Dranchuk correlation

Brief

Liquid loading is a phenomenon when the gas phase does't provide sufficient transport energy to lift the liquids out of the well.

In 1969 Turner et al. published an empirical correlation defining the Liquid loading gas velocity.

Math & Physics

equation on gas compressibility factor z
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

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

where

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

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

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

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

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

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

$z$ = gas compressibility factor, dimensionless

$P$ = Pressure, psia

$T$ = Temperature, °R

$P_{pc}$ = Pseudo critical pressure, psia

$T_{pc}$ = Pseudo critical temperature, °R

$SG_g$ = gas specific density