Difference between revisions of "Valko - McCain bubble point pressure correlation"

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__TOC__
 
__TOC__
  
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=== Brief ===
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== Valko - McCain bubble point pressure correlation ==
  
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[[Valco - McCain correlation|Valco - McCain]] is an empirical correlation for the '''bubble point''' pressure published in '''2003''' <ref name={Valco - McCain}/>.
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[[Valko - McCain bubble point pressure correlation|Valko - McCain]] is an empirical correlation for the '''bubble point''' pressure published in '''2003''' <ref name={Valko - McCain}/>.
  
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=== Math & Physics ===
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[[File:Valko McCain Bubble Point Pressure.png|thumb|right|400px|link=https://www.pengtools.com/pvtCalculator?paramsToken=de71e4cc29541ab2117e07408864410c|Valko McCain Bubble Point Pressure correlation in the PVT Software]]
  
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:<math> P_{bp} = e^{2.498 + 0.713 \alpha + 0.0075 \alpha^2}</math><ref name= {Valco - McCain}/>
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== Math & Physics ==
 +
 
 +
:<math> P_{bp} = e^{2.498 + 0.713 z + 0.0075 z^2}</math><ref name= PracticalPVT/>
  
 
where:
 
where:
 +
 +
:<math> z = z1 + z2 + z3 + z4</math>
 +
 +
:<math> z1 =  A_0+ A_1 ln(R_{sb}) + A_2 ln^2(R_{sb}) + A_3 ln^3(R_{sb})</math>
  
 
A0 = -4.814074834<br/>
 
A0 = -4.814074834<br/>
−
A1 = 0.7480913
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A1 = 0.7480913<br/>
 
A2 = 0.1743556<br/>
 
A2 = 0.1743556<br/>
−
A3 = 0.0206<br/>
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A3 = -0.0206<br/>
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:<math> \alpha1 =  A_0+ A_1 log(R_{sb}) + A_2 log^2(R_{sb}) - A_3 log^3(R_{sb})</math>
+
 
 +
:<math> z2 = B_0 + B_1 API_{oil} + B_2 {API_{oil}}^2 + B_3 {API_{oil}}^3</math>
  
 
B0 = 1.27<br/>
 
B0 = 1.27<br/>
−
B1 = 0.0449<br/>
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B1 = -0.0449<br/>
 
B2 = 4.36e-4<br/>
 
B2 = 4.36e-4<br/>
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B3 = 4.76e-6<br/>
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B3 = -4.76e-6<br/>
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:<math> \alpha2 = B_0 - B_1  Y_{oil_API}+ B_2 Y^2_{oil_API} - B_3 Y^3_{oil_API}</math>
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 +
:<math> z3 = C_0 + C_1 SG_{g} + C_2 SG^2_{g} + C_3 SG^3_{g}</math>
  
 
C0 = 4.51<br/>
 
C0 = 4.51<br/>
−
C1 = 10.84<br/>
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C1 = -10.84<br/>
 
C2 = 8.39<br/>
 
C2 = 8.39<br/>
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C3 = 2.34<br/>
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C3 = -2.34<br/>
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:<math> \alpha3 = C_0 - C_1 SG_{g} + C_2 SG^2_{g} - C_3 SG^3_{g}</math>
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 +
:<math> z4 = D_0 + D_1 T + D_2 T^2 + D_4 T^3</math>
  
 
D0 = -7.2254661<br/>
 
D0 = -7.2254661<br/>
 
D1 = 0.043155<br/>
 
D1 = 0.043155<br/>
−
D2 = 8.55e-5<br/>
+
D2 = -8.55e-5<br/>
 
D3 = 6.00696e-8<br/>
 
D3 = 6.00696e-8<br/>
−
:<math> \alpha4 = D_0 + D_1 T - D_2 T^2 + D_4 T^3</math>
 
  
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:<math> \alpha = \alpha1 + \alpha2 + \alpha3 + \alpha4</math>
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== Application range ==
 +
:<math>  1.8 \le R_s \le 394.7 </math>
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:<math> 0.725 \le SG_o \le 1.029 </math>
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:<math>  0.555 \le SG_g \le 1.685 </math>
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:<math>  15.6 \le T, C \le 172.2 </math>
 +
 
 +
== Example. Calculation of the bubble point pressure ==
 +
Example source <ref name=DW/>
 +
===Input data===
 +
:<math>R_s</math> = 60 sm3/sm3
 +
:<math>SG_o</math> = 0.85 or 35 API
 +
:<math>SG_g</math> = 0.75
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:<math>T</math> = 90C or 363K
 +
Calculate bubble point pressure?
 +
===Solution===
 +
z1=-0.2422<br/>
 +
z2=0.0294<br/>
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z3=0.1122<br/>
 +
z4=-0.0594<br/>
 +
:<math>ln(P_b)</math> = 2.4557
 +
:<math>Pb</math> = 11.65MPa or 115 atm
  
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=== Discussion  ===
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The solution is available in the online PVT calculator software at [https://www.pengtools.com/pvtCalculator?paramsToken=de71e4cc29541ab2117e07408864410c www.pengtools.com]
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=== Application range ===
+
 
−
=== Nomenclature ===
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== Nomenclature ==
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:<math> A_0..A_{3} </math> = coefficients
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:<math> API_{oil} </math> = oil specific gravity, °API
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:<math> B_0..B_{3} </math> = coefficients
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:<math> A_0..A_3 </math> = coefficients
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:<math> C_0..C_{3} </math> = coefficients
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:<math> B_0..B_3 </math> = coefficients
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:<math> D_0..D_{4} </math> = coefficients
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:<math> C_0..C_3 </math> = coefficients
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:<math> P </math> = pressure, MPA
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:<math> D_0..D_4 </math> = coefficients
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:<math> P_{bp} </math> = bubble point pressure, MPA
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:<math> P_{bp} </math> = bubble point pressure, MPa
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:<math> R_s </math> =  oil gas ration, m3/m3
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:<math> R_s </math> =  solution oil gas ratio, sm3/sm3
 
:<math> SG_g </math> = gas specific gravity, dimensionless
 
:<math> SG_g </math> = gas specific gravity, dimensionless
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:<math> T </math> = temperature, °R
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:<math> SG_o </math> = oil specific gravity, dimensionless
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:<math> Y_{oil_API} </math> = oil API gravity, dimensionless
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:<math> T </math> = temperature, °K
  
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=== References ===
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== References ==
 
<references>
 
<references>
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<ref name={Valco - McCain}>
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<ref name={Valko - McCain}>
 
{{cite journal
 
{{cite journal
 
  |last1= Valkó |first1=P. P.
 
  |last1= Valkó |first1=P. P.
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  |url=http://dx.doi.org/10.1016/S0920-4105(02)00319-4
 
  |url=http://dx.doi.org/10.1016/S0920-4105(02)00319-4
 
  |url-access=registration  
 
  |url-access=registration  
 +
}}</ref>
 +
 +
<ref name=PracticalPVT>
 +
{{cite journal
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|last1= Afanasyev |first1=Vitaliy
 +
|last2= Moskvin |first2=Igor
 +
|last3= Wolcott |first3=Ken
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|last4= McCain |first4=W.D.
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|title=Practical PVT Calculations for black oils
 +
|journal=YUKOS publication
 +
|date=2004
 +
}}</ref>
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<ref name=DW>
 +
{{cite book
 +
|last1= Wolcott |first1=Don
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|title=Applied Waterflood Field Development
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|date=2009
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|publisher=Energy Tribune Publishing Inc
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|place=Houston
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|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>
 
}}</ref>
 
</references>
 
</references>
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{{#seo:
 
{{#seo:
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|title=Valco - McCain correlation
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|title=Valko - McCain bubble point pressure correlation
 
|titlemode= replace
 
|titlemode= replace
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|keywords=Valco - McCain correlation, oil bubble point
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|keywords=Valko - McCain correlation, oil bubble point
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|description=Valco - McCain correlation is an empirical correlation for the oil bubble point pressure published in 2003.
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|description=Valko - McCain correlation is an empirical correlation for the oil bubble point pressure published in 2003.
 
}}
 
}}

Latest revision as of 08:50, 28 September 2020

Valko - McCain bubble point pressure correlation

Valko - McCain is an empirical correlation for the bubble point pressure published in 2003 [1].

Valko McCain Bubble Point Pressure correlation in the PVT Software

Math & Physics

P_{bp} = e^{2.498 + 0.713 z + 0.0075 z^2}[2]

where:

z = z1 + z2 + z3 + z4
z1 = A_0+ A_1 ln(R_{sb}) + A_2 ln^2(R_{sb}) + A_3 ln^3(R_{sb})

A0 = -4.814074834
A1 = 0.7480913
A2 = 0.1743556
A3 = -0.0206

z2 = B_0 + B_1 API_{oil} + B_2 {API_{oil}}^2 + B_3 {API_{oil}}^3

B0 = 1.27
B1 = -0.0449
B2 = 4.36e-4
B3 = -4.76e-6

z3 = C_0 + C_1 SG_{g} + C_2 SG^2_{g} + C_3 SG^3_{g}

C0 = 4.51
C1 = -10.84
C2 = 8.39
C3 = -2.34

z4 = D_0 + D_1 T + D_2 T^2 + D_4 T^3

D0 = -7.2254661
D1 = 0.043155
D2 = -8.55e-5
D3 = 6.00696e-8

Application range

1.8 \le R_s \le 394.7
0.725 \le SG_o \le 1.029
0.555 \le SG_g \le 1.685
15.6 \le T, C \le 172.2

Example. Calculation of the bubble point pressure

Example source [3]

Input data

R_s = 60 sm3/sm3
SG_o = 0.85 or 35 API
SG_g = 0.75
T = 90C or 363K

Calculate bubble point pressure?

Solution

z1=-0.2422
z2=0.0294
z3=0.1122
z4=-0.0594

ln(P_b) = 2.4557
Pb = 11.65MPa or 115 atm

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

Nomenclature

API_{oil} = oil specific gravity, °API
A_0..A_3 = coefficients
B_0..B_3 = coefficients
C_0..C_3 = coefficients
D_0..D_4 = coefficients
P_{bp} = bubble point pressure, MPa
R_s = solution oil gas ratio, sm3/sm3
SG_g = gas specific gravity, dimensionless
SG_o = oil specific gravity, dimensionless
T = temperature, °K

References

  1. ↑ Valkó, P. P.; McCain, W.D. (2003). "Reservoir oil bubblepoint pressures revisited; solution gas–oil ratios and surface gas specific gravities."Free registration required. J. Pet. Sci. Eng. 37 (3–4): 153-169. 
  2. ↑ Afanasyev, Vitaliy; Moskvin, Igor; Wolcott, Ken; McCain, W.D. (2004). "Practical PVT Calculations for black oils". YUKOS publication. 
  3. ↑ Wolcott, Don (2009). Applied Waterflood Field DevelopmentPaid subscription required. Houston: Energy Tribune Publishing Inc. 
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