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

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=== Brief ===
 
=== Brief ===
  
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[[Velarde correlation]] is the fitting equation of the classic '''Standing and Katz''' <ref name=Standing&Katz /> gas compressibility factor correlation.
+
[[Velarde correlation]] is ...
  
 
=== Math & Physics ===
 
=== Math & Physics ===
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:<math>R_s = \frac{R_{sr}}{$R_{sb}}</math>
+
:<math>R_s = \frac{R_{sr}}{R_{sb}}</math>
  
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:<math>R_{sr} = (\alpha1 * Pr^{\alpha2}) + (1 - \alpha1) * Pr^\alpha3))</math><ref name= Velarde/>
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:<math>R_{sr} = \alpha1 \times Pr^{\alpha2} + (1 - \alpha1) \times Pr^{\alpha3}</math><ref name= Velarde/>
  
 
where:
 
where:
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A4 = 1.056052<br/>
 
A4 = 1.056052<br/>
  
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:<math> \alpha1 = A0 * SG^{A_1}_{gas} Y^{A_2}_{oil_API} {(T- 459.67)}^{A_3} P^{A_3}_{bp} </math>
+
:<math> \alpha1 = A_0 \times SG^{A_1}_{gas} \times Y^{A_2}_{oil_API} \times {(T- 459.67)}^{A_3} \times P^{A_3}_{bp} </math>
  
 
B0 = 0.1004<br/>
 
B0 = 0.1004<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>\alpha2 = B_0 \times SG^{B_1}_{gas} \times Y^{B_2}_{oil_API} \times {(T - 459.67)}^{B_3} \times P^{B_4}_{bp}</math>
  
 
C0 = 0.9167<br/>
 
C0 = 0.9167<br/>
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C4 = 0.047094<br/>
 
C4 = 0.047094<br/>
  
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:<math>\alpha3 = C_0 SG^{C_1}_{gas} Y^{C_2}_{oil_API} *{(T - 459.67)}^{C_3} P^{C_4}_{bp}</math>
+
:<math>\alpha3 = C_0 \times SG^{C_1}_{gas} \times Y^{C_2}_{oil_API} \times {(T - 459.67)}^{C_3} \times P^{C_4}_{bp}</math>
  
 
=== Discussion  ===
 
=== Discussion  ===
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=== Workflow  ===
 
=== Workflow  ===
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To solve the [[Dranchuk correlation| Dranchuk]] equation use the iterative secant method.
 
−
 
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To find the pseudo critical properties from the gas specific gravity <ref name=Standing&Katz />:
 
−
 
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:<math>  P_{pc} =  ( 4.6+0.1\ SG_g-0.258\ SG^2_g ) \times 10.1325 \times 14.7</math>
 
−
 
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:<math>  T_{pc} =  ( 99.3+180\ SG_g-6.94\ SG^2_g ) \times 1.8 </math>
 
−
 
 
=== Application range ===  
 
=== Application range ===  
−
 
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:<math>  0.2 \le P_{pr} < 30 ; 1.0 < T_{pr} \le 3.0 </math><ref name= Dranchuk/>
 
−
 
−
and
 
−
 
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:<math>  P_{pr} < 1.0 ; 0.7 < T_{pr} \le 1.0</math><ref name= Dranchuk/>
 
−
 
 
=== Nomenclature ===
 
=== Nomenclature ===
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:<math> A_1..A_{11} </math> = coefficients
+
:<math> A_1..A_{4} </math> = coefficients
 +
:<math> B_1..B_{4} </math> = coefficients
 +
:<math> C_1..C_{4} </math> = coefficients
 
:<math> \rho_r </math> = reduced density, dimensionless
 
:<math> \rho_r </math> = reduced density, dimensionless
 
:<math> P </math> = pressure, psia
 
:<math> P </math> = pressure, psia

Revision as of 08:34, 8 June 2017

Brief

Velarde correlation is ...

Math & Physics

R_s = \frac{R_{sr}}{R_{sb}}
R_{sr} = \alpha1 \times Pr^{\alpha2} + (1 - \alpha1) \times Pr^{\alpha3}[1]

where:

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

\alpha1 = A_0 \times SG^{A_1}_{gas} \times Y^{A_2}_{oil_API} \times {(T- 459.67)}^{A_3} \times P^{A_3}_{bp}

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

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

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

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

Discussion

Why the Velarde correlation?

Workflow

Application range

Nomenclature

A_1..A_{4} = coefficients
B_1..B_{4} = coefficients
C_1..C_{4} = coefficients
\rho_r = reduced density, dimensionless
P = pressure, psia
P_{pc} = pseudo critical pressure, psia
P_{pr} = pseudoreduced pressure, dimensionless
SG_g = gas specific gravity, dimensionless
T = temperature, °R
T_{pc} = pseudo critical temperature, °R
T_{pr} = pseudoreduced temperature, dimensionless
Y_{oil_API} = oil API gravity, dimensionless
z = gas compressibility factor, dimensionless

References

  1. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Velarde

Cite error: <ref> tag with name "Standing.26Katz" defined in <references> is not used in prior text.
Cite error: <ref> tag with name "Dranchuk" defined in <references> is not used in prior text.

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