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

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Line 8: Line 8:
 
:<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/>
+
:<math>R_{sr} = \alpha1 \times P^{\alpha2}_r + (1 - \alpha1) \times P^{\alpha3}_r</math>
  
 
where:
 
where:
Line 14: Line 14:
 
:<math>P_r = \frac{P-0.101}{P_b}</math>
 
:<math>P_r = \frac{P-0.101}{P_b}</math>
  
A0 = 1.8653e-4<br/>
+
A0 = 1.8653e-4<br/><ref name= PracticalPVT/>
 
A1 = 1.672608<br/>
 
A1 = 1.672608<br/>
 
A2 = 0.929870<br/>
 
A2 = 0.929870<br/>
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:<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>
 
:<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>
  
B0 = 0.1004<br/>
+
B0 = 0.1004<br/><ref name= PracticalPVT/>
 
B1 = -1.00475<br/>
 
B1 = -1.00475<br/>
 
B2 = 0.337711<br/>
 
B2 = 0.337711<br/>
Line 30: Line 30:
 
:<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>
 
:<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>
  
C0 = 0.9167<br/>
+
C0 = 0.9167<br/><ref name= PracticalPVT/>
 
C1 = -1.48548<br/>
 
C1 = -1.48548<br/>
 
C2 = -0.164741<br/>
 
C2 = -0.164741<br/>
Line 67: Line 67:
 
  |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>

Revision as of 08:28, 28 September 2020

Brief

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

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}

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

 \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

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

\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

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

\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

Discussion

Why the Velarde correlation?

Application range

Nomenclature

 A_1..A_{4} = coefficients
 B_1..B_{4} = coefficients
 C_1..C_{4} = coefficients
 P = pressure, MPA
 P_b = bubble point pressure, MPA
 SG_g = gas specific gravity, dimensionless
 T = temperature, °R
 Y_{oil_API} = oil API gravity, dimensionless


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. 

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