Velarde solution gas oil ratio correlation

Brief

Velarde correlation is the fitting equation of the classic Standing and Katz 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

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

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 :

$P_{pc} = ( 4.6+0.1\ SG_g-0.258\ SG^2_g ) \times 10.1325 \times 14.7$

$T_{pc} = ( 99.3+180\ SG_g-6.94\ SG^2_g ) \times 1.8$

Application range

$0.2 \le P_{pr} < 30 ; 1.0 < T_{pr} \le 3.0$

and

$P_{pr} < 1.0 ; 0.7 < T_{pr} \le 1.0$

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