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

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__TOC__
 
__TOC__
  
=== Brief ===
+
== Velarde solution gas oil ratio correlation ==
  
[[Velarde correlation]] is the fitting equation of the classic '''Standing and Katz''' <ref name=Standing&Katz /> gas compressibility factor correlation.
+
[[Velarde solution gas oil ratio correlation]] is an empirical correlation for the '''solution gas oil ratio''' published in '''1997'''. <ref name=Velarde />
  
=== Math & Physics ===
+
[[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>R_s = \frac{R_{sr}}{$R_{sb}}</math>
 
  
:<math>R_{sr} = (\alpha1 * Pr^{\alpha2}) + (1 - \alpha1) * Pr^\alpha3))</math>
+
== Math & Physics ==
 +
:<math>R_s = \frac{R_{sr}}{R_{sb}}</math>
 +
 
 +
:<math>R_{sr} = \alpha1 \times P^{\alpha2}_r + (1 - \alpha1) \times P^{\alpha3}_r</math>
  
 
where:
 
where:
  
A0 = 1.8653e-4<br/>
+
:<math>P_r = \frac{P-0.101}{P_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>
 +
 
 +
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/>
  
:<math> \alpha1 = A0 * SG^{A_1}_{gas} * Y^{A_2}_{oil_API} * {(T- 459.67)}^{A_3} * 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 SG^{B_1}_{gas}  * Y^{B_2}_{oil_API} {(T - 459.67)}^{B_3} * 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>\a3 = C_0 SG^{C_1}_{gas} * Y^{C_2}_{oil_API} *{(T - 459.67)}^{C_3} P^{C_4}_{bp}</math>
+
== Example. Calculation of the solution gas oil ratio ==
 
+
Example source <ref name=DW/>
<ref name= Dranchuk/>
+
===Input data===
 
+
:<math>R_s</math> = 60 sm3/sm3
 
+
:<math>SG_o</math> = 0.85 or 35 API
=== Discussion  ===
+
:<math>SG_g</math> = 0.75
Why the [[Velarde correlation]]?
+
:<math>T</math> = 90C or 363K
 
+
:<math>P_b</math> = 11.65 MPa
=== Workflow  ===
+
Calculate solution gas oil ratio at p = 10 MPa?
To solve the [[Dranchuk correlation| Dranchuk]] equation use the iterative secant method.
 
 
 
To find the pseudo critical properties from the gas specific gravity <ref name=Standing&Katz />:
 
 
 
:<math> P_{pc} = ( 4.6+0.1\ SG_g-0.258\ SG^2_g ) \times 10.1325 \times 14.7</math>
 
 
 
:<math> T_{pc} =  ( 99.3+180\ SG_g-6.94\ SG^2_g ) \times 1.8 </math>
 
  
=== Application range ===  
+
===Solution===
 +
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/>
  
:<math>  0.2 \le P_{pr} < 30 ; 1.0 < T_{pr} \le 3.0 </math><ref name= Dranchuk/>
+
The solution is available in the online PVT calculator software at [https://www.pengtools.com/pvtCalculator?paramsToken=de71e4cc29541ab2117e07408864410c www.pengtools.com]
  
and
+
== Application range ==
 +
:<math>  2.35 \le R_s \le 322 </math>
 +
:<math>  0.754 \le SG_o \le 0.989 </math>
 +
:<math>  0.555 \le SG_g \le 1.245 </math>
 +
:<math>  21.1 \le T, C \le 160 </math>
  
:<math> P_{pr} < 1.0 ; 0.7 < T_{pr} \le 1.0</math><ref name= Dranchuk/>
+
== Nomenclature ==
 
+
:<math> API_{oil} </math> = oil specific gravity, °R
=== Nomenclature ===
+
:<math> A_0..A_{4} </math> = coefficients
:<math> A_1..A_{11} </math> = coefficients
+
:<math> B_0..B_{4} </math> = coefficients
:<math> \rho_r </math> = reduced density, dimensionless
+
:<math> C_0..C_{4} </math> = coefficients
:<math> P </math> = pressure, psia
+
:<math> P </math> = pressure, MPa
:<math> P_{pc} </math> = pseudo critical pressure, psia
+
:<math> P_b </math> = bubble point pressure, MPa
:<math> P_{pr} </math> = pseudoreduced pressure, dimensionless
+
:<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> T_{pc} </math> = pseudo critical temperature, °R
+
:<math> T </math> = temperature, °K
:<math> T_{pr} </math> = pseudoreduced temperature, dimensionless
 
:<math> Y_{oil_API} </math> = oil API gravity, dimensionless
 
:<math> z </math> = gas compressibility factor, dimensionless
 
  
=== References ===
+
== References ==
 
<references>
 
<references>
 
+
<ref name=Velarde>
<ref name=Standing&Katz>{{cite journal
+
{{cite journal
  |last1= Standing |first1=M. B.
+
  |last1= Velarde |first1=J.
  |last2= Katz |first2=D. L.
+
  |last2= Blasingame |first2=T. A.
  |title=Density of Natural Gases
+
|last3= McCain Jr. |first3=W. D.
  |journal=Transactions of the AIME
+
  |title=Correlation of Black Oil Properties At Pressures Below Bubble Point Pressure - A New Approach
  |publisher=Society of Petroleum Engineers
+
  |journal=Presented at the Annual Technical Meeting of CIM, Calgary, Alberta
  |number=SPE-942140-G
+
  |publisher=Petroleum Society of Canada
  |date=December 1942
+
  |number=PETSOC-97-93
|volume=146
+
  |date=1997
  |url=https://www.onepetro.org/journal-paper/SPE-942140-G
+
  |url=https://www.onepetro.org/conference-paper/PETSOC-97-93
 
  |url-access=registration  
 
  |url-access=registration  
 
}}</ref>
 
}}</ref>
 
+
<ref name=PracticalPVT>
<ref name= Dranchuk >{{cite journal
+
{{cite journal
  |last1= Dranchuk |first1=P. M.
+
  |last1= Afanasyev |first1=Vitaliy
  |last2= Abou-Kassem |first2=H.
+
  |last2= Moskvin |first2=Igor
  |title=Calculation of Z Factors For Natural Gases Using Equations of State
+
|last3= Wolcott |first3=Ken
  |journal=The Journal of Canadian Petroleum
+
|last4= McCain |first4=W.D.
  |number=PETSOC-75-03-03
+
  |title=Practical PVT Calculations for black oils
  |date=July 1975
+
  |journal=YUKOS publication
  |volume=14
+
|date=2004
  |url=https://www.onepetro.org/journal-paper/PETSOC-75-03-03
+
}}</ref>
  |url-access=registration
+
<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>
  
 
[[Category:pengtools]]
 
[[Category:pengtools]]
 
[[Category:PVT]]
 
[[Category:PVT]]
 +
 +
 +
{{#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.