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

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(Created page with "__TOC__ === Brief === Velarde correlation is the fitting equation of the classic '''Standing and Katz''' <ref name=Standing&Katz /> gas compressibility factor correlatio...")
 
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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 = A0 * SG^{A_1}_{gas} Y^{A_2}_{oil_API} {(T- 459.67)}^{A_3} 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 SG^{B_1}_{gas} Y^{B_2}_{oil_API} {(T - 459.67)}^{B_3} 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/>
  
−
:<math>\a3 = 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 SG^{C_1}_{gas} Y^{C_2}_{oil_API} *{(T - 459.67)}^{C_3} P^{C_4}_{bp}</math>
  
 
<ref name= Dranchuk/>
 
<ref name= Dranchuk/>

Revision as of 08:18, 8 June 2017

Brief

Velarde correlation is the fitting equation of the classic Standing and Katz [1] gas compressibility factor correlation.

Math & Physics

R_s = \frac{R_{sr}}{$R_{sb}}
R_{sr} = (\alpha1 * Pr^{\alpha2}) + (1 - \alpha1) * Pr^\alpha3))

where:

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

\alpha1 = A0 * SG^{A_1}_{gas} Y^{A_2}_{oil_API} {(T- 459.67)}^{A_3} P^{A_3}_{bp}

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

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

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

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

[2]


Discussion

Why the Velarde correlation?

Workflow

To solve the Dranchuk equation use the iterative secant method.

To find the pseudo critical properties from the gas specific gravity [1]:

P_{pc} = ( 4.6+0.1\ SG_g-0.258\ SG^2_g ) \times 10.1325 \times 14.7
T_{pc} = ( 99.3+180\ SG_g-6.94\ SG^2_g ) \times 1.8

Application range

0.2 \le P_{pr} < 30 ; 1.0 < T_{pr} \le 3.0 [2]

and

P_{pr} < 1.0 ; 0.7 < T_{pr} \le 1.0[2]

Nomenclature

A_1..A_{11} = 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. ↑ 1.0 1.1 Standing, M. B.; Katz, D. L. (December 1942). "Density of Natural Gases"Free registration required. Transactions of the AIME. Society of Petroleum Engineers. 146 (SPE-942140-G). 
  2. ↑ 2.0 2.1 2.2 Dranchuk, P. M.; Abou-Kassem, H. (July 1975). "Calculation of Z Factors For Natural Gases Using Equations of State"Free registration required. The Journal of Canadian Petroleum. 14 (PETSOC-75-03-03). 
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