Dranchuk correlation

Brief

Dranchuk correlation is the fitting equation of the classic Standing and Katz gas compressibility factor correlation.

Math & Physics

A1 = 0.3265
A2 = –1.0700
A3 = –0.5339
A4 = 0.01569
A5 = –0.05165
A6 = 0.5475
A7 = –0.7361
A8 = 0.1844
A9 = 0.1056
A10 = 0.6134
A11 = 0.7210

$z = 1-z+ \left(A_1 +\frac{A_2}{T_{pr}} +\frac{A_3}{T^3_{pr}} +\frac{A_4}{T^4_{pr}} +\frac{A_5}{T^5_{pr}} \right)\ \rho_r+ \left(A_6 +\frac{A_7}{T_{pr}} +\frac{A_8}{T^2_{pr}} \right)\ \rho^2_r -A_9\ \left(\frac{A_7}{T_{pr}}+\frac{A_8}{T^2_{pr}}\right) +A_{10}\ \left(1+A_{11}\ \rho^2_r\right)\ \frac{\rho^2_r}{T^3_{pr}} \ e^{(-A_{11}\ \rho^2_r)}$

where

$\rho_r = \frac{0.27\ P_{pr}}{{z\ T_{pr}}}$

$P_{pr} = \frac{P}{P_{pc}}$

$T_{pr} = \frac{T}{T_{pc}}$

Workflow

To solve the Dranchuk equation use the iterative secant method.

To find the pseudo critical properties given the gas specific gravity:

$P_{pc} = 4.6+0.1\ SG_g-0.258\ SG^2_g$

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

Discussion

To avoid the Liquid loading the gas velocity should be above the Liquid loading velocity.

The higher the gas rate the higher the gas velocity.

The lower the wellhead flowing pressure the higher the gas rate.

The bigger the tubing ID the higher the gas rate.

In case when the gas rate is limited by the Reservoir deliverability smaller tubing ID will increase the gas velocity.

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

$z$ = gas compressibility factor, dimensionless