Fanning correlation

Brief

The Fanning correlation is the name used to refer to the calculation of the hydrostatic pressure difference and the friction pressure loss for the dry gas.

Fanning correlation is the default VLP correlation for the dry gas wells in the PQplot.

Math & Physics

Following the law of conservation of energy the basic steady state flow equation is:

$144 \frac{\Delta p}{\Delta h} = \rho_g + \rho_g \frac{f v_g^2 }{2 g_c D} + \rho_g \frac{\Delta{(\frac{v_g^2}{2g_c}})}{\Delta h}$

Colebrook–White equation for the Darcy's friction factor:

$\frac{1}{\sqrt{f}}= -2 \log \left( \frac { \varepsilon} {3.7 D} + \frac {2.51} {\mathrm{Re} \sqrt{f}} \right)$

Reynolds number:

$Re = 1488\ \frac {\rho_g v_g D}{\mu_g}$

$\rho_g = \frac{28.967\ SG_g\ p}{z\ 10.732\ T_R}$

$v_{SG} = \frac{q_g \times 10^6}{86400 A_p}\ \frac{14.7}{p}\ \frac{T_K}{520}\ \frac{z}{1}$

Discussion

Why Fanning correlation ?

The Gray correlation was found to be the best of several initially tested ...

— Nitesh Kumar l

Nomenclature

$h$ = depth, ft

$f$ = friction factor, dimensionless

$p$ = pressure, psia

$Re$ = Reynolds number, dimensionless

$SG$ = specific gravity, dimensionless

$T$ = temperature, °R or °K, follow the subscript

$v$ = velocity, ft/sec

$WOR$ = water-oil ratio, bbl/bbl

$z$ = gas compressibility factor, dimensionless

Greek symbols

$\varepsilon$ = absolute roughness, ft

$\varepsilon'$ = pseudo wall roughness, ft

$\mu$ = viscosity, cp

$\rho$ = density, lb_m/ft³

$\bar \rho$ = slip density, lb_m/ft²

$\sigma$ = surface tension of liquid-air interface, dynes/cm

Subscripts

g = gas
K = °K
L = liquid
m = gas/liquid mixture
o = oil
R = °R
SL = superficial liquid
SG = superficial gas
w = water