a
a = 10.313(log(T − 460)) − 36.44
T= temperature in F
γAPI= stock tank oil gravity, API
Rs= the solution GOR, scf/STB
1.5.3 Ng and Egbogah (1983)
Note: OFM reference





1.8653 − 0.025086γ
− 0.5644 log(T )  

API
 
 10 
= 10
µ
 −1
od




where:
µod= dead oil viscosity, cp
γAPI=oil API gravity, API
T=temperature, F
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Where:
1.5.4 Beal (1946)
Note: Reference taken from OFM document


a

1.8 x10 7  360 
µ
=  0.32 +


od 
4.53  T + 200 
γ
API


where:








8.33 . 
0.43 +


γ

API

a = 10
γAPI=oil API gravity, API
T=temperature, F
1.6 Saturated Oil Viscosity (µosat)
µ o = Aµ od
B
Where:
A = 10.715( Rs + 100) −0.515
B = 5.44( Rs + 150)
−0.338
µod=dead oil viscosity, cp- use Beggs dead oil correlation above
Rs= solution GOR, scf/stb
1.6.2 Khan (1987)
Note: Reference taken from Eclipse pg. 457
 p 
µ o = µ ob  
 pb 
µ ob =
−.0.14
0.09γ g
1
−4
e (− 2.5 x10 )( p − pb )
0.5
Rs 3θ r (1 − γ o )
4.5
3
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1.6.1 Beggs and Robinson (1975)
Note: Reference taken from Eclipse Pg. 456
where:
µob=the viscosity at the bubble point, cp
Rs= solution gas ratio, scf/STB
θr=T/460
T= temperature, R
γo=the specific gravity of oil
γg=the specific gravity of the solution gas
pb= the bubble point pressure, psia
p=pressure of interest,psia
1.6.3 Chew and Connally (1959)
Note: Reference taken from OFM
µ o = Aµ od
b
where:
b=




 


 
0.68
0.25
0.062
+ 1.1 −3 + 3.74 −3
−5
10 10 Rs 10 10 Rs 10 10 Rs
8.62
where:
µod=dead oil viscosity, cp- Use Beal dead oil correlation (McCain, pg 107 or from section
above)
Rs= solution GOR, scf/stb
1.6.4 Hanafy et al (1997)
Note: Reference taken from McCain document pg 108
The Hanafy correlation for oil viscosity at pressures below or above the bubble point is
given by:
3
µ o = exp 7.296 ρ o − 3.095 ,
where the oil density is in g/cm3.
(
)
Density can be calculated below the bubble point by using the McCain & Hill or
Standing Density correlations (found in the Density correlations section of this
document).
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A = 10
Rs  2.2 x10 − 7  Rs −  7.4 x10 − 4  
By correlating on density, Hanafy was able to use a single equation to represent both
saturated and unsaturated oils.
1.7 UnSaturated Oil Viscosity (µounsat)
1.7.1 Khan (1987)
Note: Reference taken from Eclipse manual, pg. 459
µ o = µ ob e 9.6 x10
−5
( p − pb )
Can use the Khan saturated eqn to determine oil viscosity at Pb from Saturated eqn
0.5
0.09γ g
µ ob =
1
4.5
3
Rsb 3θ r (1 − γ o )
where:
1.7.2 Vasquez & Beggs (1980)
Note: Reference taken from McCain pg 108, cross referenced with Eclipse pg. 458
Note: The Vasquez & Beggs correlation has been mislabeled as the Beggs & Robinson
correlation in some of the SLB applications. Please note that the Vasquez and Beggs
correlation is a derivation of the sat viscosity Beggs & Robinson correlation.
P
µ o = µ ob  
 Pb 
m
where:
[
(
)]
m = 2.6 P1.187 exp − 11.513 − 8.98 x10 −5 P
and viscosity at Pb can be calculated using the Beggs and Robinson Saturated eqn
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µob=the viscosity at the bubble point, cp
Rsb= solution gas ratio, scf/STB
θr=T/460
T= temperature, R
γo=the specific gravity of oil
γg=the specific gravity of the solution gas
pb= the bubble point pressure, psia
p=pressure of interest,psia
µ ob = Aµ od
B
Where:
A = 10.715( Rs + 100) −0.515
B = 5.44( Rs + 150)
−0.338
and
µod=dead oil viscosity, cp- use Beggs dead oil correlation above
µob= oil viscosity at bubble point pressure, cp- use Beggs saturated correlation as
described above
P=pressure, psi
Pb=bubble point pressure, psia
1.7.3 Beal (1946)
Note: Reference taken from McCain pg 108
(
)
and viscosity at Pb can be calculated using the Beggs and Robinson Saturated eqn
µ ob = Aµ od
B
Where:
A = 10.715( Rs + 100) −0.515
B = 5.44( Rs + 150)
−0.338
and
µod=dead oil viscosity, cp- use Beggs dead oil correlation above
µob= oil viscosity at bubble point pressure, cp- use Beggs saturated correlation as
described above
P=pressure, psi
Pb=bubble point pressure, psia
1.7.4 Hanafy et al (1997)
Note: Reference taken from McCain pg 108
The Hanafy correlation for oil viscosity at pressures below or above the bubble point is
given by:
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The Beal correlation for oil viscosity at pressures above the bubble point is given by:
1.6
0.56
µ o = µ ob + 0.001 0.024µ ob + 0.038µ ob ( p − pb )
(
)
µ o = exp 7.296 ρ o − 3.095
where the oil density is in g/cm3.
3
For Density above Pb, the Density above bubble point correlation must be used. The
inputs for this correlation require ρob and coave. For both of these inputs, a correlation can
be used (ie, McCain & Hill for ρob and Vasquez and Beggs for coave.)
By correlating on density, Hanafy was able to use a single equation to represent both
saturated and unsaturated oils.
1.8 Saturated Oil Compressibility (cosat)
1.8.1 McCain, Rollins, and Villena (1988)
Referenced by OFM document, cross ref.d by McCain pg 189
For Rsb= known and Pb=known
For Rsb= known and Pb=unknown
c o = exp{[− 7.633 − 1.497 ln(P ) + 1.115 ln(T ) + 0.533 ln(γ API ) + 0.184 ln(Rsb )]}
For Rsb= unknown and Pb=unknown
[
]
c o = exp{ − 7.114 − 1.394 ln(P ) + 0.981ln(T ) + 0.770 ln(γ API ) + 0.446 ln(γ g ) }
where:
co= isothermal compressibility, psi-1
Rsb= solution gas-oil ratio at bubble point pressure, scf/stb
γg=weighted average of separator gas and stock tank gas specific gravities
T= temperature, R
1.8.2 Spivey, Valkó, McCain (2003)
Note: Reference taken from McCain document, pg 104
Spivey, Valkó, and McCain proposed to calculate compressibility below the bubble point
using the following equation:
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co = exp{[− 7.573 − 1.450 ln (P ) − 0.383 ln (Pb ) + 1402 ln (T ) + 0.256 ln (γ API ) + 0.449 ln (Rsb )]}
co = −
1
Bo
 ∂Bo

 ∂p
 ∂R

 − B g  s
 ∂p
T
 
 
 T 
The oil formation volume factor(Bo) and solution gas oil ratio (Rs) is calculated using a
selected correlation; the gas formation volume factor is calculated using:
Bg =
p sc zT
Tsc p
where z is calculated using the z and Tc, Pc correlations.
The derivatives are evaluated numerically using a central difference formula.
Please note that the Spivey correlation is heavily dependent on the Rs, Bo correlations.
Reduce errors by choosing the best Rs and Bo correlations. McCain’s independent study
shows the ranges of error for different Rs, Bo correlation inputs in Table 40. The Rs
correlation referenced is used to determine the Rs used in the Bo correlation if it is not
given as experimental data.
1.9.1 Spivey, Valkó, McCain (2003)
Note: Reference taken from McCain document, pg 105
The Spivey, Valkó, and McCain correlation for compressibility of unsaturated oils is
given by Eqs.:
A = A0 + A1 ln (γ API ) + A2 ln (γ API ) + A3 ln (γ API )
2
3
B = B0 + B1 ln (γ g SP ) + B2 ln (γ g SP ) + B3 ln (γ g SP )
2
3
C = C 0 + C1 ln ( pb ) + C 2 ln ( pb ) + C 3 ln ( pb )
2
3
2
 p 
 p 
 p
D = D0 + D1 ln  + D2 ln  + D3 ln
 pb 
 pb 
 pb
2
3
E = E0 + E1 ln (Rsb ) + E 2 ln (Rsb ) + E3 ln (Rsb )



3
F = F0 + F1 ln (T ) + F2 ln (T ) + F3 ln (T )
y = A+ B+C + D+ E + F
2
3
Finally:
co = 11.84 + 4.8 y + 1.5 y 2 + 0.6 y 3
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1.9 UnSaturated Oil Compressibility (counsat)
The coefficients for Eqs:
A0 =
B0 =
C0 =
D0 =
E0 =
D0 =
-13.25
-0.0718
17.6
0.396
-6.58
-31.0
A1 =
B1 =
C1 =
D1 =
E1 =
D1 =
13.75
-0.0882
-6.192
-0.915
2.28
17.78
A2 =
B2 =
C2 =
D2 =
E2 =
D2 =
-4.8
0.0422
0.848
0.379
-0.449
-3.742
A3 =
B3 =
C3 =
D3 =
E3 =
D3 =
0.556
-2.0
-0.0447
-0.0653
0.0406
0.282
Eq. co gives the average compressibility needed in the equations for calculating density
and formation volume factor at pressures above the bubble point pressure. The
compressibility at pressure p is given by:
co = co +
∂co
( p − pb )
∂p
(
)
Note: Compressibility units are in microsips.
Where: 1 sip = 1/psi = 0.000145037957 1/Pa
1 microsip = 0.000145037957E-6 1/Pa = 1.45037957E-10 1/MPa
1.9.2 Vasquez and Beggs (1980)
Reference taken from OFM, cross-referenced by McCain, pg 106
co =
5 Rsb + 17.2T − 1180γ g + 12.61γ API − 1433
Px10 5
where:
coave= average isothermal compressibility, psi-1
Rsb= solution gas-oil ratio at bubble point pressure, scf/stb
γg=average gas specific gravity (air=1)
γAPI=stock tank oil API gravity, API
T= temperature, F
P=pressure, psia
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where the derivative of the average compressibility with respect to pressure is given by:
2
∂c o
 p 
 p  
4.8 + 3.0 y + 1.8 y 2 
 + 3D 3 ln

D + 2 D 2 ln
=

p  
 1
p
p
∂p
 b
 b 

1.9.3 Petrosky and Farshad
Note: Reference taken from OFM
0.3272T 0.6729 P − 0.5906
c = 1.705 x10 − 7 Rs 0.69357γ 0.1885γ
o
g
API
where:
co= isothermal compressibility, psi-1
Rs= solution GOR, scf/stb
γg=average gas specific gravity (air=1)
γAPI=oil API gravity, API
T= temperature, F
P=pressure, psia
1.9.4 Calhoun (1947)
Note: Reference taken from Cade cou.for code document- OMNIworks
If GOB ≥0.65
co = 5.17 x10 −5 − 5.6 x10 −5 GOB
If 0.65 < GOB>0.5
co = 8.25 x10 −5 − 1.4375 x10 −4 GOB + 6.25 x10 −5 GOB 2
If GOB≤0.5:
co = 6.65625 *10 −5 − 8.0625 x10 −5 GOB
where:
co= isothermal compressibility, psi-1
Rs= solution GOR, scf/stb
γg100 =corr gas specific gravity (air=1)- use Vasquez correction
γoil =oil specificgravity
Bo= oil FVF, rb/stb
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GOB = (γ oil + 0.000218γ g100 psia Rs ) / Bo
1.9.5 Trube (1957)- not included
The Trube correlation did extremely poor when tested and was removed from the
toolbox. The Trube correlation is based on graphical correlations and the eqns below
were taken from the Cade software –cou.for code document- OMNIworks
GO60 = γoil + 0.00046(T − 60)
0.83
 Rs 

Pb60 Pb1 = 

γ
 g100 psia 
1.76875
XX = −1.58915 +
GO60
YY = 0.00091T − 0.125γ API
( Pb60 Pb1 x10 XX − 1.4)
Pb60 Pb1 x10 YY − 1.4
Pb60 = Pb * Pb60 Pb2
Pb60 Pb2 =
(
)
Note: If Pb isn't given, use Standing’s Psat correlation.
Evaluate Pc
If GO60 ≤0.61
Pc = 722.56919983418 − 283.226962804 xGO 60
If GO60 ≥ 0.89:
Pc = 2771.71011634246 − 2838.08872177941xGO 60
If 0.80<GO60>0.61:
Pc = 1548 .0665856385 − 4786 . 3958177941 xGO 60 + 8097 . 4062132680 8 xGO 60 2
− 4808 .7037100294 8 xGO 60 3
If 0.89<GO60>0.80:
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Where:
co= isothermal compressibility, psi-1
GO60=Specific gravity of oil at 60 F
Rs= solution GOR, scf/stb
Pb60=Bubble point pressure at 60F
γg100 =corr gas specific gravity (air=1)- use Vasquez correction
γoil =oil specificgravity
γoAPI=oil API Gravity
T= temperature, F
P=pressure, psia
Pc = −31283.2871780454 + 108152.671717126 xGO60 − 120383.434508582 xGo60 2
+ 43447.2139597765 xGO60 3
To determine Tc, review the PTC.FOR cade software code.
Note: Fig 4 of Sutton (1984) from Trube (1957) to evaluate the pseudo critical
temperature of the reservoir fluid.
To determine the Cr: review the CRR.FOR Cade software code in OMNIWORKS.
Evaluate Reduced Pc, Tc and oil compressibility:
Tr = (T + 459.67) / Tc
Pr = P / Pc
co = cr / Pc
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Part 2-Gas Correlations
General Eqns and Knowledge
Stock-Tank Gas-Oil Ratio (Rst)
The Valkó-McCain correlation for stock-tank gas-oil ratio, when separator conditions are
known, is given:
2
A = A0 + A1 ln ( p SP ) + A2 ln ( p SP )
B = B0 + B1 ln (TSP ) + B2 ln (TSP )
C = C 0 + C1γ API + C 2γ API
2
2
z = A+ B+C
(
R ST = exp 3.955 + 0.83 z − 0.024 z 2 + 0.075 z 3
)
A0 =
B0 =
C0 =
-8.005
1.224
-1.587
A1 =
B1 =
C1 =
2.7
-0.5
-2
4.41×10
A2 =
B2 =
C2 =
-0.161
0
-5
-2.29×10
Solution Gas Oil Ratio at Pb (Rsb)
• When separator conditions are known, the solution gas-oil ratio is estimated by:
Rsb = RSP + RST
where:
Rsp is the gas oil ratio at separator conditions
Rst is stock tank gas oil ratio
•
When separator conditions are unknown use eqn below to estimate the solution
gas-oil ratio:
Rsb = 1.1618RSP
Weighted Gas Gravity (γgwt.ave):
γ g wtave =
γ gSP RSP + γ gST RST
RSP + RST
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Coefficients for Valkó, McCain Stock-Tank Gas-Oil Ratio Correlation
Stock-Tank Gas Gravity (γgST)
•
The Valkó-McCain correlation for stock-tank gas gravity, when separator
conditions are known, is given:
A = A0 + A1 ln ( p SP ) + A2 ln ( p SP ) + A3 ln ( p SP ) + A4 ln ( p SP )
2
3
B = B0 + B1 ln (RSP ) + B2 ln (RSP ) + B3 ln (RSP ) + B4 ln (RSP )
2
3
C = C 0 + C1γ API + C 2γ API + C 3γ API + C 4γ API
2
3
3
E = E0 + E1 TSP + E 2 TSP + E3 TSP + E 4 TSP
2
3
4
4
D = D0 + D1γ g SP + D2γ g SP + D3γ g SP + D4γ g SP
2
4
4
4
z = A+ B+C + D+ E
•
When separator conditions are not known, the weighted average gas gravity of the
surface gases is estimated with Eq:
γ g = 1.066γ g SP
Gas density (ρg)
Gas densities are calculated by:
pM
ρg =
zRT
If a value of 10.732 psia cuft/lbmole is used for the universal gas constant, R, then
pressure should be in psia, temperature should be in oR.
The molecular weight of the gas can be calculated as
γg
Ma =
28.9625
The resulting density will be in lb/cuft.
Gas Formation Volume Factor (Bg)
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γ g ST = 1.219 + 0.198 z + 0.0845 z 2 + 0.03z 3 + 0.003z 4
Gas formation volume factor is defined as the volume of gas at reservoir temperature and
pressure required to produce one standard cubic foot of gas at the surface. The equation
for gas formation volume factor is derived using the real gas equation:
p zT
B g = sc
Tsc p
Z factor
Standing and Katz proposed a graphical correlation of gas z-factors plotted against
pseudoreduced pressures and pseudoreduced temperatures. The graphical correlations for
pseudocritical temperature, pseudocritical pressure, and z-factor must be replaced by
equations or tables.
Estimating z-factors is a three-step procedure:
1. Tc and Pc correlations are used
2. Pr and Tr are calculated
3. Z correlation is used
Note: These pseudocritical properties do not in any way reflect the true critical pressures
and critical temperatures of the gas mixture; they are simply parameters used in the zfactor correlation.
Gas component properties used in Tc, Pc correlations
Component Tc (R) pc (psia)
MW (g/mol) y min
C1
343.00 666.4
16.043
0.19
C2
549.59 706.5
30.07
0.02
C3
665.73 616.0
44.097
0.0
iC4
734.13 527.9
58.123
0.0
nC4
765.29 550.6
58.123
0.0
iC5
828.77 490.4
72.15
0.0
nC5
845.47 488.6
72.15
0.0
C6
913.27 436.9
86.177
0.0
C7+
972.37 396.8
100.204
0.0
y max
0.95
0.19
0.13
0.03
0.06
0.03
0.04
0.05
0.128
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These pseudoreduced properties are defined as
p
p pr ≡
p pc
T
T pr ≡
T pc
where absolute values of pressures and temperatures are used.
2.1.1 Calculating Tc, Pc from known gas gravity
2.1.1.1 Sutton (1985)
Note: Reference taken from McCain pg 84-85
Calculate the gas specific gravity of the hydrocarbon fraction of the gas

∑ y i MWi 


i = H 2 S ,CO2 ; N 2
γ g −

28.9625 


γ
=
gHC
y HC
where
y HC = 1 −
∑y
i
i = H 2 S ;CO2 ; N 2
T pc = 169.2 + 349.5γ g − 74.0γ g
2
where:
Ppc= pseudocritical pressure, psia
Tpc=pseudocritical temperature, R
γg=average specific gas gravity (air=1)
Calculate the mole-fraction weighted average critical temperature and pressure as:
T pcm = y HC T pcHC +
∑ yiT pci
i = H 2 S ;CO2 ; N 2
Ppcm = y HC PpcHC +
∑y P
i pci
i = H 2 S ;CO2 ; N 2
Apply the Wichert-Aziz sour gas correction to obtain the pseudocrital temperature and
pressure for the gas
{(
ε = 120 y CO2 + y H 2 S
)
0.9
(
− y CO2 + y H 2 S
) }+ 15{y
1.6
0.5
CO2
− y H 2S
4
}
T pc = T pcm − ε
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Calculate the pseudocritical temperature and pressure for the hydrocarbon fraction:
2
Ppc = 756.8 − 131.0γ g − 3.6γ g


T pcm − ε
Ppc = Ppcm 

 T pcm + y H 2 S (1 − y H 2 S )ε 
2.1.1.2. Standing (1977)
Note: Reference taken from McCain pg 83-84
Dry Gas Equations
Ppc = 677 + 15.0γ g − 37.5γ g
T pc = 168 + 325γ g − 12.5γ g
2
2
Wet Gas Equations
2
Ppc = 706 − 51.7γ g − 11.1γ g
2
where:
Ppc= pseudocritical pressure, psia
Tpc=pseudocritical temperature, R
γg=average specific gas gravity (air=1)
Calculate the gas specific gravity of the hydrocarbon fraction of the gas

∑ y i MWi 


i = H 2 S ,CO2 ; N 2
γ g −

28.9625 


γ
=
gHC
y HC
where
y HC = 1 −
∑y
i
i = H 2 S ;CO2 ; N 2
Calculate the pseudocritical temperature and pressure for the hydrocarbon fraction:
Ppc = 706 − 51.7γ g − 11.1γ g
T pc = 187 + 330γ g − 71.5γ g
2
2
Calculate the mole-fraction weighted average critical temperature and pressure as:
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T pc = 187 + 330γ g − 71.5γ g
T pcm = y HC T pcHC +
Ppcm = y HC PpcHC +
∑yT
i pci
i = H 2 S ;CO2 ; N 2
∑y P
i pci
i = H 2 S ;CO2 ; N 2
Apply the Wichert-Aziz sour gas correction to obtain the pseudocrital temperature and
pressure for the gas
{(
ε = 120 y CO2 + y H 2 S
)
0.9
(
− y CO2 + y H 2 S
) }+ 15{y
1.6
0.5
CO2
− y H 2S
4
}
T pc = T pcm − ε


T pcm − ε
Ppc = Ppcm 

 T pcm + y H 2 S (1 − y H 2 S )ε 
Tpc =
K2
J
p pc =
Tpc
Schlumberger Private
2.1.1.3 Piper, McCain, Corredor (1993)
Note: Reference taken from McCain pg 83
J
where the Stewart, Burkhard, Voo parameters J and K are:
3
T
J = α o + ∑ α i y i  c
i =1
 pc

 + α 4γ g + α 5γ g2
i
3
 T 
K = β o + ∑ β i yi  c  + β 4γ g + β 5γ g2
 p 
i =1
 c i
{
}
where yi ∈ yH 2 S , yCO2 , y N 2 and the coefficients α i and β i are given in the table below:
i
0
1
2
3
αi
1.1582E-01
-4.5820E-01
-9.0348E-01
-6.6026E-01
βi
3.8216E+00
-6.5340E-02
-4.2113E-01
-9.1249E-01
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4
5
7.0729E-01 1.7438E+01
-9.9397E-02 -3.2191E+00
2.1.2 Calculating Tc, Pc from known gas composition:
2.1.2.1 Piper, McCain, Corredor (1993)
Note: Reference taken from McCain pg 85
Tpc =
K2
J
p pc =
Tpc
J
3
T
J = α 0 + ∑ α i y i  c
i =1
 pc
8

T
 + α 4 ∑ y j  c
j =1
i
 pc
(
8


 + β 4 ∑ y j  Tc

 p
j =1
c
i

)
2

 + β 6 yC M C + β 7 y C M C
7+
7+
7+
7+

j
(
)
2
where:
αi
5.2073E-02
1.0160E+00
8.6961E-01
7.2646E-01
8.5101E-01
2.0818E-02
-1.506E-04
i
0
1
2
3
4
6
7
βi
-3.9741E-01
1.0503E+00
9.6592E-01
7.8569E-01
9.8211E-01
4.5536E-01
-3.7684E-03
yi=mole fraction of sour gas components, N2, H2S, CO2
yj= mole fraction of C1, C2,C3, iC4, nC4, iC5, nC5, C6
yC7+= mole fraction of C7+
MC7+=MW of C7+
2.1.2.2 Stewart, Burkhardt, and Voo (1959)
Note: Reference taken from McCain pg 86-87
1. The boiling point of the C7+ fraction is estimated from a correlation by Whitson:
(
TbC7 + = 4.5579M C 7 +
0.15178
γ C7 +
)
0.15427 3
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3
 T
K = β 0 + ∑ β i yi  c
 p
i =1
c


 + α 6 y C7 + M C7 + + α 7 y C7 + M C7 +
j
where:
MC7+=MW of C7+
γC7+=relative density of C7+ (relative to water)
2. Lee-Kessler equations are used to estimate the pseudocritical temperature and pressure
of the C7+ fraction:
10 5
Tc C7 + = 341.7 + 811γ C7 + + 0.4244 + 0.1174γ C7 + Tb C7 + + 0.4669 − 3.2623γ C7 +
Tb C7 +
(
)
(
)

0.0566 
2.2898 0.11857  10 −3
pc C7 + = exp 8.3634 −
− 0.24244 +
+
2

γ C7 +
γ
γ C7 +  Tb C7 +

C
7+


3.648 0.47227  10 −7 
1.6977  10 −10 

+ 1.4685 +
+
−
0
.
42019
+
2
2 
3

 Tb C 2 
γ
γ
γ
T
C
C
C
b
C
7+
7+
7+

 7+

 7 + 
where:
TbC7+= boiling point of heptanes plus fraction, R
2
 T 
 2
 + ∑ y i  c  


 i 3  i  p c  i 
 T 
1
K = ∑ yi  c 
3 i  p c 
i
4. the mole-fraction weighted pseudocritical temperature and pressure are obtained from:
K2
T pcm =
J
T pcm
p pcm =
J
5. Wichert-Aziz sour gas correction is applied to obtain the pseudocritical temperature
and pressure for the gas.
T
1
J = ∑ y i  c
3 i  pc
{(
ε = 120 y CO2 + y H 2 S
)
0.9
(
− y CO2 + y H 2 S
) }+ 15{y
1.6
0.5
CO2
− y H 2S
4
}
T pc = T pcm − ε


T pcm − ε
p pc = p pcm 

 T pcm + y H 2 S 1 − y H 2 S ε 
(
)
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3. parameters J and K are evaluated using where the sums are taken over all components
of the gas:
2.1.2.3 Sutton (1985)
Note: Reference taken from McCain pg 86-87
1. the boiling point of the C7+ fraction is estimated from Whitson’s correlationError!
Bookmark not defined.,
(
)
0.15427 3
TbC7 + = 4.5579M C 7 +
γ C7 +
2. estimate the pseudocritical temperature and pressure of the C7+ fraction.
0.15178
(
)
(
Tc C7 + = 341.7 + 811γ C7 + + 0.4244 + 0.1174γ C7 + Tb C7 + + 0.4669 − 3.2623γ C7 +
)T10
5
b C7 +

0.0566 
2.2898 0.11857  10 −3
− 0.24244 +
+
pc C7 + = exp 8.3634 −
2

γ C7 +
γ
γ C7 +  Tb C7 +

C
+
7


3.648 0.47227  10 −7 
1.6977  10 −10 


+ 1.4685 +
+
− 0.42019 +
3
2
2
2 



γ
γ
T
γ
T
C7 +
C7 +
C7 +

 b C7 +

 b C7 + 
3. Parameters J and K are then evaluated :
2
7+
Schlumberger Private
 T 
 2
 + ∑ y i  c  


 i 3  i  p c  i 
 T 
1
K = ∑ yi  c 
3 i  p c 
i
4. apply an adjustment factor to the parameters J and K:
J′ = J −εJ
K′ = K −εK
where εJ and εK are evaluated from:
1   T 
2   T 
FJ =  y c  +  y 2  c 
3   p c  C
3   p c  C
T
1
J = ∑ y i  c
3 i  pc
7+
ε J = 0.6081FJ + 1.1325 FJ − 14.004 FJ y C7 + + 64.434 FJ y C7 +
2
2
 T 
2
3
ε K =  c  0.3129 y C7 + − 4.8156 y C7 + + 27.3751 yC7 +
 p 
c C

7+
5. the mole-fraction weighted pseudocritical temperature and pressure are obtained from:
K ′2
T pcm =
J′
T pcm
p pcm =
J′
6. the Wichert-Aziz sour gas correction is applied to obtain the pseudocritical
temperature and pressure for the gas.
0.9
1.6
0.5
4
ε = 120 y CO2 + y H 2 S
− y CO2 + y H 2 S
+ 15 y CO2 − y H 2 S
[
{(
]
)
(
) }
{
}
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T pc = T pcm − ε


T pcm − ε
p pc = p pcm 

 T pcm + y H 2 S 1 − y H 2 S ε 
(
)
2.2 Calculating Z Factor
Z factor’s main inputs are Tr and Pr. These pseudoreduced properties are defined as:
pr ≡
Tr ≡
p
p pc
T
T pc
2.2.1 Dranchuk (1975)
Note: Reference taken from McCain, p 80.
Schlumberger Private
F (z ) = 0
 

A
A 
A
A  2
A
A
F ( z ) = z − 1 +  A1 + 2 + 33 + 44 + 55  ρ r +  A6 + 7 + 82  ρ r
Tr Tr
Tr Tr 
Tr
Tr 
 

2

 A7 A8  5
2 ρr
2 


− A9 
+ 2  ρ r + A10 1 + A11 ρ r
exp
−
ρ
A

11
r
3
Tr

 Tr Tr 
(
)
(
)
the reduced density ρ r is given by
p
ρ r = 0.27 r
zTr
and the coefficients
2


A7 A8  ρ r
A2 A3 A4 A5  ρ r
dF




= 1 +  A1 +
+
+
+
+ 2 A6 +
+
Tr Tr 3 Tr 4 Tr 5  z
Tr Tr 2  z
dz


(
) (
2
5
A
A ρ
A ρ
2
2
4
2
− 5 A9  7 + 82  r + 2 10 3 r 1 + A11 ρ r − A11 ρ r exp − A11 ρ r
Tr z
 Tr Tr  z
)

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2.2.2 Hall and Yarborough (1973)
Note: Reference taken from McCain, p 79.
z=
0.06125 p pr t
y
e −1.2(1−t )
2
where t is defined as
1
t≡
T pr
and y is the solution of
F (y) = 0
where F is given by
F ( y ) = −0.06125 p pr te −1.2(1−t ) +
2
(
)
)
+ 90.7t − 242.2t 2 + 42.4t 3 y (2.18+ 2.82t )
may be solved using Newton-Raphson iteration, which requires evaluation of the
derivative of F with respect to y:
dF 1 + 4 y + 4 y 2 − 4 y 3 + y 4
=
− 29.52t − 19.52t 2 + 9.16t 3 y
4
dy
(1 − y )
(
(
)
)
+ (2.18 + 2.82t ) 90.7t − 242.2t 2 + 42.4t 3 y (1.18+ 2.82t )
2.3 Calculating Gas Viscosity
2.3.1 Lee, Gonzales, Eakin (1966)
Note: Reference taken from McCain, p 89.
µg =
(
K exp xρ g
y
)
10 4
where the gas density ρ g is in g/cm3 and can be calculated by:
ρg =
K=
pMg
and z can be calculated using a z factor correlation
zRT
(9.379 + 0.01607 M a )T 1.5
(209.2 + 19.26 M a + T )
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(
y + y 2 + y3 − y 4
− 14.76t − 9.76t 2 + 4.58t 3 y 2
3
(1 − y )
where Ma is the apparent molecular weight, calculated as
M a = γ g * 28.9625
x = 3.448 +
986.4
+ 0.01009 M a
T
y = 2.447 - 0.2224 x
2.3.2 Carr, Kobayashi, Burroughs (1954)
Note: Reference taken from McCain, p. 90
µ g = µ1
ex
T pr
(
(
) (
)
)
(γ ))
(γ ))
+ y N 2 9.59 × 10 -3 + 8.48 × 10 -3 log10 (γ g )
(
(3.73 × 10
+ y CO2 6.24 × 10 -3 + 9.08 × 10 -3 log10
+ y H 2S
-3
+ 8.49 × 10 log10
-3
g
g
T= temperature in F
x = b0 + b1T pr + b2T pr + b3T pr
2
3
b0 = a 0 + a1 p pr + a 2 p pr + a 3 p pr
3
b1 = a 4 + a5 p pr + a 6 p pr + a 7 p pr
3
2
2
b2 = a8 + a 9 p pr + a10 p pr + a11 p pr
2
3
b3 = a12 + a13 p pr + a14 p pr + a15 p pr
2
3
And the coefficients are:
a0 =-2.46211820
a4 =2.80860949
a1 =2.97054714
a5 =-3.49803305
-1
a2 =-2.86264054×10
a6=3.60373020×10-1
a3 =8.05420522×10-3
a8=-7.93385684×10-1 a12=8.39387178×10-2
a9 =1.39643306
a13 =-1.86408848×10-1
a10 =-1.49144925×10 a14 =2.03367881×10-2
1
a7 =-1.04432413×10-2 a11 =4.41015512×10-3 a15 =-6.09579263×10-4
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where:
µ1 = 1.709 × 10 -5 - 2.062 × 10 -6 γ g T + 8.188 × 10 -3 - 6.15 × 10 -3 log10 (γ g )
2.4 Calculating Gas Compressibility
The coefficient of isothermal compressibility:
cg = −
1 ∂V
V ∂p
T
Solving the real gas law equation of state for V and substituting in the above equation,
p ∂  znRT 
1 ∂V
1 1 ∂z
 = −

cg = −
=−
V ∂p T
znRT ∂p  p  T p z ∂p T
or, defining the pseudoreduced compressibility cpr:
1
1  ∂z 
c pr ≡ c g p pc =
− 
p pr z  ∂p pr 
T pr
cg =
c pr
p pc
Note: To mainain consistency, the compressibility correlation may not be chosen
independently of the z-factor correlation. However, this requires that the partial
derivative of z with respect to pseudoreduced pressure at constant pseudoreduced
temperature
2.4.1 Hall, Yarborough (1973)
Note: Reference taken from McCain, p 81-82.
For the Hall-Yarborough correlation, the derivative of z with respect to ppr is evaluated as
follows.
1
t=
T pr
A = 0.06125te −1.2(1−t )
2
y=
Ap pr
z
where z is evaluated using the Hall-Yarborough correlation.
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The compressibility is then calculated from the definition of the pseudoreduced
compressibility:
 ∂F

 ∂p
 pr

 = −A

y
 ∂F 
1+ 4y + 4y2 − 4y3 + y4
 =

− 29.52t − 19.52t 2 + 9.16t 3 y
4
y
∂
(1 − y )
 p pr

(
(
)
)
+ (2.18 + 2.82t ) 90.7t − 242.2t 2 + 42.4t 3 y (1.18+ 2.82t )
 ∂F 


 ∂p 
pr
y

dy
=−
dp pr
 ∂F 


 ∂y  pr
dz
A  Ap pr
= −  2
dp pr
y  y
 dy


 dp pr




Schlumberger Private
Finally, we calculate the pseudoreduced compressibility:
1
1  ∂z 
c pr =
− 
p pr z  ∂p pr 
T pr
2.4.2 Dranchuk, Abou-Kassem (1975)
Note: Reference taken from McCain, p 82.
1. The reduced density is evaluated using the equation below, where z is obtained from
the DAK z-factor correlation:
p
ρ r = 0.27 r
zTr
2. The derivative z function is calculated by:

A
A  
A
A 
A
A
dz
=  A1 + 2 + 33 + 44 + 55  + 2 A6 + 7 + 82  ρ r
dρ r 
Tr Tr
Tr Tr 
Tr
Tr  
2
 A7 A8  4
2
2
4 ρ r exp − A11 ρ r


−5 A9 
+ 2  ρ r + 2 A10 1 + A11 ρ r − A11 ρ r
3
Tr
 Tr Tr 
(
)
(
)
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where:
A1 =
A2 =
A3 =
A4 =
0.3265
-1.0700
-0.5339
0.01569
A5 =
A6 =
A7 =
A8 =
-0.05165
0.5475
-0.7361
0.1844
A9 =
A10 =
A11 =
0.1056
0.6134
0.7210
3. Finally, we have
x
1−
1+ x
c pr =
pr
where:
x=
ρr
z
 dz

 dρ r



3. Water Correlations
Note: Reference taken from McCain, pg 110
The water density at stnd conditions is calculated by:
ρ wSC = 62.368 + 0.438603S + 1.60074 x10 −3 S 2
The density at res conditions is then:
ρ
ρ w = wSC
Bw
where:
ρw=lbm/ft3
TF is the fluid temperature in F
P is the pressure of interest, in psi
S is NaCl =the salinity in wt % (1%=10,000 ppm)
3.2 Solution Gas-Water Ratio
3.2.1 McCain (1990)
Note: Reference taken from McCain, pg 111
The solubility of methane in pure water is estimated from Eqs:
A = A0 + A1T + A2T 2 + A3T 3
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3.1 Water Density
B = B0 + B1T + B2T 2 + B3T 3
(
)
C = C 0 + C1T + C 2T 2 + C 3T 3 + C 4T 4 × 10 −7
Rsw pure = A + Bp + Cp 2
The coefficients in Eqs.
A0 =
A1 =
A2 =
A3 =
8.15839
-2
-6.12265×10
-4
1.91663×10
-7
-2.1654×10
B0 =
B1 =
B2 =
B3 =
-2
1.01021×10
-5
-7.44241×10
-7
3.05553×10
-10
-2.94883×10
C0 =
C1 =
C2 =
C3 =
C4 =
-9.02505
0.130237
-4
-8.53425×10
-6
2.34122×10
-9
-2.37049×10
Eq. y and Rswbrine are used to correct the solution-gas water ratio for the effects of salinity:
y = 0.0840655 S T −0.285854
Schlumberger Private
Rsw brine = Rsw pure 10 − y
where S is weight percent solids.
3.3 Water FVF
3.3.1 Meehan (1980)
Note: Reference taken from Eclipse, pg 447, Eqn not originally documented by author,
believed to be a rearrangement of the Meehan compressibility eqn
(
)
B w = a + bp + cp 2 S c
[
(
)
(
)
S c = 1 + NaCl 5.1x10 −8 p + 5.47 x10 −6 − 1.96 x10 −10 p (TF − 60 ) + − 3.23x10 −8 + 8.5 x10 −13 p (TF − 60)
ü For gas-free water
a = 0.9947 + 5.8 x10 −6 TF + 1.02 x10 −6 TF
2
b = −4.228 x10 −6 + 1.8376 x10 −8 TF − 6.77 x10 −11 TF
c = 1.3 x10 −10 − 1.3855 x10 −12 TF + 4.285 x10 −15 TF
2
2
ü For gas saturated water
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2
]
a = 0.9911 + 6.35 x10 −6 TF + 8.5 x10 −7 TF
2
b = −1.093 x10 −6 − 3.497 x10 −9 TF + 4.57 x10 −12 TF
c = −5 x10 −11 + 6.429 x10 −13 TF − 1.43 x10 −15 TF
2
2
where:
TF is the fluid temperature in F
P is the pressure of interest, in psi
NaCl is the salinity (1%=10,000 ppm)
3.3.2 McCain (1990) Bw above Pb
Note: Reference taken from McCain, pg 110.
where:
Bwp= FVF at Pb bbl/STB, use McCains Bw for saturated systems (#3 below)
cw= water compressibility- use McCain Saturate correlation at Pb
3.3.3 McCain (1990) Bw below Pb
Note: Reference taken from McCain, pg 110.
McCain presented equations for volume and pressure corrections for water formation
volume factor for water saturated with natural gas:
B w = (1 + ∆V wT )(1 + ∆Vwp )
where:
∆VwT = −1.0001 × 10 −2 + 1.33391 × 10 −4 T + 5.50654 × 10 −7 T 2
∆Vwp = −1.95301 × 10 −9 pT − 1.72834 × 10 −13 p 2T
−3.58922 × 10 −7 p − 2.25341 × 10 −10 p 2
Temp=F and P is in psia
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The water formation volume factor at pressures above the bubble point pressure is
obtained from the formation volume factor at the bubble point and the coefficient of
isothermal compressibility:
Bw = Bwp e −cw ( p − pb )
3.4 Water Viscosity
3.4.1 Meehan (1980)
Note: Reference taken from OFM
µ
w
=µ* f
where:
µ* = A + B / T
A = −0.04518 + 0.009313S − 0.000393S 2
B = 70.634 + 0.09576 S 2
and f is the Pressure correction:
f = 1 + 3.5 x10 −12 p 2 (TF − 40)
Schlumberger Private
where:
TF is the fluid temperature in F
P is the pressure of interest, in psi
S is NaCl =the salinity in wt % (1%=10,000 ppm)
3.4.2 McCain (1990)
Note: Reference taken from OFM and McCain p. 112
The water viscosity is estimated from Eqs.:
A = A0 + A1 S + A2 S 2 + A3 S 3
B = B0 + B1 S + B2 S 2 + B3 S 3 + B4 S 4
µ w1 = AT B
(
µ w = µ w1 0.9994 + 4.0295 × 10 −5 p + 3.1062 × 10 −9 p 2
)
where S is weight percent solids, and the coefficients of Eqs. are given:
A0 =
A1 =
A2 =
A3 =
2
1.09574×10
-8.40564
-1
3.13314×10
-3
8.72213×10
B0 =
B1 =
B2 =
B3 =
B4 =
-1.12166
-2
2.63951×10
-4
-6.79461×10
-5
-5.47119×10
-6
1.55586×10
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3.4.3 Kestin, Khalifa, Correia (1981)
Note: Reference taken from author’s paper- J. Chem. Eng. Data", Vol. 23, p 328
First, convert pressure from psi to MPa, temperature from deg F to deg C, and salinity
from weight fraction to moles per kg water:
p = p oilfield / 145.037949
T=
5
(Toilfield − 32)
9
C=
1000  S 


58.448  100 − S 
Calculate saturation concentration Cs from Kestin’s Eq. 11:
C s = 6.044 + 0.28 × 10 −2 T + 0.36 × 10 −2 T 2
Calculate β * from
2
β * = 2.5C * − 2.0C * + 0.5C *
3
Calculate β w from Kestin’s Eq. 7:
β w = −1.297 + 0.574 × 10 −1 T − 0.697 × 10 −3 T 2
+0.447 × 10 −5 T 3 − 0.105 × 10 −7 T 4
Calculate β s from Kestin’s Eq. 9:
E
β s = 0.545 + 0.28 × 10 −2 T − β w
E
Calculate β from Kestin’s Eqs. 6 and 8:
β = βs β * + βw
E
Calculate A and B from Kestin’s Eqs. 15 and 16, respectively:
A = 0.3324 × 10 −1 C + 0.3624 × 10 −2 C 2 − 0.1879 × 10 −3 C 3
B = −0.396 × 10 −1 C + 0.102 × 10 −1 C 2 − 0.702 × 10 −3 C 3
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Calculate a normalized concentration C * :
C
C* =
Cs
Calculate the ratio of the viscosity of water at temperature T and zero pressure to that of
 µ w 0 (T ) 
 , from
water at 20 deg C and zero pressure, log10  0
 µ (20 ) 

 w
t = 20 − T
 µ w 0 (T )  2.55 × 10 −8 t 4 + 3.06 × 10 −6 t 3 − 1.303 × 10 −3 t 2 + 1.2378t
=
log10  0

96 + T
 µ w (20 ) 
Calculate the logarithm of the ratio of brine viscosity to viscosity of pure water at the
 µ 0 (T , c ) 
 , from Kestin’s Eq. 14:
desired temperature and zero pressure, log10 
 µ 0 (T ) 

 w
0
0
 µ (T ) 
 µ (T , c ) 

 = A + B log10  w
log10 
0
 µ 0 (20 ) 

(
)
µ
T

 w

 w
Calculate brine viscosity at the temperature of interest and zero pressure µ 0 (T , c ) from
µ 0 (T , c ) = µ w (20 ) × 10 X
0
= 1002 × 10 X
Calculate brine viscosity at temperature T and pressure p in units µPa ⋅ s from Kestin’s
Eq. 5:
βp 

µ ( p, T , c ) = µ 0 (T , c )1 +

 1000 
Note that this equation has a factor 1000 in the denominator that is not in the Kestin
paper. The code as implemented in FLProp, with the factor 1000, gave correct results
when compared with the experimental data tabulated in the Kestin paper (within 0.5%,
which is their claimed accuracy), for several points I checked for different temperatures,
pressures, and salt concentrations.
Finally, we convert the viscosity from metric units µPa ⋅ s to oilfield units of centipoise:
µ
µ oilfield =
1000
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 µ 0 (T , c ) 
 µ 0 (T ) 
 + log10  w

X = log10 
0

 µ 0 (20 ) 
(
)
µ
T
 w

 w

3.5 Water Compressibility
3.5.1 Osif revised by Spivey, Valko and McCain, Unsaturated (P>Pb)
Note: Reference taken from McCain, pg 108
At temperatures above 209.3 F,
1
 1  ∂Bw 
 =
c w = −

 Bw  ∂p T (7.033 p + 0.5415S − 537.0T + 403,300 )
At temperatures less than 209.3 F, a form of Osif’s correlation, modified to fit the
Dodson and Standing Graphical correlation is used:
cw =
1
(ap + 0.5415S − 537.0T + b)
b = 2.86078 *10 −5 + 6.1291 *10 2 T + 3.39464T 2 − 1.74086 *10 −2 T 3
where:
T=temperature,F
P =pressure,psia
S is the salinity in mg/L (1 mg/L =1 part per million (ppm) and 1wt% = 10,000 ppm)
3.5.2 Meehan (1980)
Note: Reference taken from Eclipse, pg 445
(
)
c w = S c a + bTF + cTF x10 −6
2
where:
a = 3.8546 − 0.000134 p
b = −0.01052 + 4.77 x10 −7 p
c = 3.9267 x10 −5 − 8.8 x10 −10 p
S c = 1 + NaCl 0.7 (−0.052 + 0.00027TF − 1.14 x10 −6 TF + 1.121x10 −9 TF )
2
3
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Where:
a = −1.9476 *10 −3 + 3.06273 *10 −1 T − 2.33668 *10 −3 T 2 + 4.94205 *10 −6 T 3
where:
TF is the fluid temperature in F
P is the pressure of interest, in psi
NaCl is the salinity (1%=10,000 ppm)
3.5.3 McCain (1990) Saturated cw (P < Pb)
Note: Reference taken from OFM
At pressures below the bubble point pressure, the coefficient of isothermal
compressibility is calculated from
B g  ∂Rsw 
 ∂B 


c w = − w  +
 ∂p  T Bw  ∂p  T
 ∂B 
where −  w  is obtained from Eq.
 ∂p  T
Schlumberger Private
 ∂B 
1
c w = − w  =
 ∂p  T (7.033 p + 0.5415S − 537.0T + 403,300 )
and
 ∂Rsw 

 = (B + 2Cp )10 − y ,
∂
p

T
where B and C are obtained from
B = B0 + B1T + B2T 2 + B3T 3
(
)
C = C 0 + C1T + C 2T 2 + C 3T 3 + C 4T 4 × 10 −7
A0 =
A1 =
A2 =
A3 =
8.15839
-2
-6.12265×10
-4
1.91663×10
-7
-2.1654×10
B0 =
B1 =
B2 =
B3 =
-2
1.01021×10
-5
-7.44241×10
-7
3.05553×10
-10
-2.94883×10
C0 =
C1 =
C2 =
C3 =
C4 =
-9.02505
0.130237
-4
-8.53425×10
-6
2.34122×10
-9
-2.37049×10
And
y is obtained from Eq.
y = 0.0840655 S T −0.285854
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PVT Toolbox- Correlation Equations –last modified March 10, 2004
Nomenclature
Latin
Bg
Bo
Bob
cg
co
co
ppcHC
ppcm
psep
psc
pSP
ps1
ppr
pr
R
R1
Rs
Rsb
RSP
RST
Rsw
S
T
TbC7+
Tf
Tpc
TpcHC
Tpcm
Tpr
Tr
Ts1
Ts2
gas formation volume factor, bbl/Mscf
oil formation volume factor, bbl/STB
oil formation volume factor at the bubble point pressure, bbl/STB
gas compressibility, psi-1
oil compressibility, psi-1
average undersaturated oil compressibility between bubble point pressure and reservoir
pressure, psi-1
= pseudoreduced compressibility, dimensionless
= water compressibility, psi-1
= gravitational acceleration, 32.2 ft/sec2
= conversion constant, 32.2 lbm/slug
= additional gas production, scf/STB
= Stewart, Burkhardt, Voo parameter, °R/psi
= Sutton parameter, °R/psi
= Stewart, Burkhardt, Voo parameter, °R2/psi
= Sutton parameter, °R2/psi
= molecular weight, lbm/lb-mole
= molecular weight, lbm/lb-mole
= number of lb-moles
= pressure, psia
= bubble point pressure, psia
= pseudocritical pressure, psia
= pseudocritical pressure of hydrocarbon fraction, psia
= mole-fraction weighted average pseudocritical pressure of mixture, psia
= separator pressure, psia
= standard pressure, psia
= separator pressure, psia (synonym for psep)
= primary separator pressure, psia
= pseudoreduced pressure, dimensionless
= reduced pressure, dimensionless
= universal gas constant, 10.732 (psi×ft3/(lb-mole×°R)
= primary separator gas-liquid ratio, scf/STB
= solution gas-oil ratio, scf/STB
= solution gas-oil ratio at original bubble point pressure, scf/STB
= separator gas-oil ratio, scf/STB
= stock-tank gas-oil ratio, scf/STB
= solution gas-water ratio, scf/STB
= salinity, mg/l or weight percent solids
= temperature, °R (in gas equations) or °F (in oil or water equations), unless otherwise
noted
= boiling point of heptanes plus fraction, °R
= temperature, °R (in gas equations) or °F (in oil or water equations), unless otherwise
noted. (synonym for T)
= pseudocritical temperature, °R
= pseudocritical temperature of hydrocarbon fraction, °R
= mole-fraction weighted average pseudocritical temperature of mixture, °R
= pseudoreduced temperature, dimensionless
= reduced temperature, dimensionless
= primary separator temperature, °F
= secondary separator temperature, °F
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cpr
cw
g
gc
Gpa
J
J´
K
K´
Ma
M
n
p
pb
ppc
=
=
=
=
=
=
Greek
separator temperature, °F
standard temperature, °R
separator temperature, °F (synonym for Tsep)
volume, ft3
vapor equivalent of separator liquid, scf/STB
mole fraction of hydrocarbon gases, dimensionless
mole fraction of component i, dimensionless
real gas deviation factor, dimensionless
=
=
=
=
=
=
=
=
γAPI
γC7+
γg
γg1
γg100
γgHC
γgR
γgSP
γgST
= API gravity, °API
= specific gravity of heptanes plus fraction, g/cm3
= gas specific gravity, (air=1.0)
= gas specific gravity from first stage separator, (air=1.0)
= separator gas specific gravity for separator pressure of 100 psig, (air=1.0)
= gas specific gravity of hydrocarbon fraction, (air=1.0)
= reservoir gas specific gravity, (air=1.0)
= separator gas specific gravity, (air=1.0)
= gas specific gravity of stock-tank vent gas, (air=1.0)
= weighted average surface gas specific gravity, (air=1.0)
= oil specific gravity, g/cm3
= Wichert-Aziz parameter, °R
= Sutton correction parameter, °R/psi
= Sutton correction parameter, °R2/psi
= viscosity, cp
= dead oil viscosity, cp
= kinematic viscosity, centistokes
= density, lbm/ft3
= apparent density of light hydrocarbon fraction, lbm/ft3
= reservoir liquid density, lbm/ft3
= reservoir liquid density at bubble point pressure, lbm/ft3
= pseudoliquid density, lbm/ft3
= reduced density, dimensionless
= density of stock-tank liquid, lbm/ft3
γg wt avg
γo
ε
eJ
eK
µ
µoD
ν
ρ
ρa
ρo
ρob
ρpo
ρr
ρSTO
Subscripts and Superscripts
C7+
g
o
pc
pr
w
=
=
=
=
=
=
heptanes plus fraction
gas
oil
pseudocritical property
pseudoreduced property
water
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Tsep
Tsc
TSP
V
Veq
yHC
yi
z
References:
Saturate oil density correlation reference:
Correlation
Year
Paper Reference
1
Standing
1977
2
McCain &
Hill
1995
Standing, M.B.: Volumetric and Phase Behavior of Oilfield
Hydrocarbon Systems, 9th Printing, Society of Petroleum
Engineers of AIME, Dallas (1977).
McCain, W.D. Jr., and Hill, N.C.: “Correlations for Liquid
Densities and Evolved Gas Specific Gravities for Black Oils
During Pressure Depletion,” paper SPE 30773 presented at the
1995 SPE Annual Technical Conference and Exhibition,
Dallas, Oct. 22-25.
Unsaturate oil density and McCain Mass balance:
1
Correlation
McCain
Year
1990
Paper Reference
McCain, W. D., Jr.: The Properties of Petroleum Fluids, 2nd Ed.,
PennWell Books, Tulsa (1990).
Oil Formation Volume Factor (Bo)
Year
Glaso
1980
Glasø, Ø.: “Generalized Pressure-VolumeTemperature Correlations,” JPT (May 1980) 785-95.
Standing
1947
Vasquez & Beggs
1980
Standing, M.B.: “A Pressure-Volume-Temperature
Correlation for Mixtures of California Oils and
Gases,” Drill. Prod. Prac. API (1947) 275-287
Vazquez, M.E., and Beggs, H.D.: “Correlations for
Fluid Physical Property Prediction,” JPT (June 1980)
968-70.
1993
4
Petrosky &
Farshad
Farshad &
Leblanc
1992
5
Al-Marhoun 2
1992
Kartoatmodjo &
Schmidt
1994
Casey-Cronquist
1992
1
2
3
6
7
8
Paper Reference
Petrosky, J. and Farshad, F.: “Pressure Volume
Temperature Correlation for the Gulf of Mexico.”
68th Soc. Pet. Eng. Anna. Tech. Con., Houston, TX,
Oct 3-6 1993, SPE 26644.
Farshad, F. F, Leblanc, J. L, Garber, J. D. and Osorio,
J. G.: ” Empirical Correlation for Colombian Crude
Oils,” SEP 24538 (1992).
Al-Marhoun, M. A.: “New Correlation for formation
VolumeFactor of oil and gas Mixtures, ” Journal of
Canadian Petroleum Technology (March 1992) 2226.
Kartoatmodjo, T., and Schmidt, Z.: “Large data bank
improves crude physical property correlations,” OGJ
(July 1994) 51-55.
Casey, J. M. and Cronquist, C.: “Estimate GOR and
FVF using dimensionless PVT analysis,” World Oil
Inputs
Required
Rs @ P,T; γgsp, γo,
T
Rs @ P,T; γgsp, γo,
T
Rs @ P,T, γg100,
γoAPI, T
*Where: γg100
inputs are γgsp,
Psep, Tsep
Rs @ P,T; γgsp, γo,
T
Rs @ P,T; γgsp, γo,
T
Rs @ P,T; γgsp, γo,
T
Rs @ P,T, γg100,
γoAPI, T
*Where: γg100
inputs are γgsp,
Psep, Tsep
Rsb, γoAPI, T,
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Correlation
Almedhaideb
1997
9
10
11
Al-Shammasi
1999
Elksharkawy &
Alikhan
1997
McCain Mass
Balance
1990
FVF using dimensionless PVT analysis,” World Oil
(November 1992), 83-87.
Almehaideb, R. A.: “IMPROVED PVT
CORRELATIONS FOR UAE CRUDE OILS,” SPE
37691, SPE Middle East Oil Show CONF (Manamah,
Bahrain, 3/15 –18/97) PROC V1, pp 109-120, 1997.
Al-Shammasi A. A. “Bubble Point Pressure and Oil
Formation Volume Factor Correlations”, SPE 53185
(1999)
Elsharkawy, A. M.. and Alikhan, A. A.: “Correlations
for predicting solution gas/oil ratio, oil formation
volume factor, and undersaturated oil
compressibility.” Journal of Petroleum Science and
Engimeering 17, (1997), 292-302.
McCain, W. D., Jr.: The Properties of Petroleum
Fluids, 2nd Ed., PennWell Books, Tulsa (1990).
12
Pref, Pb
Rs @ P,T, γo, T
Rs @ P,T; γgsp, γo,
T
Rs @ P,T; γgsp, γo,
T
Rs @ P,T; γgwtave,
ρo @ P, T, ρo @s.c. ,
T
* For DensityUse density
correlations
Pb Correlations Studied
Year
1980
2
Standing
1947
3
Lasater
1958
4
Vasquez
1980
Paper Reference
Glasø, Ø.: “Generalized Pressure-Volume-Temperature
Correlations,” JPT (May 1980) 785-95.
Standing, M.B.: “A Pressure-Volume-Temperature
Correlation for Mixtures of California Oils and Gases,”
Drill. Prod. Prac. API (1947) 275-287
Lasater, J. A.:” Bubble Point Pressure Correlation,” SPE
Paper 957-G, (MAY 1958).
Vazquez, M.E., and Beggs, H.D.: “Correlations for Fluid
Physical Property Prediction,” JPT (June 1980) 968-70.
5
Al-Marhoun
1988
Al-Marhoun, M. A.: “PVT Correlations for Middle East
Crude Oils,” JPT (MAY 1988) 650-66, Trans, 285, SPE
Paper 13718
6
Petrosky
1993
Petrosky, J. and Farshad, F.: “Pressure Volume
Temperature Correlation for the Gulf of Mexico.” 68th Soc.
Pet. Eng. Anna. Tech. Con., Houston, TX, Oct 3-6 1993,
SPE 26644.
7
Farshad
1992
Farshad, F. F, Leblanc, J. L, Garber, J. D. and Osorio, J. G.:
” Empirical Correlation for Colombian Crude Oils,” SEP
24538 (1992)
Inputs required
Rsb, γgwt.ave, γoAPI,
T
Rsb, γgsp, γoAPI, T
Rsb, γgwt.ave, γo, T
Rsb, γg100, γoAPI, T
*Where: γg100
inputs are γgsp,
Psep, Tsep
Rsb, γgsp, γoAPI, T
Rsb, γgsp, γoAPI,
T
Rsb, γgsp, γoAPI,
T
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1
Correlation
Glaso
8
Kartoatmodjo 1994
Kartoatmodjo, T., and Schmidt, Z.: “Large data
bank improves crude physical property
correlations,” OGJ (July 1994) 51-55.
9
Valkó
2003
10
Velarde
1999
11
Labedi
1990
12
Al-Shammasi
1999
Rs Correlations Studied
Correlation
Year
1
Glaso
1980
2
Standing
1947
3
Lasater
1958
4
Vasquez &
Beggs
1980
5
Petrosky &
Farshad
1993
6
Kartoatmodjo
& Schmidt
1994
7
CaseyCronquist
1992
Paper Reference
Glasø, Ø.: “Generalized Pressure-VolumeTemperature Correlations,” JPT (May
1980) 785-95.
Standing, M.B.: “A Pressure-VolumeTemperature Correlation for Mixtures of
California Oils and Gases,” Drill. Prod.
Prac. API (1947) 275-287
Lasater, J. A.:” Bubble Point Pressure
Correlation,” SPE Paper 957-G, (MAY
1958).
Vazquez, M.E., and Beggs, H.D.:
“Correlations for Fluid Physical Property
Prediction,” JPT (June 1980) 968-70.
Petrosky, J. and Farshad, F.: “Pressure
Volume Temperature Correlation for the
Gulf of Mexico.” 68th Soc. Pet. Eng.
Anna. Tech. Con., Houston, TX, Oct 3-6
1993, SPE 26644.
Kartoatmodjo, T., and Schmidt, Z.: “Large
data bank improves crude physical
property correlations,” OGJ (July 1994)
51-55.
Casey, J. M. and Cronquist, C.: “Estimate
GOR and FVF using dimensionless PVT
analysis,” World Oil (November 1992),
83-87.
Rsb, γgsp, γoAPI,
T
Rsb, γgsp, γoAPI,
T
Rsb, γgsp, γoAPI,
T
Inputs Required
γgsep, γoAPI, T, P,
Pb, yN2,yCO2,
yH2S
γgsep, γoAPI, T, P
γgsep, γo, T, P
Rs, γg100, γoAPI, T,P
*Where: γg100 inputs
are γgsp, Psep, Tsep
γgsep, γoAPI, T,
Pb
Rs, γg100, γoAPI, T,P
*Where: γg100 inputs
are γgsp, Psep, Tsep
Rsb, T, P, Pb
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Valkó, P.P, and McCain, W.D. Jr.: “Reservoir oil
bubblepoint pressures revisited; solution gas-oil
ratios and surface gas specific gravities,” J. Pet. Sci.
Eng. (2003) 153-169.
Velarde, J., Blasingame, T.A., and McCain,
W.D.Jr.: “Correlation of Black Oil Properties at
Pressures Below Bubble Point Pressure – A New
Approach,” J. Can. Pet. Tech., (Special Edition
1999) 62-68.
Labedi, R.M.: “Use of Production Data to Estimate
the Saturation Pressure, Solution Gas and Chemical
Composition of Reservoir Fluids,” paper SPE 21164
presented at the SPE Latin American Petroleum
Conference, Rio de Janeiro, 14-19 October 1990.
Al-Shammasi A. A. “Bubble Point Pressure and Oil
Formation Volume Factor Correlations”, SPE
53185 (1999).
Rsb, γg100,
γoAPI, T
*Where: γg100
inputs are γgsp,
Psep, Tsep
Rsb, γgsp, γoAPI,
T
8
1999
Velarde,
Basingame,
McCain
Velarde, J., Blasingame, T.A., and
McCain, W.D.Jr.: “Correlation of Black
Oil Properties at Pressures Below Bubble
Point Pressure – A New Approach,” J.
Can. Pet. Tech., (Special Edition 1999) 6268.
γgsep, γoAPI, T, P,
Rsb, Pb
Dead Oil Viscosity (µod) correlations
Paper Reference
1
Beggs
1975
2
Glaso
1980
3
Ng and
Egbogah
1983
4
Beal
1946
Beggs, H.D., and Robinson, J.R.: “Estimating
the Viscosity of Crude Oil Systems,” JPT
(September 1975) 1140-1141.
Glasø, Ø.: “Generalized Pressure-VolumeTemperature Correlations,” JPT (May 1980)
785-95
Ng, J.T.H. and Egbogah, E.O.; "An Improved
Temperature-Viscosity Correlation for Crude
Oil Systems," paper 83-34-32 presented at the
34th Annual Technical Meeting of the
Petroleum Society of CIM, Banff, May 10-13,
1983.
Beal, C.; "The Viscosity of Air, Water,
Natural Gas, Crude Oil and Its Associated
Gases at Oil Field Temperatures and
Pressures," Trans., AIME, 165, (1946) 94115.
Live Oil Viscosity (Saturated)
Correlation Year
Paper Reference
1
Beggs
1975
2
Khan
1987
3
Chew
1959
4
Hanafy
1997
Beggs, H.D., and Robinson, J.R.: “Estimating
the Viscosity of Crude Oil Systems,” JPT
(September 1975) 1140-1141.
Kahn, S.A. et al.: “Viscosity Correlations for
Saudi Arabian Crude Oils,” paper SPE 15720
presented at the 1987 SPE Middle East Oil
Show, Manama, Bahrain, 7-10 March.
Chew, J.N. and Connally, C.A.; "A Viscosity
Correlation for Gas-Saturated Crude Oils",
Trans., AIME, 216, (1959) 23-25.
Hanafy, H.H., Macary, S.M., El-Nady, Y.M.,
Bayomi, A.A., and Batanony, M.H.: “A New
Approach for Predicting the Crude Oil
Properties,” paper SPE 37439 presented at the
SPE Production Operations Symposium,
Oklahoma City, 9-11 March 1997.
Inputs
Required
?oAPI, T
?oAPI, T
?oAPI, T
?oAPI , T
Inputs
Required
Rs, µODàγoAPI,
T
Pb, P, γgsep, Rs,
γoAPI, T
Rs, µODàγoAPI,
T
ρo at P,T of
interest- * use
sat oil density
correlation to
calculate
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Correlation Year
Live Oil Viscosity (Unsaturated) correlations
1
Correlation Year
Khan
1987
2
Vasquez
Paper Reference
Kahn, S.A. et al.: “Viscosity Correlations for
Saudi Arabian Crude Oils,” paper SPE
15720 presented at the 1987 SPE Middle
East Oil Show, Manama, Bahrain, 7-10
March.
1980
Vazquez, M.E., and Beggs, H.D.:
“Correlations for Fluid Physical Property
Prediction,” JPT (June 1980) 968-70.
3
4
Beal
1946
Hanafy
1997
Pb, P, µobàuse
default Sat
correlation
µobà Rsb,
µODàγoAPI, T
Pb, P, µobàuse
default Sat
correlation
µobà Rsb,
µODàγoAPI, T
ρo at P,T of interest* use sat oil density
correlation to
calculate
Live Oil Compressibility (Saturated) Correlations
1
Correlation Year
McCain
1988
2
Spivey
2003
Paper Reference
McCain, W.D, Jr., Rollins, J.B., and Villena,
A.J.: “The Coefficient of Isothermal
Compressibility of Black Oils at Pressures
Below the Bubblepoint,” SPEFE (September
1988), 659-662.
Spivey, J.P., Valkó, P.P., and McCain,
W.D., Jr., “Coefficients of Isothermal
Compressibility of Oilfield Fluid Systems,”
unpublished, 2003.
Inputs Required
Rsb, γg wt ave., Pb, P,
T, γoAPI
Boàuse default Bo
correlation, inputs Rs,
?gsep, T, ?oAPI
Bgà z, T, P use
default z correlation
Live Oil Compressibility (UnSaturated) Correlations
1
Correlation Year
Spivey
2003
2
Vasquez
1980
Paper Reference
Spivey, J.P., Valkó, P.P., and McCain,
W.D., Jr., “Coefficients of Isothermal
Compressibilityof Oilfield Fluid
Systems,” unpublished, 2003.
Vazquez, M.E., and Beggs, H.D.:
“Correlations for Fluid Physical Property
Prediction,” JPT (June 1980) 968-70.
Inputs Required
P, Pb, Rsb, ?gsep,
?oAPI, T
P, Rsb, ?g wt.aave,
?oAPI, T
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Beal, C.; "The Viscosity of Air, Water,
Natural Gas, Crude Oil and Its Associated
Gases at Oil Field Temperatures and
Pressures," Trans., AIME, 165, (1946) 94115.
Hanafy, H.H., Macary, S.M., El-Nady,
Y.M., Bayomi, A.A., and Batanony, M.H.:
“A New Approach for Predicting the Crude
Oil Properties,” paper SPE 37439 presented
at the SPE Production Operations
Symposium, Oklahoma City, 9-11 March
1997.
Inputs required
Pb, P, µobàγgsep,
Rsb, γoAPI, T
3
Petrosky
1998
4
Calhoun
1947
5
Trube
1957
Petrosky, G.E., and Farshad, F.F.:
“Pressure-Volume-Temperature
correlations for Gulf of Mexico Crude
Oils,” SPEREE (October 1998) 416-420.
Calhoun, J.C. Jr.: Fundamentals of
Reservoir Engineering, U. of Oklahoma
Press, Norman OK (1947) 35.
Trube, A.S.: "Compressibility of
Undersaturated Hydrocarbon Reservoir
Fluids," Trans., AIME (1957) 210, 341344
P, Rsb, ?g wt.aave,
?oAPI, T
P, T, Rsb, Bo, ?oAPI,
?g100à ?gsep, Tsep, Psep
P, T, Rsb, Bo, ?oAPI,
?g100à ?gsep, Tsep, Psep
Known gas gravity Tc, Pc
Year
Paper Reference
1
Piper
1993
Piper, L.D., McCain, W.D. Jr., and
Corredor, J.H.: “Compressibility Factors
for Naturally-Occurring Petroleum
Gases,” paper SPE 26668 presented at
the 1993 Annual Technical Conference
and Exhibition, Houston, Texas, 3-6
October.
2
Standing
1977
3
Sutton
1985
Standing, M.B.: Volumetric and
Phase Behavior of Oilfield
Hydrocarbon Systems, 9th Printing,
Society of Petroleum Engineers of
AIME, Dallas (1977).
Sutton, R.P.: “Compressibility
Factors for High Molecular Weight
Reservoir Gases,” paper SPE 14265
presented at the SPE Annual
Technical Meeting and Exhibition,
Las Vegas, 22-25 September, 1985.
Inputs
Required
γg, mole
fraction (y),
Tci, Pci, MW
for CO2, N2,
H2S
γgwtave, mole
fraction (y),
Tci, Pci, MW
for CO2, N2,
H2S
γg, mole
fraction (y),
Tci, Pci, MW
for CO2, N2,
H2S
Known gas composition Tc, Pc
Correlation
Year
Paper Reference
1
Piper
1993
Piper, L.D., McCain, W.D. Jr., and
Corredor, J.H.: “Compressibility Factors
for Naturally-Occurring Petroleum
Gases,” paper SPE 26668 presented at
the 1993 Annual Technical Conference
and Exhibition, Houston, Texas, 3-6
October.
2
Stewart
1959
Stewart, W.F., Burkhardt, S.F., Voo,
D.: “Prediction of Pseudocritical
Parameters for Mixtures,” paper
presented at the AIChE Meeting,
Inputs
Required
mole fraction
(y), Tci, Pci,
for CO2, N2,
H2S, C1-C6
yC7+, MWC7+
mole fraction
(y), Tci, Pci,
for CO2, N2,
H2S, C1-C6
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PVT Toolbox- Correlation Equations –last modified March 10, 2004
Schlumberger Private
Correlation
3
Sutton
1985
Kansas City, Missouri, 18 May,
1959.
Sutton, R.P.: “Compressibility
Factors for High Molecular Weight
Reservoir Gases,” paper SPE 14265
presented at the SPE Annual
Technical Meeting and Exhibition,
Las Vegas, 22-25 September, 1985.
γC7+, MWC7+
mole fraction
(y), Tci, Pci,
for CO2, N2,
H2S, C1-C6
γC7+, MWC7+
z factor correlations
1
2
Correlation
Dranchuk
Year
1975
Hall and
Yarborough
1973
Paper Reference
T, Pref, Tc, Pc
Gas Viscosity
1
Correlation
Lee et al.
Year
1966
2
Carr et al.
1954
Paper Reference
Lee, Gonzalez, and Eakin: “The
Viscosity of Natural Gases,” JPT
(August 1966).
Carr, N.L., Kobayashi, R., and
Burrows, D.B.: “Viscosity of
Hydrocarbon Gases Under Pressure,”
Trans. AIME (1954) 201, 264-272
Inputs Required
T, γg, ρg
Trà T, Tc,
Prà P, Pc
γg
Gas Compressibility
1
2
Correlation
Dranchuk
Year
1975
Hall and
Yarborough
1973
Paper Reference
Dranchuk, P. M. and Abou-Kassem, J.
H.: “Calculation of Z Factors For
Natural Gases Using Equations of
State,” Journal of Canadian Petroleum
Technology (July-Sep. 1975) 34-36
Hall, K. R. and Yarborough, L.: “A
new equation of state for Z-factor
calculations,” OGJ (June 18, 1973) 8292.
Inputs Required
T, Pref, Tc, Pc
T, Pref, Tc, Pc
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Schlumberger Private
Dranchuk, P. M. and Abou-Kassem, J.
H.: “Calculation of Z Factors For
Natural Gases Using Equations of
State,” Journal of Canadian Petroleum
Technology (July-Sep. 1975) 34-36
Hall, K. R. and Yarborough, L.: “A
new equation of state for Z-factor
calculations,” OGJ (June 18, 1973) 8292.
Inputs Required
T, Pref, Tc, Pc
Solution Gas Water Ratio (GWR, Rsw)
End
note #
1
Correlation
Year
Paper Reference
Culberson and
McKetta
1951
2
Spivey, Valkó, and
McCain
2003
3
Price
1979
4
McCain
1990
Culbertson, O.L., and McKetta, J.J., Jr.: “Phase
Equilibria in Hydrocarbon-Water Systems III –The
Solubility of Methane in Water at Pressures to
10,000 psia,” Trans. AIME (1951) 192, 223-226.
Spivey, J.P., Valkó, P.P., and McCain, W.D., Jr.,
“Coefficients of Isothermal Compressibility of
Oilfield Fluid Systems,” unpublished, 2003.
Price, L.C.: “Aqueous Solubility of Methane at
Elevated Pressures and Temperatures,” AAPG Bull.
(September 1979) 63, 1527-1533.
McCain, W. D., Jr.: The Properties of Petroleum
Fluids, 2nd Ed., PennWell Books, Tulsa
(1990).
Water FVF (Bw)
2
Spivey
2003
Spivey, J.P., Valkó, P.P., and McCain, W.D., Jr.,
“Coefficients of Isothermal Compressibilityof Oilfield
Fluid Systems,” unpublished, 2003.
Eqn taken from Eclipse Manual, pg 447- Source
believed to be from original Meehan Compressibility
paper
Meehan, D.N.; "A Correlation For Water
Compressibility," Pet. Eng. Int., (Nov. 1980) 125126.
Water Viscosity, µw
Year
1980
Paper Reference
1
Correlation
Meehan
2
McCain
1990
McCain, W. D., Jr.: The Properties of Petroleum
Fluids, 2nd Ed., PennWell Books, Tulsa (1990).
3
Kestin et al.
1978
Kestin, J., Khalifa, H.E., Abe, Y., Grimes, C.E.,
Sookiazian, H., and Wakeham, W.A.: “Effect of
Pressure on the Viscosity of Aqueous NaCl Solutions
in the Temperature Range 20-150°C,” J. Chem. Eng.
Data 23, No. 4 (1978) 328-336.
Meehan, D.N.; "Estimating Water Viscosity at
Reservoir Conditions," Pet. Eng. Int., (July 1980) 117118.
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PVT Toolbox- Correlation Equations –last modified March 10, 2004
Schlumberger Private
Year
1980
Paper Reference
1
Correlation
Meehan
Water Compressibility
Year
1990
Paper Reference
1
Correlation
Meehan
2
Osif
1998
Osif, T.L.: “The Effects of Salt, Gas, Temperature, and
Pressure on the Compressibility of Water,” SPERE
(February 1988) 175-180.
3
Spivey
(*Osif
revised)
2003
Spivey, J.P., Valkó, P.P., and McCain, W.D., Jr.,
“Coefficients of Isothermal Compressibilityof Oilfield Fluid
Systems,” unpublished, 2003.
Meehan, D.N.; "A Correlation For Water Compressibility,"
Pet. Eng. Int., (Nov. 1980) 125-126.
Schlumberger Private
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PVT Toolbox- Correlation Equations –last modified March 10, 2004