Difference between revisions of "Velarde solution gas oil ratio correlation"

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__TOC__
 
__TOC__
  
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=== Brief ===
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== Velarde solution gas oil ratio correlation ==
  
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[[Velarde correlation]] is an empirical correlation for the '''solution gas oil ratio''' published in '''1999'''.
+
[[Velarde solution gas oil ratio correlation]] is an empirical correlation for the '''solution gas oil ratio''' published in '''1997'''. <ref name=Velarde />
  
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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|Velarde solution gas oil ratio correlation in the PVT Software]]
 +
 
 +
== Math & Physics ==
 
:<math>R_s = \frac{R_{sr}}{R_{sb}}</math>
 
:<math>R_s = \frac{R_{sr}}{R_{sb}}</math>
  
−
:<math>R_{sr} = \alpha1 \times P^{\alpha2}_r + (1 - \alpha1) \times P^{\alpha3}_r</math><ref name= Velarde/>
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:<math>R_{sr} = \alpha1 \times P^{\alpha2}_r + (1 - \alpha1) \times P^{\alpha3}_r</math>
  
 
where:
 
where:
  
−
:<math>P_r = \frac{P}{P_{bp}}</math>
+
:<math>P_r = \frac{P-0.101}{P_b}</math>
  
−
A0 = 1.8653e-4<br/>
+
:<math> \alpha1 = A_0 \times SG^{A_1}_g \times Y^{A_2}_{oil_API} \times {(1.8 T- 459.67)}^{A_3} \times P^{A_3}_b </math>
 +
 
 +
A0 = 1.8653e-4<ref name= PracticalPVT/><br/>
 
A1 = 1.672608<br/>
 
A1 = 1.672608<br/>
 
A2 = 0.929870<br/>
 
A2 = 0.929870<br/>
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A4 = 1.056052<br/>
 
A4 = 1.056052<br/>
  
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:<math> \alpha1 = A_0 \times SG^{A_1}_g \times Y^{A_2}_{oil_API} \times {(T- 459.67)}^{A_3} \times P^{A_3}_{bp} </math>
+
:<math>\alpha2 = B_0 \times SG^{B_1}_g \times Y^{B_2}_{oil_API} \times {(1.8 T - 459.67)}^{B_3} \times P^{B_4}_b</math>
  
−
B0 = 0.1004<br/>
+
B0 = 0.1004<ref name= PracticalPVT/><br/>
 
B1 = -1.00475<br/>
 
B1 = -1.00475<br/>
 
B2 = 0.337711<br/>
 
B2 = 0.337711<br/>
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B4 = 0.302065<br/>
 
B4 = 0.302065<br/>
  
−
:<math>\alpha2 = B_0 \times SG^{B_1}_g \times Y^{B_2}_{oil_API} \times {(T - 459.67)}^{B_3} \times P^{B_4}_{bp}</math>
+
:<math>\alpha3 = C_0 \times SG^{C_1}_g \times Y^{C_2}_{oil_API} \times {(1.8 T - 459.67)}^{C_3} \times P^{C_4}_b</math>
  
−
C0 = 0.9167<br/>
+
C0 = 0.9167<ref name= PracticalPVT/><br/>
 
C1 = -1.48548<br/>
 
C1 = -1.48548<br/>
 
C2 = -0.164741<br/>
 
C2 = -0.164741<br/>
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C4 = 0.047094<br/>
 
C4 = 0.047094<br/>
  
−
:<math>\alpha3 = C_0 \times SG^{C_1}_g \times Y^{C_2}_{oil_API} \times {(T - 459.67)}^{C_3} \times P^{C_4}_{bp}</math>
+
== Example. Calculation of the solution gas oil ratio ==
 +
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
 +
:<math>T</math> = 90C or 363K
 +
:<math>P_b</math> = 11.65 MPa
 +
Calculate solution gas oil ratio at p = 10 MPa?
  
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=== Discussion  ===
+
===Solution===
−
Why the [[Velarde correlation]]?
+
Pr = 0.8493<br/>
 +
a1=0.1545<br/>
 +
a2=1.8812<br/>
 +
a3=0.5431<br/>
 +
Rsr=0.8874<br/>
 +
Rs=53.24 sm3/sm3<br/>
  
−
=== Workflow  ===
+
The solution is available in the online PVT calculator software at [https://www.pengtools.com/pvtCalculator?paramsToken=de71e4cc29541ab2117e07408864410c www.pengtools.com]
−
=== Application range ===
+
 
−
=== Nomenclature ===
+
== Application range ==
−
:<math> A_1..A_{4} </math> = coefficients
+
:<math>  2.35 \le R_s \le 322 </math>
−
:<math> B_1..B_{4} </math> = coefficients
+
:<math>  0.754 \le SG_o \le 0.989 </math>
−
:<math> C_1..C_{4} </math> = coefficients
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:<math>  0.555 \le SG_g \le 1.245 </math>
−
:<math> P </math> = pressure, MPA
+
:<math>  21.1 \le T, C \le 160 </math>
−
:<math> P_{bp} </math> = bubble point pressure, MPA
+
 
 +
== Nomenclature ==
 +
:<math> API_{oil} </math> = oil specific gravity, °R
 +
:<math> A_0..A_{4} </math> = coefficients
 +
:<math> B_0..B_{4} </math> = coefficients
 +
:<math> C_0..C_{4} </math> = coefficients
 +
:<math> P </math> = pressure, MPa
 +
:<math> P_b </math> = bubble point pressure, MPa
 +
:<math> P_r </math> = reduced pressure, MPa
 +
:<math> R_s </math> =  solution oil gas ratio, sm3/sm3
 +
:<math> R_{rb} </math> = solution oil gas ratio at bubble point pressure, sm3/sm3
 +
:<math> R_{rs} </math> =  reduced solution oil gas ratio, sm3/sm3
 
:<math> SG_g </math> = gas specific gravity, dimensionless
 
:<math> SG_g </math> = gas specific gravity, dimensionless
−
:<math> T </math> = temperature, °R
+
:<math> SG_o </math> = oil specific gravity, dimensionless
−
:<math> Y_{oil_API} </math> = oil API gravity, dimensionless
+
:<math> T </math> = temperature, °K
−
 
 
  
−
=== References ===
+
== References ==
 
<references>
 
<references>
 
<ref name=Velarde>
 
<ref name=Velarde>
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  |url=https://www.onepetro.org/conference-paper/PETSOC-97-93
 
  |url=https://www.onepetro.org/conference-paper/PETSOC-97-93
 
  |url-access=registration  
 
  |url-access=registration  
 +
}}</ref>
 +
<ref name=PracticalPVT>
 +
{{cite journal
 +
|last1= Afanasyev |first1=Vitaliy
 +
|last2= Moskvin |first2=Igor
 +
|last3= Wolcott |first3=Ken
 +
|last4= McCain |first4=W.D.
 +
|title=Practical PVT Calculations for black oils
 +
|journal=YUKOS publication
 +
|date=2004
 +
}}</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>
 
}}</ref>
 
</references>
 
</references>
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[[Category:pengtools]]
 
[[Category:pengtools]]
 
[[Category:PVT]]
 
[[Category:PVT]]
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 +
 +
{{#seo:
 +
|title=Velarde solution gas oil ratio GOR correlation
 +
|titlemode= replace
 +
|keywords=Velarde correlation
 +
|description=Velarde correlation is an empirical correlation for the solution gas oil ratio (GOR) published in 1997.
 +
}}

Latest revision as of 08:54, 28 September 2020

Velarde solution gas oil ratio correlation

Velarde solution gas oil ratio correlation is an empirical correlation for the solution gas oil ratio published in 1997. [1]

Velarde solution gas oil ratio correlation in the PVT Software

Math & Physics

R_s = \frac{R_{sr}}{R_{sb}}
R_{sr} = \alpha1 \times P^{\alpha2}_r + (1 - \alpha1) \times P^{\alpha3}_r

where:

P_r = \frac{P-0.101}{P_b}
\alpha1 = A_0 \times SG^{A_1}_g \times Y^{A_2}_{oil_API} \times {(1.8 T- 459.67)}^{A_3} \times P^{A_3}_b

A0 = 1.8653e-4[2]
A1 = 1.672608
A2 = 0.929870
A3 = 0.247235
A4 = 1.056052

\alpha2 = B_0 \times SG^{B_1}_g \times Y^{B_2}_{oil_API} \times {(1.8 T - 459.67)}^{B_3} \times P^{B_4}_b

B0 = 0.1004[2]
B1 = -1.00475
B2 = 0.337711
B3 = 0.132795
B4 = 0.302065

\alpha3 = C_0 \times SG^{C_1}_g \times Y^{C_2}_{oil_API} \times {(1.8 T - 459.67)}^{C_3} \times P^{C_4}_b

C0 = 0.9167[2]
C1 = -1.48548
C2 = -0.164741
C3 = -0.09133
C4 = 0.047094

Example. Calculation of the solution gas oil ratio

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
P_b = 11.65 MPa

Calculate solution gas oil ratio at p = 10 MPa?

Solution

Pr = 0.8493
a1=0.1545
a2=1.8812
a3=0.5431
Rsr=0.8874
Rs=53.24 sm3/sm3

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

Application range

2.35 \le R_s \le 322
0.754 \le SG_o \le 0.989
0.555 \le SG_g \le 1.245
21.1 \le T, C \le 160

Nomenclature

API_{oil} = oil specific gravity, °R
A_0..A_{4} = coefficients
B_0..B_{4} = coefficients
C_0..C_{4} = coefficients
P = pressure, MPa
P_b = bubble point pressure, MPa
P_r = reduced pressure, MPa
R_s = solution oil gas ratio, sm3/sm3
R_{rb} = solution oil gas ratio at bubble point pressure, sm3/sm3
R_{rs} = reduced solution oil gas ratio, sm3/sm3
SG_g = gas specific gravity, dimensionless
SG_o = oil specific gravity, dimensionless
T = temperature, °K

References

  1. ↑ Velarde, J.; Blasingame, T. A.; McCain Jr., W. D. (1997). "Correlation of Black Oil Properties At Pressures Below Bubble Point Pressure - A New Approach"Free registration required. Presented at the Annual Technical Meeting of CIM, Calgary, Alberta. Petroleum Society of Canada (PETSOC-97-93). 
  2. ↑ 2.0 2.1 2.2 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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