# Velarde correlation

## Contents

### Brief

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

### Math & Physics

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

where:

$P_r = \frac{P}{P_{bp}}$

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

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

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

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

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

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

### Discussion

Why the Velarde correlation?

### Nomenclature

$A_1..A_{4}$ = coefficients
$B_1..B_{4}$ = coefficients
$C_1..C_{4}$ = coefficients
$P$ = pressure, MPA
$P_{bp}$ = 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). . Presented at the Annual Technical Meeting of CIM, Calgary, Alberta. Petroleum Society of Canada (PETSOC-97-93).