Difference between revisions of "McCain Oil density correlation"

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__TOC__
 
__TOC__
  
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=== Brief ===
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== McCain Oil density correlation==
  
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[[McCain Oil density correlation|McCain]] is an empirical correlation for the '''oil density''' published in '''1995''' <ref name= M1995/>.
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[[McCain Oil density correlation|McCain correlation]] is an empirical correlation for the '''oil density''' published in '''1995''' <ref name= M1995/>.
  
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[[File:McCain Oil density.png|thumb|right|400px|link=http://www.pengtools.com/pvtCalculator|Oil density in the PVT Tool]]
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[[File:McCain Oil density.png|thumb|right|400px|https://www.pengtools.com/pvtCalculator?paramsToken=de71e4cc29541ab2117e07408864410c|McCain oil density correlation in the PVT Software]]
  
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=== Math & Physics ===
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== Math & Physics ==
  
 
Pseudoliquid density:
 
Pseudoliquid density:
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Apparent liquid density:
 
Apparent liquid density:
  
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:<math>\rho_a = -49.8930 + 85.0149\ SG_g - 3.70373\ SG_g\ \rho_{po} + 0.0479818\ SG_g\ \rho_{po}^2 + 2.98914\ \rho_{po} - 0.0356888\ \rho_{po}^2 </math>
+
:<math>\rho_a = a_0 + a_1\ SG_{gSP} + a_2\ SG_{gSP}\ \rho_{po} + a_3\ SG_{gSP}\ \rho_{po}^2 + a_4\ \rho_{po} +a_5\ \rho_{po}^2 </math>
 +
:<math>a_0 = -49.8930</math>
 +
:<math>a_1 = 85.0149</math>
 +
:<math>a_2 = - 3.70373</math>
 +
:<math>a_3 = 0.0479818</math>
 +
:<math>a_4 = 2.98914</math>
 +
:<math>a_5 =- 0.0356888</math>
  
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Next pseudoliquid density:
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Next pseudoliquid density<ref name= M1990/>:
 
:<math>\rho_{po} = \frac{R_s\ SG_g + 4,600\ SG_o}{73.71+R_s\ SG_g\ / \rho_a}</math>
 
:<math>\rho_{po} = \frac{R_s\ SG_g + 4,600\ SG_o}{73.71+R_s\ SG_g\ / \rho_a}</math>
  
 
Iterate until pseudoliquid densities are equal.
 
Iterate until pseudoliquid densities are equal.
  
−
Adjust density to the pressure of interest:
+
Next adjust density to the pressure of interest:
  
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:<math>\rho_{bs} = \rho_{po} + \triangle \rho_p </math>
+
:<math>\rho_{bs} = \rho_{po} + \triangle \rho_P </math>
  
 
where
 
where
  
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:<math>\rho_{p} = \left ( 0.617 + 16.181 \times 10^{-0.0425\ \rho_{po}} \right) \frac{P}{1000} - 0.01 \left ( 0.299 + 263 \times 10^{-0.0603\ \rho_{po}}\right)\ \left (\frac{P}{1000}\right)^2 </math>
+
:<math>\triangle \rho_{P} = \left ( 0.167 + 16.181 \times 10^{-0.0425\ \rho_{po}} \right) \frac{P}{1000} - 0.01 \left ( 0.299 + 263 \times 10^{-0.0603\ \rho_{po}}\right)\ \left (\frac{P}{1000}\right)^2 </math>
−
 
 
  
 
Adjust density to the temperature of interest:
 
Adjust density to the temperature of interest:
  
−
:<math>\rho_{o} = \rho_{bs} + \triangle \rho_t </math>
+
:<math>\rho_{o} = \rho_{bs} + \triangle \rho_T </math>
  
 
where
 
where
  
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:<math>\rho_{t} = (0.00302 + 1.505\ \rho_{bs}^{-0.951}) (T - 60)^{0.938}</math>
+
:<math>\triangle \rho_T = (0.00302 + 1.505\ \rho_{bs}^{-0.951}) (T - 60)^{0.938} - (0.0216 - 0.0233\ (10^{-0.0161\ \rho_{bs}})) (T - 60)^{0.475}</math>
  
 +
Oil density above the bubble point pressure:
  
−
:<math> - (0.0216 - 0.0233\ (10^{-0.0161\ \rho_{bs}})) (T - 60)^{0.475} </math>
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:<math>\rho_{o} = \rho_{b}\ e^{c_o\ (P - P_b)} </math>
  
 +
== Example. Calculation of the oil density ==
 +
Example source <ref name=DW/>
 +
===Input data===
 +
:<math>R_s</math> = 53.24 sm3/sm3
 +
:<math>SG_o</math> = 0.85 or 35 API
 +
:<math>SG_g</math> = 0.75
 +
:<math>T</math> = 90C or 363K
 +
:<math>P</math> = 10 MPa
 +
Calculate oil density at p = 10 MPa?
  
 +
===Solution===
 +
:<math>\rho_o</math> = 749.645 kg/m3
  
−
Adjust density above the bubble point pressure:
+
The solution is available in the online PVT calculator software model at [https://www.pengtools.com/pvtCalculator?paramsToken=de71e4cc29541ab2117e07408864410c www.pengtools.com]
  
−
=== Discussion  ===
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== Application range ==
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=== Application range ===
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Description of the Data Used<ref name= M1995/>:
−
Description of the Data Used<ref name= BR1975/>:
 
  
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:<math>  20 \le R_s \le 2,070 </math>
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:<math>  133 \le P_b \le 6,700 </math>
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:<math>  0.75 \le SG_o \le 0.96 </math>
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:<math>  77 \le T \le 327 </math>
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:<math>  0 \le P \le 5250 </math>
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:<math>  18 \le R_{sb} \le 1,975 </math>
−
:<math>  70 \le T \le 295 </math>
+
:<math>  0.76 \le SG_o \le 0.95 </math>
 +
:<math>  0.556 \le SG_g \le 1.237 </math>
 +
:<math>  31.3 \le \rho_{ob} \le 55.77 </math>
  
−
Number of oil systems = 600<BR/>
+
Number of data sets = 684<BR/>
−
Number of dead oil observations = 460<BR/>
 
−
Number of live oil observations = 2,073<BR/>
 
  
−
=== Nomenclature ===
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== Nomenclature ==
−
:<math> A </math> = coefficient
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:<math> c_o </math> = oil compressibility, 1/psia
−
:<math> B </math> = coefficient
 
−
:<math> m </math> = coefficient
 
 
:<math> P </math> = pressure, psia
 
:<math> P </math> = pressure, psia
 
:<math> R_s </math> =  solution gas-oil ratio, scf/stb
 
:<math> R_s </math> =  solution gas-oil ratio, scf/stb
 +
:<math> SG_g </math> = gas specific gravity, dimensionless
 +
:<math> SG_{gSP} </math> = gas specific gravity at separator pressure, dimensionless
 
:<math> SG_o </math> = oil specific gravity, dimensionless
 
:<math> SG_o </math> = oil specific gravity, dimensionless
 
:<math> T </math> = temperature, °F
 
:<math> T </math> = temperature, °F
−
:<math> x </math> = coefficient
 
  
−
:<math> \mu </math> = viscosity, cP
+
:<math> \rho_{a} </math> = apparent density of surface gas if it were a liquid, lb<sub>m</sub>/ft<sup>3</sup>
 +
:<math> \rho_{ob} </math> = liquid density at the bubble point pressure, lb<sub>m</sub>/ft<sup>3</sup>
 +
:<math> \rho_{bs} </math> = liquid density at reservoir pressure and 60°F, lb<sub>m</sub>/ft<sup>3</sup>
 +
:<math> \rho_o </math> = oil density, lb<sub>m</sub>/ft<sup>3</sup>
 +
:<math> \rho_{po} </math> = pseudoliquid formed by recombination of surface gas and liquid at standard conditions, lb<sub>m</sub>/ft<sup>3</sup>
 +
:<math> \triangle \rho_{P} </math> = adjustment to liquid density due to pressure, lb<sub>m</sub>/ft<sup>3</sup>
 +
:<math> \triangle \rho_{T} </math> = adjustment to liquid density due to temperature, lb<sub>m</sub>/ft<sup>3</sup>
  
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====Subscripts====
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===Subscripts===
 
:b - bubble point <BR/>
 
:b - bubble point <BR/>
−
:od - dead oil <BR/>
+
:g - gas<BR/>
−
:os - saturated oil <BR/>
+
:o - oil
−
:o   - undersaturated oil <BR/>
 
  
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=== References ===
+
== References ==
 
<references>
 
<references>
 
<ref name=M1995>{{cite journal
 
<ref name=M1995>{{cite journal
Line 90: Line 110:
 
}}</ref>
 
}}</ref>
  
 +
<ref name=M1990>{{cite book
 +
|last1=McCain|first1=W.D. Jr.
 +
|title=Properties of Petroleum Fluids
 +
|edition=2
 +
|date=1990
 +
|publisher=PennWell Corp.
 +
|place=Oklahoma
 +
|url=http://www.pennwellbooks.com/petroleum/oil-gas-production/the-properties-of-petroleum-fluids-2nd-edition/
 +
|ISBN=978-0878143351
 +
}}</ref>
 +
<ref name=DW>
 +
{{cite book
 +
|last1= Wolcott |first1=Don
 +
|title=Applied Waterflood Field Development
 +
|date=2009
 +
|publisher=Energy Tribune Publishing Inc
 +
|place=Houston
 +
|url=https://www.amazon.com/Applied-Waterflood-Field-Development-Wolcott/dp/0578023946/ref=sr_1_1?ie=UTF8&qid=1481788841&sr=8-1&keywords=Don+wolcott
 +
|url-access=subscription
 +
}}</ref>
 
</references>
 
</references>
  
 
[[Category:pengtools]]
 
[[Category:pengtools]]
 
[[Category:PVT]]
 
[[Category:PVT]]
 +
 +
{{#seo:
 +
|title=McCain Oil density correlation
 +
|titlemode= replace
 +
|keywords=density of oil, petroleum engineering, PVT
 +
|description=McCain Oil density correlation is an empirical correlation for the oil density published in 1995.
 +
}}

Latest revision as of 18:41, 23 November 2023

McCain Oil density correlation

McCain correlation is an empirical correlation for the oil density published in 1995 [1].

McCain oil density correlation in the PVT Software

Math & Physics

Pseudoliquid density:

\rho_{po} = 52.8 - 0.01 R_{sb}

Apparent liquid density:

\rho_a = a_0 + a_1\ SG_{gSP} + a_2\ SG_{gSP}\ \rho_{po} + a_3\ SG_{gSP}\ \rho_{po}^2 + a_4\ \rho_{po} +a_5\ \rho_{po}^2
a_0 = -49.8930
a_1 = 85.0149
a_2 = - 3.70373
a_3 = 0.0479818
a_4 = 2.98914
a_5 =- 0.0356888

Next pseudoliquid density[2]:

\rho_{po} = \frac{R_s\ SG_g + 4,600\ SG_o}{73.71+R_s\ SG_g\ / \rho_a}

Iterate until pseudoliquid densities are equal.

Next adjust density to the pressure of interest:

\rho_{bs} = \rho_{po} + \triangle \rho_P

where

\triangle \rho_{P} = \left ( 0.167 + 16.181 \times 10^{-0.0425\ \rho_{po}} \right) \frac{P}{1000} - 0.01 \left ( 0.299 + 263 \times 10^{-0.0603\ \rho_{po}}\right)\ \left (\frac{P}{1000}\right)^2

Adjust density to the temperature of interest:

\rho_{o} = \rho_{bs} + \triangle \rho_T

where

\triangle \rho_T = (0.00302 + 1.505\ \rho_{bs}^{-0.951}) (T - 60)^{0.938} - (0.0216 - 0.0233\ (10^{-0.0161\ \rho_{bs}})) (T - 60)^{0.475}

Oil density above the bubble point pressure:

\rho_{o} = \rho_{b}\ e^{c_o\ (P - P_b)}

Example. Calculation of the oil density

Example source [3]

Input data

R_s = 53.24 sm3/sm3
SG_o = 0.85 or 35 API
SG_g = 0.75
T = 90C or 363K
P = 10 MPa

Calculate oil density at p = 10 MPa?

Solution

\rho_o = 749.645 kg/m3

The solution is available in the online PVT calculator software model at www.pengtools.com

Application range

Description of the Data Used[1]:

133 \le P_b \le 6,700
77 \le T \le 327
18 \le R_{sb} \le 1,975
0.76 \le SG_o \le 0.95
0.556 \le SG_g \le 1.237
31.3 \le \rho_{ob} \le 55.77

Number of data sets = 684

Nomenclature

c_o = oil compressibility, 1/psia
P = pressure, psia
R_s = solution gas-oil ratio, scf/stb
SG_g = gas specific gravity, dimensionless
SG_{gSP} = gas specific gravity at separator pressure, dimensionless
SG_o = oil specific gravity, dimensionless
T = temperature, °F
\rho_{a} = apparent density of surface gas if it were a liquid, lbm/ft3
\rho_{ob} = liquid density at the bubble point pressure, lbm/ft3
\rho_{bs} = liquid density at reservoir pressure and 60°F, lbm/ft3
\rho_o = oil density, lbm/ft3
\rho_{po} = pseudoliquid formed by recombination of surface gas and liquid at standard conditions, lbm/ft3
\triangle \rho_{P} = adjustment to liquid density due to pressure, lbm/ft3
\triangle \rho_{T} = adjustment to liquid density due to temperature, lbm/ft3

Subscripts

b - bubble point
g - gas
o - oil

References

  1. ↑ 1.0 1.1 McCain, W.D. Jr.; Hill, N. C. (1995). "Correlations for Liquid Densities and Evolved Gas Specific Gravities for Black Oils During Pressure Depletion"Free registration required. Society of Petroleum Engineers (SPE-30773-MS). 
  2. ↑ McCain, W.D. Jr. (1990). Properties of Petroleum Fluids (2 ed.). Oklahoma: PennWell Corp. ISBN 978-0878143351. 
  3. ↑ Wolcott, Don (2009). Applied Waterflood Field DevelopmentPaid subscription required. Houston: Energy Tribune Publishing Inc. 
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